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Actuators, Volume 10, Issue 11 (November 2021) – 29 articles

Cover Story (view full-size image): With the growing interest in human–robot interaction, a series of assistive devices have been created in recent decades. However, due to the lack of easily integrable resources, the development of these custom-made devices is lengthy and expensive. To solve this issue, SMARCOS is proposed, a novel off-the-shelf smart variable stiffness actuator for human-centred robotic applications. This modular actuator combines compliant elements, sensors, low-level controllers, and high-bandwidth communication. The characterisation of the actuator is presented, as well as two use-cases wherein the benefits of the technology are exploited. The actuator, with its lightweight design, can serve as a building block for robotic applications, facilitating their development. View this paper
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19 pages, 815 KiB  
Article
Predefined-Time Control of Full-Scale 4D Model of Permanent-Magnet Synchronous Motor with Deterministic Disturbances and Stochastic Noises
by Nain de la Cruz and Michael Basin
Actuators 2021, 10(11), 306; https://doi.org/10.3390/act10110306 - 21 Nov 2021
Cited by 13 | Viewed by 2828
Abstract
This paper presents a predefined-time convergent robust control algorithm that allows the control designer to set the convergence time in advance, independently of initial conditions, deterministic disturbances, and stochastic noises. The control law is consequently designed and verified by simulations for a full-scale [...] Read more.
This paper presents a predefined-time convergent robust control algorithm that allows the control designer to set the convergence time in advance, independently of initial conditions, deterministic disturbances, and stochastic noises. The control law is consequently designed and verified by simulations for a full-scale 4-degrees-of-freedom (4D) permanent-magnet synchronous motor (PMSM) system in cases of a disturbance-free system with completely measurable states, a disturbance-free system with incompletely measurable states, a system with incompletely measurable states in the presence of deterministic disturbances, and a system with incompletely measurable states in the presence of both deterministic disturbances and stochastic noises. Numerical simulations are provided for the full-scale 4D PMSM system in order to validate the obtained theoretical results in each of the considered cases. To the best of our knowledge, this is the first attempt to design a predefined-time convergent control law for multi-dimensional systems with incompletely measurable states in the presence of both deterministic disturbances and stochastic noises. Full article
(This article belongs to the Special Issue Finite-Time/Fixed-Time Control for Mechanical Systems)
Show Figures

Figure 1

Figure 1
<p>(<b>Above</b>) Permanent-magnet synchronous motor. (<b>Below</b>) Model block diagram.</p>
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<p>Convergence of the states of the system (<a href="#FD5-actuators-10-00306" class="html-disp-formula">5</a>) to the origin.</p>
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<p>Time history of the control input <math display="inline"><semantics> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> </semantics></math>.</p>
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<p>Convergence of the states of the system (<a href="#FD15-actuators-10-00306" class="html-disp-formula">15</a>) and the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>) to the origin.</p>
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<p>Time history of the control input <math display="inline"><semantics> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> </semantics></math> based on the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>).</p>
Full article ">Figure 6
<p>Convergence of the states of the system (<a href="#FD21-actuators-10-00306" class="html-disp-formula">20</a>) and the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>) to the origin in the presence of deterministic disturbances.</p>
Full article ">Figure 7
<p>Time history of the nominal control input <math display="inline"><semantics> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> </semantics></math> based on the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>).</p>
Full article ">Figure 8
<p>Time history of the compensator control input (<a href="#FD23-actuators-10-00306" class="html-disp-formula">22</a>) <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, based on the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>), against the disturbance <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>K</mi> <mn>5</mn> </msub> <msub> <mi>u</mi> <mi>q</mi> </msub> <mo>=</mo> <mn>4024.14</mn> <mrow> <mo>(</mo> <mn>0.1</mn> <mi>t</mi> <mo>+</mo> <mn>0.001</mn> <mi>cos</mi> <mrow> <mo>(</mo> <mn>10</mn> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>Convergence of the states of the system (<a href="#FD24-actuators-10-00306" class="html-disp-formula">23</a>) and the estimates produced by observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>) to the origin in the presence of deterministic disturbances and stochastic noises.</p>
Full article ">Figure 10
<p>Time history of the nominal control input <math display="inline"><semantics> <msub> <mi>u</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> </semantics></math> based on the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>) for the stochastic system (<a href="#FD24-actuators-10-00306" class="html-disp-formula">23</a>).</p>
Full article ">Figure 11
<p>Time history of the compensator control input (<a href="#FD23-actuators-10-00306" class="html-disp-formula">22</a>) <math display="inline"><semantics> <mrow> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>, based on the estimates produced by the observer (<a href="#FD16-actuators-10-00306" class="html-disp-formula">16</a>), against the disturbance <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>K</mi> <mn>5</mn> </msub> <msub> <mi>u</mi> <mi>q</mi> </msub> <mo>=</mo> <mn>4024.14</mn> <mrow> <mo>(</mo> <mn>0.1</mn> <mi>t</mi> <mo>+</mo> <mn>0.001</mn> <mi>cos</mi> <mrow> <mo>(</mo> <mn>10</mn> <mi>t</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>, in the presence of a white noise with diffusion <math display="inline"><semantics> <msubsup> <mi>v</mi> <mn>2</mn> <mrow> <mn>0.75</mn> </mrow> </msubsup> </semantics></math>.</p>
Full article ">
18 pages, 6440 KiB  
Article
Design, 3D FEM Simulation and Prototyping of a Permanent Magnet Spherical Motor
by Umut Yusuf Gündoğar and Sibel Zorlu Partal
Actuators 2021, 10(11), 305; https://doi.org/10.3390/act10110305 - 21 Nov 2021
Cited by 4 | Viewed by 3828
Abstract
In recent years, large tilt angles, uniform magnetic flux distributions, strong forces, and large torques for motors have increasingly become important for robotics, biomedical, and automotive applications that have multi-degrees of freedom (MDOFs) motion. Generally, one-degree of-freedom motors are applied in MDOF motion. [...] Read more.
In recent years, large tilt angles, uniform magnetic flux distributions, strong forces, and large torques for motors have increasingly become important for robotics, biomedical, and automotive applications that have multi-degrees of freedom (MDOFs) motion. Generally, one-degree of-freedom motors are applied in MDOF motion. These situations cause the systems to have very complex and large structures. In order to address these issues, a 2-DOF surface permanent magnet spherical motor with a new mechanical design for the movement of the rotor with a large tilt angle of ±45° was designed, simulated, produced and tested in this paper. The motor consisted of a 4-pole permanent magnet rotor and a 3-block stator with 18 coils. In this study, the mechanical structure of the proposed spherical permanent magnet motor surrounded the rotor with two moving parts to move at a large tilt angle of ±45° without using any mechanical components such as spherical bearings, joint bearings, and bearing covers. Thus, the tilt angle, force, and torque values of the proposed motor have been improved according to MDOF motion motors using spherical bearings, bearing covers, or joint bearings in their mechanical structures in the literature. Ansys Maxwell software was used for the design and simulation of the motor. Three-dimensional (3D) finite element method (FEM) analysis and experimental studies were carried out on the force, torque, and magnetic flux density distribution of the motor. Then, simulation results and experimental results were compared to validate the 3D FEM simulations results. Full article
(This article belongs to the Special Issue Design and Application of Actuators with Multi-DOF Movement)
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Figure 1

Figure 1
<p>The design of the spherical permanent magnet motor.</p>
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<p>Structures of the motor stator with coils (<b>a</b>), separator rings and stator blocks (<b>b</b>), the rotor with permanent magnets (<b>c</b>), fixed base and moving parts (<b>d</b>), and a housing and covers (<b>e</b>).</p>
Full article ">Figure 3
<p>The working principle for the motor rotating around the <span class="html-italic">X</span>-axis: (<b>a</b>) top view of the rotor that is at α = 45°; (<b>b</b>) <span class="html-italic">YZ</span> cross-section view of the rotor that is at α = 45°.</p>
Full article ">Figure 4
<p>The working principle for the motor rotating around the <span class="html-italic">Y</span>-axis: (<b>a</b>) top view of the rotor that is at β = 45°; (<b>b</b>) <span class="html-italic">XZ</span> cross-section view of the rotor that is at β = 45°.</p>
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<p>Model of surface permanent magnets and the rotor.</p>
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<p>Magnetic field distributions of the motor under no-load conditions: (<b>a</b>) magnetic field vectors from the top view of the motor; (<b>b</b>) magnetic field distribution from the isometric view of the motor.</p>
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<p>Magnetic field distributions in the air gap of the motor under no-load conditions: (<b>a</b>) magnetic field distribution in the air gap from the top view of the motor; (<b>b</b>) magnetic field distribution in the air gap of the motor.</p>
Full article ">Figure 8
<p>Magnetic field distributions of the motor at loaded conditions rotating around the <span class="html-italic">X</span>-axis: (<b>a</b>) view of the motor that is at α = 0°; (<b>b</b>) view of the motor that is at α = +45°; (<b>c</b>) view of the motor that is at α = −45°.</p>
Full article ">Figure 9
<p>Magnetic field distributions of the motor at loaded conditions rotating around the <span class="html-italic">Y</span>-axis: (<b>a</b>) view of the motor that is at β = 0°; (<b>b</b>) view of the motor that is at β = +45°; (<b>c</b>) view of the motor that is at β = −45°.</p>
Full article ">Figure 10
<p>Magnetic flux density distributions in the air gap of the motor under loaded conditions rotating around the <span class="html-italic">X</span>-axis from α = 0° to α = ±45° (<b>a</b>) and rotating around the <span class="html-italic">Y</span>-axis from β = 0° to β = ±45° (<b>b</b>).</p>
Full article ">Figure 11
<p>Force values of the motor at the loaded condition rotating around the <span class="html-italic">X</span>-axis from α = 0° to α = ±45° (<b>a</b>) and rotating around the <span class="html-italic">Y</span>-axis from β = 0° to β = ±45° (<b>b</b>).</p>
Full article ">Figure 12
<p>Torque values of the motor in the loaded condition rotating around the <span class="html-italic">X</span>-axis from α = 0° to α = ±45° (<b>a</b>) and rotating around the <span class="html-italic">Y</span>-axis from β = 0° to β = ±45° (<b>b</b>).</p>
Full article ">Figure 13
<p>Stator and coils of the motor.</p>
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<p>Rotor and permanent magnets of the motor.</p>
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<p>Mechanical parts of motor.</p>
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<p>The gaussmeter device and the motor for the measurements of magnetic flux density.</p>
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<p>Experimental setup for the measurements of forces and torques.</p>
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<p>Measured and simulation results of the magnetic flux density in the air gap of the motor at no-load conditions.</p>
Full article ">Figure 19
<p>Measured and simulation results of the magnetic flux density in the air gap of the motor rotating around the <span class="html-italic">X</span>-axis from α = 0° to α = ±45° (<b>a</b>) and rotating around the <span class="html-italic">Y</span>-axis from β = 0° to β = ±45° (<b>b</b>).</p>
Full article ">Figure 20
<p>Measured and simulation results for force values of motor rotating around <span class="html-italic">X</span>-axis from α = 0° to α = ±45° (<b>a</b>) and rotating around the <span class="html-italic">Y</span>-axis from β = 0° to β = ±45° (<b>b</b>).</p>
Full article ">Figure 21
<p>Measured and simulation results for the torque values of the motor rotating around the <span class="html-italic">X</span>-axis from α = 0° to α = ±45° (<b>a</b>) rotating around the <span class="html-italic">Y</span>-axis from β = 0° to β = ±45° (<b>b</b>).</p>
Full article ">
38 pages, 14591 KiB  
Article
Research on Low-Speed Driving Model of Ultrasonic Motor Based on Beat Traveling Wave Theory
by Weijun Zeng, Song Pan, Lei Chen, Weihao Ren and Xiaobin Hu
Actuators 2021, 10(11), 304; https://doi.org/10.3390/act10110304 - 19 Nov 2021
Cited by 2 | Viewed by 2056
Abstract
This paper proposes a driving method, the superimposed pulse driving method, that can make an ultrasonic motor run at a low speed. Although this method solves the periodic oscillation of speed in a traditional low-speed driving motor, it still has a small periodic [...] Read more.
This paper proposes a driving method, the superimposed pulse driving method, that can make an ultrasonic motor run at a low speed. Although this method solves the periodic oscillation of speed in a traditional low-speed driving motor, it still has a small periodic fluctuation, which affects the stability of the speed. To reduce the fluctuation rate of the motor speed, the structure model and driving model of the motor are established, based on the theory of a beat traveling wave, and the motion characteristics of the particle point are analyzed in this paper. The simulation curve of the motor speed is obtained according to the stator and rotor contact model and the transfer model. The research shows that the driving method introduced in this paper causes the stator surface to generate a traveling beat wave, and the driving end of the stator generates an intermittent reciprocating vibration and drives the rotor rotation, which is the mechanism of low-speed operation when the driving method is used to drive the motor, as well as the reason for the periodic fluctuation of the motor speed. To improve the speed stability, this paper controlled the output performance of the motor by changing the two control variables—prepressure and frequency difference—and concluded that the variation trend of the average speed and speed volatility were consistent with the variation trend of the motor’s average speed determinant and the speed volatility determinant, respectively, which is verified by the velocity measurement experiment and the vibration measurement experiment. These insights lay the theoretical foundation for the velocity adjustment and stability optimization and, finally, the application of the new driving method is prospected. Full article
(This article belongs to the Section Aircraft Actuators)
Show Figures

Figure 1

Figure 1
<p>Schematic diagram of the stator structure of the ultrasonic motor: (<b>a</b>) stator structure with teeth; (<b>b</b>) expanded equivalent model diagram of the piezoelectric composite stator; and (<b>c</b>) tooth groove section diagram.</p>
Full article ">Figure 2
<p>A schematic diagram of the stator vibration mode and contact state: (<b>a</b>) schematic diagram of the stator vibration mode; (<b>b</b>) a schematic diagram of the stator and rotor contact state; and (<b>c</b>) a motion diagram of the particle point at the stator drive end.</p>
Full article ">Figure 3
<p>A schematic diagram of the two-phase excitation response based on the superimposed pulse driving method: (<b>a</b>) a schematic diagram of the two-phase excitation response; and (<b>b</b>) a simulation diagram of the stator modal shape.</p>
Full article ">Figure 4
<p>Schematic diagram of the elliptical coordinate system and determinant coordinate system: (<b>a</b>) schematic diagram of the elliptical coordinate system; (<b>b</b>) schematic diagram for the determining factors of the elliptical motion direction in <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mi>u</mi> <mi>T</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) schematic diagram for the determining factors of the elliptical motion direction in <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>d</mi> <mi>d</mi> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mi>u</mi> <mi>T</mi> </mrow> </msub> </mrow> </semantics></math>; and (<b>d</b>) schematic diagram for the determining factors of the elliptical motion direction in <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>d</mi> <mi>d</mi> <mi>T</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 4 Cont.
<p>Schematic diagram of the elliptical coordinate system and determinant coordinate system: (<b>a</b>) schematic diagram of the elliptical coordinate system; (<b>b</b>) schematic diagram for the determining factors of the elliptical motion direction in <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mi>u</mi> <mi>T</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) schematic diagram for the determining factors of the elliptical motion direction in <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>d</mi> <mi>d</mi> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mi>u</mi> <mi>T</mi> </mrow> </msub> </mrow> </semantics></math>; and (<b>d</b>) schematic diagram for the determining factors of the elliptical motion direction in <math display="inline"><semantics> <mrow> <msub> <mi>T</mi> <mrow> <mi>a</mi> <mi>d</mi> <mi>d</mi> <mi>T</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>Contact models of the interface between the stator and the rotor.</p>
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<p>Instantaneous tangential velocity of particle point Q.</p>
Full article ">Figure 7
<p>Forward nonsliding point transfer model.</p>
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<p>Reverse sliding point transfer model.</p>
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<p>Elliptical trajectory of particle Q.</p>
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<p>Displacement variation curve of the vertical direction.</p>
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<p>Variation curve of the determining factor equation for the elliptical motion direction.</p>
Full article ">Figure 12
<p>Elliptical trajectory of particle Q.</p>
Full article ">Figure 13
<p>Displacement variation curve of the vertical direction.</p>
Full article ">Figure 14
<p>Variation curve determining factor equation for the elliptical motion direction.</p>
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<p>Elliptical trajectory of particle Q.</p>
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<p>Displacement variation curve for the vertical direction.</p>
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<p>Variation curve of the determining factor equation for the elliptical motion direction.</p>
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<p>Schematic diagram for the instantaneous velocity of the rotor.</p>
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<p>Schematic diagram of determining factors for the direction of the motion.</p>
Full article ">Figure 20
<p>The simulation curve for the determining factors of motor instantaneous speed and elliptical direction of motion with frequency difference: (<b>a</b>) simulation curve of motor instantaneous speed; and (<b>b</b>) simulation curve of determining factors for the elliptical direction of motion within one cycle of the superimposed pulse driving method.</p>
Full article ">Figure 21
<p>Simulation diagram of characteristic variables changing with frequency difference: (<b>a</b>) a simulation diagram of the motor’s average speed, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the motor’s average speed determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>o</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, changing with the frequency difference; and (<b>b</b>) a simulation diagram of the speed volatility determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>o</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, and the speed volatility, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, changing with the frequency difference.</p>
Full article ">Figure 22
<p>Simulation diagram of the characteristic variables changing with prepressure: (<b>a</b>) a simulation diagram of the motor’s average speed, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the motor’s average speed determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, changing with the prepressure; and (<b>b</b>) a simulation diagram of the speed volatility determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>, and the speed volatility, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, changing with the prepressure.</p>
Full article ">Figure 23
<p>Simulation diagram of the characteristic variables changing with prepressure: (<b>a</b>) a simulation diagram of the motor’s average speed, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the motor’s average speed determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, changing with the prepressure; and (<b>b</b>) a simulation diagram of the speed volatility determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>, and the speed volatility, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, changing with the prepressure.</p>
Full article ">Figure 24
<p>Tooling diagram of stator amplitude test with prepressure.</p>
Full article ">Figure 25
<p>Resonance frequency measurement diagram with prepressure: (<b>a</b>) a resonance frequency test kit diagram with prepressure; and (<b>b</b>) a comparison diagram of the experimental test results and theoretical calculation results with the change in prepressure.</p>
Full article ">Figure 26
<p>A stator single-phase vibration measurement experiment diagram: (<b>a</b>) vibration measurement fixture diagram; and (<b>b</b>) velocity measurement diagram of particle M on the stator surface in the vertical direction.</p>
Full article ">Figure 27
<p>Schematic diagram of the two-phase excitation response in the stator two-phase vibration measurement experiment: (<b>a</b>) a schematic diagram of the two-phase excitation response; and (<b>b</b>) a measurement diagram of the vertical velocity of particle point M on the stator surface.</p>
Full article ">Figure 28
<p>Configuration of the experiment platform.</p>
Full article ">Figure 29
<p>Motor speed measurement diagram.</p>
Full article ">Figure 30
<p>An experimental diagram of the variation trend of characteristic variables with frequency difference: (<b>a</b>) an experimental diagram of the motor’s average speed, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the motor’s average speed determining factor, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, with frequency difference; and (<b>b</b>) an experimental diagram of the speed volatility, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the speed volatility determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>, with frequency difference.</p>
Full article ">Figure 31
<p>An experimental diagram of the variation trend of characteristic variables with prepressure: (<b>a</b>) an experimental diagram of the motor’s average speed, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the motor’s average speed determining factor, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>, with prepressure; and (<b>b</b>) an experimental diagram of the speed volatility, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the speed volatility determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>, with prepressure.</p>
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<p>Experimental diagram of the trend in characteristic variables changing with multiple control variables: (<b>a</b>) an experimental diagram of the motor’s average speed, <math display="inline"><semantics> <mrow> <msub> <mi>v</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the motor’s average speed determining factor, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>a</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </mrow> </semantics></math>; and (<b>b</b>) an experimental diagram of the tendency of the speed volatility, <math display="inline"><semantics> <mrow> <msub> <mi>σ</mi> <mi>s</mi> </msub> </mrow> </semantics></math>, and the speed volatility determinant, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mrow> <mi>v</mi> <mi>i</mi> <mi>b</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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19 pages, 830 KiB  
Article
Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
by Noussaiba Gasmi, Mohamed Boutayeb, Assem Thabet, Ghazi Bel Haj Frej and Mohamed Aoun
Actuators 2021, 10(11), 303; https://doi.org/10.3390/act10110303 - 18 Nov 2021
Cited by 2 | Viewed by 1944
Abstract
The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements [...] Read more.
The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements in the observer and the control law structures which increase the number of decision variables in the constraint to be solved and offers less restrictive Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI) which is solved in two steps. First, by using a slack variable technique and an appropriate reformulation of the Young’s inequality. Second, by introducing a useful approach to transform the obtained constraint to a more suitable one easily tractable by standard software algorithms. A comparison with the standard case is provided to show the superiority of the proposed H observer-based controller which offers greater degree of freedom. The accuracy and the potential of the proposed process are shown through real time implementation of the one-link flexible joint robot to ARDUINO UNO R3 device and numerical comparison with some existing results. Full article
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<p>Block diagram of real-time implementation.</p>
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<p>Evolution of the states (solid line) and their estimates (dashed line): (<b>a</b>) Behavior of <math display="inline"><semantics> <msub> <mi>x</mi> <mn>1</mn> </msub> </semantics></math> and its estimate, (<b>b</b>) Behavior of <math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math> and its estimate, (<b>c</b>) Behavior of <math display="inline"><semantics> <msub> <mi>x</mi> <mn>3</mn> </msub> </semantics></math> and its estimate, (<b>d</b>) Behavior of <math display="inline"><semantics> <msub> <mi>x</mi> <mn>4</mn> </msub> </semantics></math> and its estimate.</p>
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<p>Evolution of the control signal <span class="html-italic">u</span>.</p>
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<p>Evolution of the states <math display="inline"><semantics> <msub> <mi>x</mi> <mn>1</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>x</mi> <mn>2</mn> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>x</mi> <mn>3</mn> </msub> </semantics></math> (solid line) and their estimates (dashed line) using the sliding window approach.</p>
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27 pages, 4634 KiB  
Article
Development and Evaluation of Energy-Saving Electro-Hydraulic Actuator
by Triet Hung Ho and Thanh Danh Le
Actuators 2021, 10(11), 302; https://doi.org/10.3390/act10110302 - 17 Nov 2021
Cited by 6 | Viewed by 3067
Abstract
This paper will develop a novel electro-hydraulic actuator with energy saving characteristics. This system is able to work in differential configurations through the shifting algorithm of the valves, meaning that this developed system can be adjusted flexibly to obtain the desirable working requirements [...] Read more.
This paper will develop a novel electro-hydraulic actuator with energy saving characteristics. This system is able to work in differential configurations through the shifting algorithm of the valves, meaning that this developed system can be adjusted flexibly to obtain the desirable working requirements including the high effectiveness of energy recovery from the load, high velocity or torque. Instead of establishing the mathematical model for the purpose of the dynamic analysis, a model of the developed actuator is built in AMESim software. The simulation results reveal that the system is able to save approximately 20% energy consumption compared with a traditional without energy recovery EHA. Furthermore, to evaluate the accuracy of the model, experiments will be performed that prove strongly that the experimental results are well matched to the results attained from the simulation model. This work also offers a useful insight into designing and analyzing hydraulic systems without experiments. Full article
(This article belongs to the Section Control Systems)
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<p>Proposed hydraulic system.</p>
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<p>(<b>a</b>) Normal-out mode. (<b>b</b>) Normal-in mode.</p>
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<p>Regenerative-out mode.</p>
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<p>(<b>a</b>) Recovery-in mode. (<b>b</b>) Recovery-out mode.</p>
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<p>(<b>a</b>) Reused normal-out mode; (<b>b</b>) reused normal-in mode; (<b>c</b>) reused regenerative-out mode.</p>
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<p>Charging accumulator mode.</p>
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<p>Unloading mode.</p>
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<p>Structure of controller.</p>
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<p>Diagram algorithm for selecting working mode.</p>
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<p>A typical pressing profile.</p>
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<p>AMESim model of the system.</p>
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<p>(<b>a</b>) Pump speed response in EHA mode; (<b>b</b>) cylinder velocity open response; (<b>c</b>) cylinder position open response; (<b>d</b>) pressure at pump ports; (<b>e</b>) torque at pump shaft.</p>
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<p>(<b>a</b>) Pump speed response in EHA mode; (<b>b</b>) cylinder velocity open response; (<b>c</b>) cylinder position open response; (<b>d</b>) pressure at pump ports; (<b>e</b>) torque at pump shaft.</p>
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<p>(<b>a</b>) Pressure of the accumulator; (<b>b</b>) hydraulic volume of the accumulator.</p>
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<p>(<b>a</b>) Cylinder position response; (<b>b</b>) consumption energy of the system for the PS, NRS and EHA strategies; (<b>c</b>) energy flow of the system for PS strategy; (<b>d</b>) energy of the system in FR and SR phases of the cycle.</p>
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<p>(<b>a</b>) Cylinder position response; (<b>b</b>) consumption energy of the system for the PS, NRS and EHA strategies; (<b>c</b>) energy flow of the system for PS strategy; (<b>d</b>) energy of the system in FR and SR phases of the cycle.</p>
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<p>Energy recovery factor versus accumulator volume under the various pressure of the accumulator.</p>
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<p>First stage model.</p>
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<p>Block diagram of experimental model.</p>
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<p>(<b>a</b>) The time history of the position; (<b>b</b>) pressure at outlet of the pump; (<b>c</b>) pressure in the inlet of the accumulator.</p>
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<p>(<b>a</b>) Speed of the pump. (<b>b</b>) Torque of the pump.</p>
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<p>(<b>a</b>) Energy of the system; (<b>b</b>) the energy recovery of the system.</p>
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23 pages, 6094 KiB  
Article
Advanced Controller Development Based on eFMI with Applications to Automotive Vertical Dynamics Control
by Johannes Ultsch, Julian Ruggaber, Andreas Pfeiffer, Christina Schreppel, Jakub Tobolář, Jonathan Brembeck and Daniel Baumgartner
Actuators 2021, 10(11), 301; https://doi.org/10.3390/act10110301 - 12 Nov 2021
Cited by 5 | Viewed by 3233
Abstract
High-level modeling languages facilitate system modeling and the development of control systems. This is mainly achieved by the automated handling of differential algebraic equations which describe the dynamics of the modeled systems across different physical domains. A wide selection of model libraries provides [...] Read more.
High-level modeling languages facilitate system modeling and the development of control systems. This is mainly achieved by the automated handling of differential algebraic equations which describe the dynamics of the modeled systems across different physical domains. A wide selection of model libraries provides additional support to the modeling process. Nevertheless, deployment on embedded targets poses a challenge and usually requires manual modification and reimplementation of the control system. The novel proposed eFMI Standard (Functional Mock-up Interface for embedded systems) introduces a workflow and an automated toolchain to simplify the deployment of model-based control systems on embedded targets. This contribution describes the application and verification of the eFMI workflow using a vertical dynamics control problem with an automotive application as an example. The workflow is exemplified by a control system design process which is supported by the a-causal, multi-physical, high-level modeling language Modelica. In this process, the eFMI toolchain is applied to a model-based controller for semi-active dampers and demonstrated using an eFMI-based nonlinear prediction model within a nonlinear Kalman filter. The generated code was successfully tested in different validation steps on the dedicated embedded system. Additionally, tests with a low-volume production electronic control unit (ECU) in a series-produced car demonstrated the correct execution of the controller code under real-world conditions. The novelty of our approach is that it automatically derives an embedded software solution from a high-level multi-physical model with standardized eFMI methodology and tooling. We present one of the first full application scenarios (covering all aspects ranging from multi-physical modeling up to embedded target deployment) of the new eFMI tooling. Full article
(This article belongs to the Special Issue Vehicle Modeling and Control)
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<p>Diagram with a trade-off between comfort and road holding and its optimal Pareto front (adapted from [<a href="#B13-actuators-10-00301" class="html-bibr">13</a>]).</p>
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<p>The eFMI workflow adapted from [<a href="#B11-actuators-10-00301" class="html-bibr">11</a>]. The highlighted path shows the workflow utilized in this work.</p>
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<p>The vertical dynamics controller and prediction model design process using the eFMI workflow (adapted from [<a href="#B14-actuators-10-00301" class="html-bibr">14</a>]).</p>
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<p>Overview of the full vehicle model and its various submodels in Modelica. The semi-active damper model is encircled.</p>
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<p>The vertical dynamics controller scheme.</p>
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<p>Overview of the closed-loop high-fidelity Modelica model of a vehicle including a semi-active damping controller.</p>
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<p>Nonlinear 2-mass system scheme (<b>a</b>) adapted from [<a href="#B18-actuators-10-00301" class="html-bibr">18</a>] and its graphical representation in Modelica (<b>b</b>).</p>
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<p>Integration of the 2 eFMUs into the ECU software framework.</p>
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<p>Coupling of the controller eFMU and the state estimator containing an eFMU prediction model.</p>
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<p>Test setup for open-loop tests to validate different parts of the eFMI workflow. The high-fidelity model described in <a href="#sec4dot1-actuators-10-00301" class="html-sec">Section 4.1</a> was used to create the synthetic excitation data.</p>
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<p>Results of comparing original Modelica simulations with the run of eFMI Production C code (Software in the Loop) in the 64-bit and 32-bit variants of the semi-active damping controller.</p>
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<p>Results from open-loop tests of the original Modelica model and the complete controller eFMU executed on the ECU. Electric currents (u_damper) for the rear left (RL) damper.</p>
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<p>Results for the estimated velocity of the body <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>x</mi> <mo>˙</mo> </mover> <mi mathvariant="normal">b</mi> </msub> </mrow> </semantics></math> and wheel <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>x</mi> <mo>˙</mo> </mover> <mi mathvariant="normal">w</mi> </msub> </mrow> </semantics></math> from the simulation in TargetLink (blue) and the reference trajectory (red).</p>
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<p>Hardware setup of the test vehicle.</p>
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<p>Comparative results from a test maneuver to validate the nonlinear Kalman filter.</p>
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<p>Comparison: Logged controller output during a test drive (eFMU on ECU) and the simulated controller with test drive excitation for the Modelica and eFMI production code (eFMU SiL) controller version. Rear left (RL) damper current (u_damper).</p>
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<p>Comparative results from a test maneuver to validate the semi-active damper controller.</p>
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13 pages, 2684 KiB  
Article
A Procedure for the Fatigue Life Prediction of Straight Fibers Pneumatic Muscles
by Francesco Durante, Michele Gabrio Antonelli, Pierluigi Beomonte Zobel and Terenziano Raparelli
Actuators 2021, 10(11), 300; https://doi.org/10.3390/act10110300 - 11 Nov 2021
Cited by 6 | Viewed by 1985
Abstract
Different from the McKibben pneumatic muscle actuator, the straight fibers one is made of an elastomeric tube closed at the two ends by two heads that ensure a mechanical and pneumatic seal. High stiffness threads are placed longitudinally into the wall of the [...] Read more.
Different from the McKibben pneumatic muscle actuator, the straight fibers one is made of an elastomeric tube closed at the two ends by two heads that ensure a mechanical and pneumatic seal. High stiffness threads are placed longitudinally into the wall of the tube while external rings are placed at some sections of it to limit the radial expansion of the tube. The inner pressure in the tube causes shortening of the actuator. The working mode of the muscle actuator requires a series of critical repeated contractions and extensions that cause it to rupture. The fatigue life duration of a pneumatic muscle is often lower than traditional pneumatic actuators. The paper presents a procedure for the fatigue life prediction of a straight-fibers muscle based on experimental tests directly carried out with the muscles instead of with specimens of the silicone rubber material which the muscle is made of. The proposed procedure was experimentally validated. Although the procedure is based on fatigue life duration data for silicone rubber, it can be extended to all straight-fibers muscles once the fatigue life duration data of any material considered for the muscles is known. Full article
(This article belongs to the Special Issue Pneumatic Muscle Actuators)
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<p>Rest and deformed configurations of: (<b>a</b>) McKibben muscle; (<b>b</b>) straight-fibers muscle.</p>
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<p>Geometric and functional parameters of a sector of the muscle.</p>
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<p>Useful graph to solve Equation (9) with respect to <span class="html-italic">ϕ</span> for a given value of the ratio <span class="html-italic">l</span>/<span class="html-italic">l</span><sub>0</sub>. If, for example, the ratio <span class="html-italic">l</span>/<span class="html-italic">l</span><sub>0</sub> is 0.7, one draws the line from origin to 0.7 on the vertical line. The abscissa of the intersection point between the drawn line and the sine function (A for the actual example) gives the value of <span class="html-italic">ϕ</span> solving Equation (9).</p>
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<p>The test bench used for the life duration tests. It is equipped with a pressure transducer, an electric 3/2 pneumatic valve and a PLC to drive the experimental tests.</p>
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<p>Flow chart of the algorithm used to control the test bench.</p>
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<p>Relationship between the stress for a null load <span class="html-italic">σ</span><sub>1</sub> and the actuator deformation <span class="html-italic">λ</span>.</p>
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<p>Relationship between the equivalent stress <span class="html-italic">σ<sub>eq</sub></span> and the actuator life duration.</p>
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<p>Typical rupture of a straight-fibers muscle in fatigue life duration tests.</p>
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33 pages, 14276 KiB  
Article
Design and Control of an Inflatable Spherical Robotic Arm for Pick and Place Applications
by Matthias Hofer, Jasan Zughaibi and Raffaello D’Andrea
Actuators 2021, 10(11), 299; https://doi.org/10.3390/act10110299 - 11 Nov 2021
Cited by 6 | Viewed by 4401
Abstract
We present an inflatable soft robotic arm made of fabric that leverages state-of-the-art manufacturing techniques, leading to a robust and reliable manipulator. Three bellow-type actuators are used to control two rotational degrees of freedom, as well as the joint stiffness that is coupled [...] Read more.
We present an inflatable soft robotic arm made of fabric that leverages state-of-the-art manufacturing techniques, leading to a robust and reliable manipulator. Three bellow-type actuators are used to control two rotational degrees of freedom, as well as the joint stiffness that is coupled to a longitudinal elongation of the movable link used to grasp objects. The design is motivated by a safety analysis based on first principles. It shows that the interaction forces during an unexpected collision are primarily caused by the attached payload mass, but can be reduced by a lightweight design of the robot arm. A control allocation strategy is employed that simplifies the modeling and control of the robot arm and we show that a particular property of the allocation strategy ensures equal usage of the actuators and valves. The modeling and control approach systematically incorporates the effect of changing joint stiffness and the presence of a payload mass. An investigation of the valve flow capacity reveals that a proper timescale separation between the pressure and arm dynamics is only given for sufficient flow capacity. Otherwise, the applied cascaded control approach can introduce oscillatory behavior, degrading the overall control performance. A closed form feed forward strategy is derived that compensates errors induced by the longitudinal elongation of the movable link and allows the realization of different object manipulation applications. In one of the applications, the robot arm hands an object over to a human, emphasizing the safety aspect of the soft robotic system. Thereby, the intrinsic compliance of the robot arm is leveraged to detect the time when the robot should release the object. Full article
(This article belongs to the Special Issue Pneumatic Actuators for Robotics and Automation)
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<p>The inflatable soft robotic arm presented in this work shown manipulating an apple. The system is made of fabric and uses three bellow-type actuators to control its two rotational degrees of freedom and adjust its joint stiffness.</p>
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<p>(<b>Left</b>) The scenario considered for investigating the safety aspect is a one degree of freedom manipulator of mass <span class="html-italic">M</span>, with a payload of mass <span class="html-italic">m</span> attached to its tip. The mass of the link is assumed to be concentrated as a point mass at the middle of the link. The radius of the link (measured from pivot point <span class="html-italic">O</span> to the tip) is <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math>. The robot collides with a human at a distance <span class="html-italic">l</span> from the pivot point, causing a resulting external force <math display="inline"><semantics> <msub> <mi>F</mi> <mi>ext</mi> </msub> </semantics></math> acting on the movable link and similarly acting on the human. The influence of gravity is not considered in this example. (<b>Right</b>) The momentum <span class="html-italic">J</span> (time integral over external force) as a function of the robot arm mass, <span class="html-italic">M</span>, and the payload mass, <span class="html-italic">m</span>. The black dot indicates the mass of the robot arm presented in this work (<span class="html-italic">M</span> = <math display="inline"><semantics> <mrow> <mn>0.2</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </mrow> </semantics></math>) and a payload mass of <span class="html-italic">m</span> = <math display="inline"><semantics> <mrow> <mn>0.16</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </mrow> </semantics></math> as used in the applications presented in the last part of this work. The distance from pivot point to collision point, <span class="html-italic">l</span>, is assumed to be two-thirds of the link radius. The initial angular velocity of the robot arm is <math display="inline"><semantics> <mrow> <mn>1.8</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi>rad</mi> </semantics></math>/<math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> corresponding to the highest angular velocity considered in this article. The momentum grows with the robot link mass and the payload mass. If we want to keep the momentum constant (moving on a colored line) and the mass of the robot arm is increased by a factor of two, the payload mass would need to be reduced by one third.</p>
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<p>Explosion view of the inflatable robotic arm: The base plate (1) mounts the outer shell of the static link (2) and features tubing connectors that allow to route the tubing internally. The conic support (3) is glued to the interior of the static link and supports the soft joint (4). The three bellow actuators (5) are arranged symmetrically around the soft joint. Tubing is connected through elbow connectors that fit into circular openings in the static and movable links. Additionally, the actuators are fixed by strings attached to the conic supports and Velcro straps on the outer shells of the links. A second conic support (6) connects to the soft joint and is glued to the movable link (7). A third conic support (8) is mounted on the top end of the movable link and houses the suction cup and the markers for the motion capture system. The tubing, the inner bladders, the strings for mounting the actuators, and the screws are not shown for better visibility.</p>
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<p>(<b>Top left</b>) The inner bladder of the movable link, the fabric for the outer shell, a support cone with the recess in the middle into which the soft joint fits, and an actuator with the tubing connected. (<b>Top right</b>) The actuators arranged around the soft joint (white cylindrical part) and connected to both links. (<b>Bottom left</b>) The deformed soft joint when the movable link is deflected. The actuators are attached to the support cones with strings. (<b>Bottom right</b>) The tip of the movable link allows us to attach different suction cups to grasp different objects, such as an apple. Markers for the motion capture system are attached for sensory feedback. The markers and the suction cup are mounted to the support cone that is glued to the interior side of the movable link tip.</p>
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<p>The left figure shows the top view of a single actuator layer. The deformation behavior mainly depends on the actuator height <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> and the off-center distance <math display="inline"><semantics> <mi>μ</mi> </semantics></math>. Choosing the angle <math display="inline"><semantics> <mrow> <mi>ψ</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> increases the footprint of the actuator and therefore the lateral stability during inflation such that the actuator does not bend sideways. The following parameter values are used for the final design: <math display="inline"><semantics> <mrow> <mi>ρ</mi> <mo>=</mo> </mrow> </semantics></math> 89 mm, <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mn>13.6</mn> </mrow> </semantics></math> mm, and <math display="inline"><semantics> <mrow> <mi>ψ</mi> <mo>=</mo> </mrow> </semantics></math> 45<math display="inline"><semantics> <msup> <mrow/> <mo>∘</mo> </msup> </semantics></math>. The figure on the right shows the side view of an inflated actuator. The nine cushions result in a total angle of approximately <math display="inline"><semantics> <mrow> <mn>210</mn> <msup> <mrow/> <mo>∘</mo> </msup> </mrow> </semantics></math>. The outer arc length of the actuator when fully inflated is approximately 340 mm, compared to a thickness of 18 mm when the actuator is fully collapsed.</p>
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<p>The pneumatic diagram of the soft robotic arm: A compressor (1) provides pressurized air at 9 bar that is fed to an air receiver (2). The pressure level is reduced to <math display="inline"><semantics> <mrow> <mn>7.5</mn> </mrow> </semantics></math> bar by means of a manual pressure regulator (3) to the level used by the vacuum generating unit (4) to operate the suction cup (5). A second manual pressure regulator (6) decreases the pressure level to <math display="inline"><semantics> <mrow> <mn>3.5</mn> </mrow> </semantics></math> bar, which is the pressure level used to operate the proportional valves controlling the actuator pressures. A manual shut off valve (7) allows us to either supply air to the additional receiver (8) or to exhaust the air of the subsequent system (as shown in the current valve position). The receiver (8) allows us to mitigate air flow delays induced by the preceding components. The pressure in receiver (8) is measured by means of a pressure sensor and referred to as the source pressure. Two additional manual pressure regulators (9) allow us to adjust the air pressure in the static and movable links (10) (approximately <math display="inline"><semantics> <mrow> <mn>0.25</mn> </mrow> </semantics></math> bar). An additional shut off valve (11) can be used to cut off the air supply from the actuators, while maintaining pressurization of the links. A safety valve (12) ensures that the actuators are exhausted in the case of an emergency. The valve is normally closed, meaning that it has to be actively opened by its solenoid (configuration shown) to supply air to the actuators. Three proportional directional valves (13) are used to control the air pressure in the three actuators (14), where each pressure is measured for feedback control. Note that only three of the five ports of each proportional valve are in use.</p>
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<p>(<b>Left</b>) The spherical robot arm when mounted horizontally to a wall. The soft joint is indicated by the black circle and the gravitational vector points in the negative <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo>→</mo> </mover> <mi>x</mi> </msub> </semantics></math> direction. The end effector point is parameterized by two extrinsic Euler angles <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </semantics></math>, both describing rotations with respect to the inertial frame, and the variable <math display="inline"><semantics> <mi>δ</mi> </semantics></math> describing a longitudinal elongation. (<b>Middle</b>) The symmetric actuator configuration with the three actuators A, B, and C in the corresponding coordinate system. (<b>Right</b>) The variables used by the control allocation strategy. Note that an increase in the actuator pressure A acts in the negative <span class="html-italic">x</span>-direction.</p>
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<p>The figure shows a visualization of the control allocation strategy. (<b>Top left</b>) The plot shows the pressure setpoints in the absolute representation, (<b>top right</b>) the virtual control inputs and (<b>bottom</b>) the resulting angular trajectories. Each of the three trajectories has a constant lower pressure level that increases from the red curve (<math display="inline"><semantics> <mrow> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>1.05</mn> </mrow> </semantics></math> bar) to the blue curve <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>1.10</mn> </mrow> </semantics></math> bar and to the green curve (<math display="inline"><semantics> <mrow> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>1.15</mn> </mrow> </semantics></math> bar). The setpoint trajectory for the virtual control inputs defines a figure-eight trajectory with a different vertical offset corresponding to different lower pressure levels that result in figure-eight trajectories in the angular space of varying magnitude. Each of the three virtual control input trajectories has the same magnitude, but results in a decreasing angular magnitude for higher values of <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>. The reason for this behavior is that the movable link is forced towards a straight orientation wrt. the static link for increasing values of <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> leading to a decrease in angular magnitude. While the set point trajectories have a simple form in the virtual control input representation, the resulting absolute pressure setpoints are rather complex, emphasizing the importance of the control allocation strategy.</p>
Full article ">Figure 9
<p>Visualization of the three virtual control input parametrizations: The first column shows parametrization 1 with the average actuator pressure used as the third virtual control input, the second column shows parametrization 2 with the lower actuator pressure level as third virtual control input (as used in this work) and the right column shows parametrization 3, where <math display="inline"><semantics> <msub> <mi>p</mi> <mi mathvariant="normal">A</mi> </msub> </semantics></math> is directly used as the third virtual control input. The periodic input signal in <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>α</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>β</mi> </msub> </mrow> </semantics></math> is indicated for parametrization 1 by the black circle in the pressure space. The virtual control input, <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi>avg</mi> </msub> <mo>=</mo> <mn>1.15</mn> </mrow> </semantics></math> bar, is a measure of the distance between the <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>α</mi> </msub> </mrow> </semantics></math>-<math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>β</mi> </msub> </mrow> </semantics></math>-plane containing the circle and the origin. The resulting actuator pressures are shown in the bottom plot and it can clearly be seen that the resulting signals are periodic and of equal magnitude with a shifted phase. For parametrization 2, the resulting curves in the pressure space are given by the black curves (section of an ellipse), lying on the three colored planes that are offset to the origin by <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>1.05</mn> </mrow> </semantics></math> bar. They result from projecting the circle of the input signals, <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>α</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>β</mi> </msub> </mrow> </semantics></math>, onto the three planes. The three actuator pressures in the bottom plot are also periodic signals with equal magnitude and a shift in phase. For parametrization 3, the curve in the pressure space is obtained by constraining the circle in <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>α</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mi>β</mi> </msub> </mrow> </semantics></math> to the plane <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi mathvariant="normal">A</mi> </msub> <mo>=</mo> <mn>1.25</mn> </mrow> </semantics></math> bar, resulting in an elliptical curve. The corresponding actuator pressures are all periodic signals, but only <math display="inline"><semantics> <msub> <mi>p</mi> <mi mathvariant="normal">B</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>p</mi> <mi mathvariant="normal">C</mi> </msub> </semantics></math> have equal magnitude. Hence, this virtual control input parametrization differs qualitatively from parametrizations 1 and 2.</p>
Full article ">Figure 10
<p>The frequency response in the <math display="inline"><semantics> <mi>α</mi> </semantics></math>-direction for different lower pressure levels <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> with the magnitude in the top plot and the phase in the bottom plot. The measured frequency responses resulting from the identification experiments are indicated by the crosses and the corresponding fits by the solid lines. For increasing values of <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>, the magnitude of the frequency response decreases and the resonance frequency of the system increases. The error between measured and fitted frequency response could be further reduced for small values of <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> by adding an additional zero to the fitted transfer function. However, we reject the extension for the sake of simplicity and in order to have a constant model structure for all values of <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>.</p>
Full article ">Figure 11
<p>The parameters of the transfer function, <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mi>α</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, as a function of the lower pressure level <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>. The red crosses indicate the parameter values from the identification experiments and the black solid lines show the first or third order polynomial fits. The stiffness parameter (top left plot) shows a linear relation with the lower pressure level, <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>.</p>
Full article ">Figure 12
<p>The figure shows a comparison of the frequency response when a payload mass is attached. The solid red line shows the (fitted) frequency response where no mass is attached and is referred to as the nominal model. The solid blue and green lines show the predicted frequency responses based on the nominal model and extrapolating the effect of the mass based on (<a href="#FD11-actuators-10-00299" class="html-disp-formula">11</a>). The blue and green crosses indicate the measured frequency response with an attached payload mass of <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </mrow> </semantics></math> or <math display="inline"><semantics> <mrow> <mn>0.2</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mrow> <mi mathvariant="normal">k</mi> <mi mathvariant="normal">g</mi> </mrow> </semantics></math>, respectively. The lower pressure level is set to <math display="inline"><semantics> <mrow> <mn>1.1</mn> </mrow> </semantics></math> bar for both experiments. The left shift of the resonance frequency is accurately predicted by the model, while the rise of resonance is slightly overestimated.</p>
Full article ">Figure 13
<p>The figure shows the angular response for each of the three experiments in which one of the three actuators is preloaded, i.e., inflated to <math display="inline"><semantics> <mrow> <mn>1.3</mn> </mrow> </semantics></math> bar for 5 <math display="inline"><semantics> <mi>min</mi> </semantics></math>. Then, sinusoidal set point trajectories for <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>SP</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mrow> <mi>β</mi> <mo>,</mo> <mi>SP</mi> </mrow> </msub> </mrow> </semantics></math> are commanded, resulting in a circle in the <math display="inline"><semantics> <mi>α</mi> </semantics></math>-<math display="inline"><semantics> <mi>β</mi> </semantics></math>-plane. Thereby, <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> is set to ambient pressure. The procedure is repeated for actuators B and C being preloaded and the same pressure setpoint trajectories are commanded. The recorded circles are shifted away from the particular actuator that was preloaded. Within each experiment, the single realizations of the circle show little variation, emphasizing the good repeatability achievable with the system.</p>
Full article ">Figure 14
<p>The cascaded control architecture employed for the soft robotic arm. The architecture is structured into a low level part that is executed at <math display="inline"><semantics> <mrow> <mn>1000</mn> <mi>Hz</mi> </mrow> </semantics></math> on an embedded hardware and a high level part that is executed on a laptop computer at <math display="inline"><semantics> <mrow> <mn>50</mn> <mi>Hz</mi> </mrow> </semantics></math>. A timescale separation between the pressure and arm dynamics is exploited, where each actuator pressure is controlled by a proportional-integral-derivative controller in a separate inner control loop. The position controller in the outer loop uses sensory feedback of the angles to compute two virtual control inputs <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi>SP</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>p</mi> <mrow> <mi>β</mi> <mo>,</mo> <mi>SP</mi> </mrow> </msub> </mrow> </semantics></math>. The gain scheduled position controller depends on the commanded value for <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> and the known payload mass <span class="html-italic">m</span>. The control allocation strategy is applied to map the virtual control inputs to the actuator pressure set points that are the reference signals for the inner loops. Feed forward control action is added to compensate for the effect of gravity and a longitudinal actuation of the arm.</p>
Full article ">Figure 15
<p>The identified closed-loop pressure dynamics for actuator A resulting from a series of pressure steps. The red curve shows the magnitude of the frequency response when the full flow capacity of the proportional valve is used (100%). The blue and green curves show the magnitude when the flow capacity is limited to 50% and 25% of the nominal value, respectively. The black dashed line indicates the <math display="inline"><semantics> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </semantics></math> line. The cutoff frequencies decrease from <math display="inline"><semantics> <mrow> <mn>22.7</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi>Hz</mi> </semantics></math> for the red curve to <math display="inline"><semantics> <mrow> <mn>2.9</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi>Hz</mi> </semantics></math> for the blue curve and <math display="inline"><semantics> <mrow> <mn>0.7</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi>Hz</mi> </semantics></math> for the green curve.</p>
Full article ">Figure 16
<p>The resulting tracking performance when relying on the feedback controller is shown in the top plot for <math display="inline"><semantics> <mi>α</mi> </semantics></math> and in the bottom plot for <math display="inline"><semantics> <mi>β</mi> </semantics></math>. The black dashed lines denote the set point trajectories and the colored lines the four cases investigated. Thereby, the following parameters are changed: the attached payload mass, <span class="html-italic">m</span>, the value set for the payload mass in the controller, <math display="inline"><semantics> <msub> <mi>m</mi> <mi mathvariant="normal">c</mi> </msub> </semantics></math>, and the lower pressure level <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>. Normally, the two values for <span class="html-italic">m</span> and <math display="inline"><semantics> <msub> <mi>m</mi> <mi mathvariant="normal">c</mi> </msub> </semantics></math> are identical, but for the sake of this investigation, we also consider differing values. The red line shows the results when no payload mass is attached and the joint stiffness is set to the lower level (<math display="inline"><semantics> <mrow> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>1.05</mn> </mrow> </semantics></math> bar) and the blue line shows the case where a payload mass is attached and the joint stiffness is set to a low level. The green line represents the case where a payload mass is attached and the joint stiffness is set to the high level (<math display="inline"><semantics> <mrow> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>1.10</mn> </mrow> </semantics></math> bar). For all three cases, the controller had knowledge of the true payload mass attached (<math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>c</mi> </msub> <mo>=</mo> <mi>m</mi> </mrow> </semantics></math>), resulting in similar tracking performance for both <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>β</mi> </semantics></math>. The purple line indicates the behavior when a payload mass is attached (<math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.17</mn> </mrow> </semantics></math> kg), but the controller assumes no payload mass (<math display="inline"><semantics> <mrow> <msub> <mi>m</mi> <mi>c</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>). The joint stiffness is set to the lower level for this case. Distinct oscillations are visible for the last case, when considering <math display="inline"><semantics> <mi>β</mi> </semantics></math>. As a consequence of the mismatch between the true mass and the value commanded to the controller, the control performance is degraded. Additionally, note the slight errors occurring in one angle, when commanding a change in the other angle and vice versa.</p>
Full article ">Figure 17
<p>The lower pressure level, <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>, as shown in the bottom plot, is rapidly increased to cause a longitudinal elongation for grasping an object. The top and middle plots show a comparison of the angles <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>β</mi> </semantics></math> when no feed forward (ff) control action is used (red curve) and when the proposed feed forward strategy is employed (blue curve). Relying on the feed forward approach reduces the maximum error in <math display="inline"><semantics> <mi>α</mi> </semantics></math> from <math display="inline"><semantics> <mrow> <mn>7.1</mn> </mrow> </semantics></math> deg to <math display="inline"><semantics> <mrow> <mn>3.5</mn> </mrow> </semantics></math> deg and in <math display="inline"><semantics> <mi>β</mi> </semantics></math> from <math display="inline"><semantics> <mrow> <mn>6.4</mn> </mrow> </semantics></math> deg to <math display="inline"><semantics> <mrow> <mn>3.0</mn> </mrow> </semantics></math> deg. In the case where no feed forward control action is used, we purely rely on the feedback controller. Note that an increase in <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> causes the robotic arm to be deflected towards the origin and vice versa for a decrease in <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>.</p>
Full article ">Figure 18
<p>A visualization of the pick and place application: The top two plots show the angles <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>β</mi> </semantics></math> and their setpoints, respectively. The arm starts from the idle position, <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>0</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mn>0</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </mrow> </semantics></math>, and picks up the object at the location, <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mn>22</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mo>−</mo> <mn>30.5</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math>, moves it to the target location at <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mn>32</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mo>−</mo> <mn>38</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math>, and then moves back to the idle location <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mn>0</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math>. The arm is raised in the positive <math display="inline"><semantics> <mi>β</mi> </semantics></math>-direction between picking the object and releasing it, to avoid interfering with the platforms where the object is picked from and released to. Releasing the object causes an error in both angles due to the sudden change of mass. The third plot shows the lower actuator pressure level, <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>, and the load mass assumed by the controller. When the suction cup points towards the object, the lower actuator pressure level is increased to cause a longitudinal elongation and pick up the object. The payload mass commanded to the controller is continuously increased from the weight of the suction cup to the combined weight of suction cup and manipulated object. When the object is released, the commanded mass is continuously decreased back to the weight of the suction cup. The bottom plot shows the control inputs of the vacuum generation unit. The red curve shows the vacuum input to generate a vacuum at the suction cup. It is activated shortly before the suction cup touches the object to ensure a reliable picking procedure. The blue curve shows the ejection impulse used to release the vacuum when placing the object.</p>
Full article ">Figure 19
<p>Visualization of the collaborative application where the robot picks up an object and hands it over to a human: The top two plots show the angles <math display="inline"><semantics> <mi>α</mi> </semantics></math> and <math display="inline"><semantics> <mi>β</mi> </semantics></math> and their setpoints, respectively. The third plot shows the lower actuator pressure level and the assumed payload mass. The bottom plot indicates the control inputs of the vacuum generation unit. The arm starts from the idle position, <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>0</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mn>0</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </mrow> </semantics></math>, picks up the object at the initial location, <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mn>22</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mo>−</mo> <mn>30.5</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math>, moves it to the final position at <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>15</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>,</mo> <mn>30</mn> <msup> <mrow/> <mo>∘</mo> </msup> <mo>)</mo> </mrow> </semantics></math>, and waits for the human interaction. The robot arm maintains the vacuum as long as the object lies in the green region corresponds to an angular range of <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>3</mn> <msup> <mrow/> <mo>∘</mo> </msup> </mrow> </semantics></math> of the setpoint in <math display="inline"><semantics> <mi>α</mi> </semantics></math> or <math display="inline"><semantics> <mi>β</mi> </semantics></math>, respectively. As soon as the human moves the object outside the green region (the time instance is indicated by the vertical, dotted black line), the payload mass assumed by the controller is adjusted, the vacuum is released and the ejection impulse is activated for <math display="inline"><semantics> <mrow> <mn>0.1</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math> to purge the vacuum. A human interaction is only expected for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>≥</mo> <mn>10</mn> </mrow> </semantics></math> s to exclude a triggering of the release condition due to transient tracking errors.</p>
Full article ">Figure A1
<p>The frequency response in <math display="inline"><semantics> <mi>β</mi> </semantics></math>-direction for different lower pressure levels <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math> with the magnitude in the top plot and the phase in the bottom plot. The measured frequency responses resulting from the identification experiments are indicated by the crosses and the corresponding fits by the solid lines.</p>
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<p>The parameters of the transfer function, <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mi>β</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mo>,</mo> <mi>m</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>, as a function of the lower pressure level <math display="inline"><semantics> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> </semantics></math>. The red crosses indicate the parameter values from the identification experiments and the black solid lines show the first or third order polynomial fits.</p>
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22 pages, 3058 KiB  
Review
Light-Responsive Soft Actuators: Mechanism, Materials, Fabrication, and Applications
by Yaoli Huang, Qinghua Yu, Chuanli Su, Jinhua Jiang, Nanliang Chen and Huiqi Shao
Actuators 2021, 10(11), 298; https://doi.org/10.3390/act10110298 - 10 Nov 2021
Cited by 23 | Viewed by 6429
Abstract
Soft robots are those that can move like living organisms and adapt to the surrounding environment. Compared with traditional rigid robots, the advantages of soft robots, in terms of material flexibility, human–computer interaction, and biological adaptability, have received extensive attention. Flexible actuators based [...] Read more.
Soft robots are those that can move like living organisms and adapt to the surrounding environment. Compared with traditional rigid robots, the advantages of soft robots, in terms of material flexibility, human–computer interaction, and biological adaptability, have received extensive attention. Flexible actuators based on light response are one of the most promising ways to promote the field of cordless soft robots, and they have attracted the attention of scientists in bionic design, actuation implementation, and application. First, the three working principles and the commonly used light-responsive materials for light-responsive actuators are introduced. Then, the characteristics of light-responsive soft actuators are sequentially presented, emphasizing the structure strategy, actuation performance, and emerging applications. Finally, this review is concluded with a perspective on the existing challenges and future opportunities in this nascent research frontier. Full article
(This article belongs to the Special Issue Soft Actuation: State of the Art and Outlook)
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Figure 1

Figure 1
<p>(<b>a</b>) Schematic of the bending mechanism of the bilayer structure [<a href="#B38-actuators-10-00298" class="html-bibr">38</a>]. Permission from WILEY-VCH. (<b>b</b>) Schematic illustration of the bending/unbending actuation of a PDA-RGO/NOA-63 actuator toward humidity changes (top panel) and periodic NIR irradiation (bottom panel) [<a href="#B41-actuators-10-00298" class="html-bibr">41</a>]. Permission from WILEY-VCH. (<b>c</b>) Photo-thermal effect of GO film and the thermally induced phase transition of LC domains upon NIR or vis irradiation [<a href="#B43-actuators-10-00298" class="html-bibr">43</a>]. Permission from American Chemical Society. (<b>d</b>) Schematic diagrams of the photo-electric conversion mechanism [<a href="#B44-actuators-10-00298" class="html-bibr">44</a>]. Permission from Springer Nature. (<b>e</b>) Transformation of trans/cis isomeric azo-benzene [<a href="#B45-actuators-10-00298" class="html-bibr">45</a>]. Permission from Springer Nature.</p>
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<p>(<b>a</b>) Actuating behavior of LCP film when heated by IR lamp. Reproduced with permission [<a href="#B61-actuators-10-00298" class="html-bibr">61</a>]. Permission from WILEY-VCH. (<b>b</b>) Schematic of the approach to optically reconfiguring an LCN actuator through selective de-crosslinking. The magenta regions represent cross-linked actuation domains, and the blue regions represent de-crosslinked, non-actuation domains. (<b>c</b>) Reconfigurable photo actuator through synergistic use of photo-chemical and photo-thermal effects [<a href="#B62-actuators-10-00298" class="html-bibr">62</a>]. Permission from WILEY-VCH.</p>
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<p>Schematic illustration of light-responsive shape memory properties: (<b>a</b>) mechanism in molecular structure; (<b>b</b>) deformation in the experiment (1) original shape, (2) stretched shapes, (3) sample cut from the stretch sample at an angle of 30° to the stretching direction, (4) curling sample upon UV light, (5) curled sample after UV light irradiation, (6) curled sample fixed at room temperature under visible light irradiation, (7) the recovered sample after reheating to 80 °C [<a href="#B71-actuators-10-00298" class="html-bibr">71</a>]. Permission from Elsevier.</p>
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<p>Schematic diagram of the structure and its manufacturing method of the light-responsive actuator. The insets are reprinted from the following sources. Bulk [<a href="#B74-actuators-10-00298" class="html-bibr">74</a>]. Permission from Wiley-VCH. Fiber/Coil/Yarns [<a href="#B75-actuators-10-00298" class="html-bibr">75</a>]. Permission from Wiley-VCH. Vacuum filtration [<a href="#B76-actuators-10-00298" class="html-bibr">76</a>]. Permission from Wiley-VCH. Hydrothermal [<a href="#B77-actuators-10-00298" class="html-bibr">77</a>]. Permission from Springer Nature. Wet spinning [<a href="#B78-actuators-10-00298" class="html-bibr">78</a>]. Permission from THE SOCIETY.</p>
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<p>(<b>a</b>) Actuating behavior of single-layer, light-responsive actuator based on polyurethane shape memory polymer [<a href="#B71-actuators-10-00298" class="html-bibr">71</a>]. Permission from Elsevier. (<b>b</b>) Schematic illustration of the fabrication process of the PDMS-CNT/chitosan actuator and its actuating behavior [<a href="#B80-actuators-10-00298" class="html-bibr">80</a>]. Permission from Royal Society of Chemistry. (<b>c</b>) Fabrication of self-folding polymer multi-layer actuator structure and its thermally actuating behavior [<a href="#B81-actuators-10-00298" class="html-bibr">81</a>]. Permission from WILEY.VCH. (<b>d</b>) Schematic diagram of the preparation of PET/LCN bilayer structure actuator by spray-coating method and photograph of a light-responsive thermoplastic actuator [<a href="#B82-actuators-10-00298" class="html-bibr">82</a>]. Permission from WILEY.VCH. (<b>e</b>) Schematic diagram of the preparation of LCEs/PDA bilayer r structure actuator using dip-coating process and samples [<a href="#B83-actuators-10-00298" class="html-bibr">83</a>]. Permission from American Chemical Society. (<b>f</b>) Schematic diagram of bilayer film preparation with spin coating.</p>
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<p>(<b>a</b>) Schematic diagram of the manufacturing process of the fiber-type actuator. (<b>b</b>) Schematic diagram of the reversible rotational motion of the twisted GO/SA fiber-based actuator under on/off light irradiation and moisture [<a href="#B87-actuators-10-00298" class="html-bibr">87</a>]. Permission from American Chemical Society. (<b>c</b>) Aspherical load produced a rapid forward and backward movement under on/off infrared light irradiation [<a href="#B78-actuators-10-00298" class="html-bibr">78</a>]. Permission from the Society.</p>
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<p>(<b>a</b>) Schematic of the preparation of bulk graphene sponge by hydrothermal method [<a href="#B77-actuators-10-00298" class="html-bibr">77</a>]. Permission from Springer Nature. (<b>b</b>) The schematic diagram of the vertical rise of graphene sponge under laser irradiation.</p>
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<p>(<b>a</b>,<b>b</b>) Analysis method of bending angle and curvature. (<b>c</b>) Schematic diagram of light-responsive behavior of GO−GMA hydrogel within a microfluidic channel; images were taken under a microscope [<a href="#B88-actuators-10-00298" class="html-bibr">88</a>]. Permission from Royal Society of Chemistry. (<b>d</b>) The bending mechanism of the bi-layer actuator is caused by the difference in thermal expansion coefficient. (<b>e</b>) Curvature changes are caused by differences in thickness [<a href="#B38-actuators-10-00298" class="html-bibr">38</a>]. (<b>f</b>) Changes in bending displacement are caused by light intensity [<a href="#B39-actuators-10-00298" class="html-bibr">39</a>]. Permission from American Chemical Society.</p>
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<p>Nature-inspired light-powered soft robot. (<b>a</b>) Bionic flower prepared by flexible actuator [<a href="#B93-actuators-10-00298" class="html-bibr">93</a>]. Permission from RSC Publishing. (<b>b</b>) Fishtail-inspired robotic fish actuator design [<a href="#B83-actuators-10-00298" class="html-bibr">83</a>]. Permission from American Chemical Society. (<b>c</b>) Grasping robot inspired by flytrap [<a href="#B92-actuators-10-00298" class="html-bibr">92</a>]. Permission from Springer Nature. (<b>d</b>) Design and lifting process of the mechanical arm [<a href="#B47-actuators-10-00298" class="html-bibr">47</a>]. Permission from American Chemical Society.</p>
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<p>(<b>a</b>) Schematic diagram of structure model of light−actuated liquid crystal film micro-valve. (<b>b</b>) Cross-sectional schematic diagram and working principle of light-actuated liquid crystal film micro−valves. (<b>c</b>) The relationship between fluid flow and irradiation time under different conditions [<a href="#B95-actuators-10-00298" class="html-bibr">95</a>]. Permission from Springer Nature. (<b>d</b>) Schematic diagram of the artery wall structure. (<b>e</b>) The light-induced movement of the silicone oil plug in a tubular actuator fixed on the substrate [<a href="#B96-actuators-10-00298" class="html-bibr">96</a>]. Permission from Springer Nature.</p>
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10 pages, 3839 KiB  
Article
Effect of Forced Liquid Cooling on the Voltage/Charge Displacement Characteristics of Stacked Piezoelectric Actuators during High-Frequency Drive
by Rina Nishida, Jianpeng Zhong and Tadahiko Shinshi
Actuators 2021, 10(11), 297; https://doi.org/10.3390/act10110297 - 10 Nov 2021
Cited by 2 | Viewed by 2481
Abstract
Piezoelectric stack actuators (PESAs) are widely used in applications requiring a fast response, high resolution, and high accuracy. The self-heating of a PESA during continuous drive with a large amplitude at high frequencies can change its voltage displacement and charge displacement characteristics. These [...] Read more.
Piezoelectric stack actuators (PESAs) are widely used in applications requiring a fast response, high resolution, and high accuracy. The self-heating of a PESA during continuous drive with a large amplitude at high frequencies can change its voltage displacement and charge displacement characteristics. These changes can lead to a loss of stability and inaccurate PESA positioning systems. In this paper, we confirmed that by using our proposed forced liquid cooling, the changes to the dynamic characteristics and the impedance of a PESA due to the fact of self-heating could be reduced. Voltage displacement curve measurements at 10 kHz demonstrated that with natural heat dissipation, the amplitude of PESA increased by 15% due to the self-heating compared to the amplitude measured at the start of driving but only by 3% with forced liquid cooling. The displacement-to-charge ratio decreased by 12% compared to that at room temperature with natural heat dissipation, while it increased by 1% during forced liquid cooling. In the measured frequency response of the voltage displacement transfer function, the increased temperature changed the gain and phase of the first and secondary vibration modes above 20 kHz with natural heat dissipation. Forced liquid cooling also reduced the variations in the frequency response of the voltage displacement transfer function. Full article
(This article belongs to the Special Issue Design and Control of High-Precision Motion Systems)
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<p>Experimental setup for forced liquid cooling of a PESA.</p>
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<p>Photograph of the preloaded PESA and cooling channel structure.</p>
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<p>(<b>a</b>) Measured voltage displacement hysteresis curves with natural heat dissipation and liquid cooling and (<b>b</b>) the same curves normalized by amplitude. A bias voltage of 50 V and a sinusoidal voltage of 24 V at a frequency of 10 kHz were applied to the PESA.</p>
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<p>Measured charge displacement curves with natural heat dissipation and liquid cooling when a bias voltage of 50 V and sinusoidal voltage of 24 V at a frequency of 10 kHz were applied to the PESA. The dashed lines are linear approximations.</p>
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<p>Measured frequency response (µm/V) of the PESA when a bias voltage of 50 V and sinusoidal voltage of 13 V were applied to the PESA with natural heat dissipation (red) and with forced liquid cooling (blue). The black line represents the frequency response with natural heat dissipation without sufficient time for the temperature to rise.</p>
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<p>Equivalent circuit of the PESA and measurement system.</p>
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<p>Impedance of the PESA when a bias voltage of 50 V and sinusoidal voltage of 13 V were applied to the PESA with natural heat dissipation (red) and with forced liquid cooling (blue). The black line represents the impedance with natural heat dissipation without sufficient time for the temperature to rise.</p>
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11 pages, 15456 KiB  
Communication
Micro-Range Actuation by Pressure-Induced Elastic Deformation of 316L Steel Membranes Produced by Laser Powder Bed Fusion
by Florian Fettweis, Bjorn Verrelst and Svend Bram
Actuators 2021, 10(11), 296; https://doi.org/10.3390/act10110296 - 6 Nov 2021
Cited by 1 | Viewed by 1997
Abstract
In this paper, fundamental research is performed on membrane type actuators made out of 316L stainless steel, manufactured with Laser powder bed fusion (LPBF). A total of six membranes with membrane thicknesses ranging from 0.6 mm up to 1.2 mm were scanned using [...] Read more.
In this paper, fundamental research is performed on membrane type actuators made out of 316L stainless steel, manufactured with Laser powder bed fusion (LPBF). A total of six membranes with membrane thicknesses ranging from 0.6 mm up to 1.2 mm were scanned using a high precision metrology system to measure the membrane for displacement at different actuating pressures. The membranes were furthermore investigated for roughness, porosity and thickness. This showed that the thinnest membranes skewed in the print direction when actuated. The remaining membranes achieved higher specific displacements than finite element simulations (FES) predicted, due to surface roughness and porosity. Membrane type actuators can be used for precise actuation within the micrometre range. LPBF allows the creation of internal pockets and membranes in a single metal piece. In opposition to the more commonly used polymers for membrane-type actuators, LPBF steel printed parts offer high stiffness and actuation force. However, due to limitations of the LPBF process on thin walls, large deviations from FES occur. In this paper, a CAD and FES compensation strategy is suggested, which makes future, more complex and effective, designs possible. Full article
(This article belongs to the Section Miniaturized and Micro Actuators)
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<p>Render of the prototype (<b>left pane</b>) with designed membrane thicknesses <math display="inline"><semantics> <mrow> <mn>0.6</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>0.8</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math> and a cross-section image (<b>right pane</b>). In the middle of the membrane the thickened part can be seen. The larger of the two threaded connections is used as feeding hole, the smaller one is used as venting hole.</p>
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<p>Schematic drawing of the membrane actuator in test setup. <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </semantics></math>, the outer radius of the membrane, is <math display="inline"><semantics> <mrow> <mn>26.0</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>. <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math>, the inner radius of the membrane and the radius of the thickened part, is <math display="inline"><semantics> <mrow> <mn>14.5</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>. The thickening is <math display="inline"><semantics> <mrow> <mn>2.9</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math> thick, whereas the membrane thickness ranges between <math display="inline"><semantics> <mrow> <mn>0.6</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.8</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>1.0</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math> up to <math display="inline"><semantics> <mrow> <mn>1.2</mn> <mtext> </mtext> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">m</mi> </mrow> </mrow> </semantics></math>. An aluminium ring clamps the actuator on the housing. The housing has a radius of <math display="inline"><semantics> <mrow> <mn>4.5</mn> <mtext> </mtext> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math> and height of <math display="inline"><semantics> <mrow> <mn>22.5</mn> <mtext> </mtext> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math>. The clamping allows the expansion of the upper membrane and suppresses the expansion of the lower membrane.</p>
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<p>Pictures of the actuator in the Nikon HN-C3030 scanning system and Zeiss CMM machine. (<b>a</b>) Front view of the prototype positioned in the Nikon HN-C3030 metrology scanning system. (<b>b</b>) Top view of the prototype positioned in the Nikon HN-C3030 metrology scanning system. (<b>c</b>) Side view of the prototype positioned in the Zeiss CMM machine.</p>
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<p>The prototypes are prepared for microscopy by cutting them in eight pieces (plus threaded hydraulic connection, which is discarded), putting them into epoxy embedding material to subsequently grind and polish them. (<b>a</b>) Top view of the of the prototype before cutting. The parts are marked and numbered before cutting. (<b>b</b>) Top view of the eight cut pieces (and the threaded connections) after cutting. (<b>c</b>) View of one of the cut pieces in the embedding material after grinding and polishing, ready for the microscope.</p>
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<p>Colour maps of the specific displacements at a certain pressure of the membranes. Bellow and at the side of each colour map the average specific displacement of a 1 <math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math> wide section, as indicated with fine black lines, in the print direction (<span class="html-italic">y</span>-axis, vertically) and perpendicular to the print direction (<span class="html-italic">x</span>-axis, horizontally) is displayed. This section gives a clear view of the skewing of the thinnest prototypes (<a href="#actuators-10-00296-f005" class="html-fig">Figure 5</a>d,f) in the direction of printing.</p>
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<p>In figure (<b>a</b>), an image of the microscope is shown, the embedding material in black and the membrane in grey. In figure (<b>b</b>), the analysed data is visualised, in red all the detected pores, in green the detected edges, in white the membrane section and the background is black. The code calculates the roughness, the porosity (pore area compared to total membrane area) and the thickness of the membrane on a pixel count basis.</p>
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<p>The specific displacement of each membrane thicker then <math display="inline"><semantics> <mrow> <mn>0.6</mn> <mtext> </mtext> </mrow> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math> in function of the membrane thickness is depicted on both charts. On the left pane, a thickness correction method is shown, which consists of a static thickness which is subtracted from the membrane thickness. The gray line depicts the FES, and the circles depict a thickness correction of 85 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math>. On the right pane a Young’s modulus correction is depicted, which consists of a reduction of the Young’s modulus used in the simulation. The gray full line depicts again the FES with a Young’s modulus of 200 <math display="inline"><semantics> <mi mathvariant="normal">G</mi> </semantics></math><math display="inline"><semantics> <mi>Pa</mi> </semantics></math>, whereas the dotted line depicts a FES with a Young’s modulus of 150 <math display="inline"><semantics> <mi mathvariant="normal">G</mi> </semantics></math><math display="inline"><semantics> <mi>Pa</mi> </semantics></math>. The thickness correction appears to be slightly more accurate in predicting the specific displacement than the Young’s modulus correction; however, the Young’s modulus correction is easier to implement.</p>
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21 pages, 5977 KiB  
Article
Extension Coordinated Multi-Objective Adaptive Cruise Control Integrated with Direct Yaw Moment Control
by Hongbo Wang, Youding Sun, Zhengang Gao and Li Chen
Actuators 2021, 10(11), 295; https://doi.org/10.3390/act10110295 - 6 Nov 2021
Cited by 6 | Viewed by 2621
Abstract
An adaptive cruise control (ACC) system can reduce driver workload and improve safety by taking over the longitudinal control of vehicles. Nowadays, with the development of range sensors and V2X technology, the ACC system has been applied to curved conditions. Therefore, in the [...] Read more.
An adaptive cruise control (ACC) system can reduce driver workload and improve safety by taking over the longitudinal control of vehicles. Nowadays, with the development of range sensors and V2X technology, the ACC system has been applied to curved conditions. Therefore, in the curving car-following process, it is necessary to simultaneously consider the car-following performance, longitudinal ride comfort, fuel economy and lateral stability of ACC vehicle. The direct yaw moment control (DYC) system can effectively improve the vehicle lateral stability by applying different longitudinal forces to different wheels. However, the various control objectives above will conflict with each other in some cases. To improve the overall performance of ACC vehicle and realize the coordination between these control objectives, the extension control is introduced to design the real-time weight matrix under a multi-objective model predictive control (MPC) framework. The driver-in-the-loop (DIL) tests on a driving simulator are conducted and the results show that the proposed method can effectively improve the overall performance of vehicle control system and realize the coordination of various control objectives. Full article
(This article belongs to the Special Issue Actuators for Intelligent Electric Vehicles)
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<p>Vehicle longitudinal dynamics model.</p>
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<p>Vehicle dynamics model.</p>
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<p>Framework of the proposed control.</p>
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<p>Vehicle following model.</p>
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<p>Sideslip angle phase plane division region.</p>
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<p>1-D extension set of car-following distance error.</p>
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<p>2-D extension set of lateral stability.</p>
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<p>1-D extension set.</p>
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<p>Fuel consumption rate and map of engine: (<b>a</b>) fuel consumption rate of engine; (<b>b</b>) engine map.</p>
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<p>DIL test hardware platform.</p>
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<p>Curve path in the simulation model.</p>
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<p>Longitudinal speed and steering wheel angle: (<b>a</b>) longitudinal speed; (<b>b</b>) steering wheel angle.</p>
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<p>Longitudinal car-following errors, (<b>a</b>) Longitudinal car-following distance error, (<b>b</b>) Relative speed.</p>
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<p>Lateral stability errors: (<b>a</b>) vehicle sideslip angle error; (<b>b</b>) yaw rate error.</p>
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<p>Phase plane of errors: (<b>a</b>) phase plane of longitudinal car-following errors; (<b>b</b>) phase plane of lateral errors.</p>
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<p><span class="html-italic">X<sub>region</sub></span> and adjustment factors: (<b>a</b>) <span class="html-italic">X<sub>region</sub></span>; (<b>b</b>) adjustment factors.</p>
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<p>Fuel consumption and longitudinal acceleration: (<b>a</b>) fuel consumption; (<b>b</b>) longitudinal acceleration.</p>
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<p>Control outputs: (<b>a</b>) throttle opening; (<b>b</b>) additional yaw moment.</p>
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<p>Brake pressure on wheels: (<b>a</b>) brake pressure with ACC; (<b>b</b>) brake pressure with ACC&amp;DYC; (<b>c</b>) brake pressure with proposed control.</p>
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20 pages, 16872 KiB  
Article
Towards Fabrication of Planar Magnetoelectric Devices: Coil-Free Excitation of Ferromagnet-Piezoelectric Heterostructures
by Dmitri Burdin, Dmitri Chashin, Leonid Fetisov, Dmitri Saveliev, Nikolai Ekonomov, Melvin Vopson and Yuri Fetisov
Actuators 2021, 10(11), 294; https://doi.org/10.3390/act10110294 - 4 Nov 2021
Cited by 3 | Viewed by 1960
Abstract
Magnetoelectric (ME) effects in composite ferromagnet-piezoelectric (FM/PE) heterostructures realize the mutual transformation of alternating magnetic and electric fields, and are used to create magnetic field sensors, actuators, inductors, gyrators, and transformers. The ME effect in composite structures is excited by an alternating magnetic [...] Read more.
Magnetoelectric (ME) effects in composite ferromagnet-piezoelectric (FM/PE) heterostructures realize the mutual transformation of alternating magnetic and electric fields, and are used to create magnetic field sensors, actuators, inductors, gyrators, and transformers. The ME effect in composite structures is excited by an alternating magnetic field, which is created using volumetric electromagnetic coils. The coil increases the size, limits the operating frequencies, and complicates the manufacture of devices. In this work, we propose to excite the ME effect in composite heterostructures using a new coil-free excitation system, similar to a “magnetic capacitor”. The system consists of parallel electrodes integrated into the heterostructure, through which an alternating current flows. Modeling and measurements have shown that the excitation magnetic field is localized mainly between the electrodes of the magnetic capacitor and has a fairly uniform spatial distribution. Monolithic FM/PE heterostructures of various designs with FM layers of amorphous Metglas alloy or nickel-zinc ferrite and PE layers of lead zirconate titanate piezoceramic were fabricated and investigated. The magnitude of the ME effect in such structures is comparable to the magnitude of the ME effect in structures excited by volumetric coils. However, the low impedance of the coil-free excitation system makes it possible to increase the operating frequency, reducing the size of ME devices and the power consumption. The use of coil-free excitation opens up the possibility of creating planar ME devices, and accelerates their integration into modern electronics and microsystem technology. Full article
(This article belongs to the Special Issue New Design and Applications for Magnetoelastic Actuators)
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<p>Schematic view of the “magnetic capacitor” excitation system. The arrows show the direction of the current in the electrodes.</p>
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<p>Spatial distribution of the electric current density in the upper electrode of “magnetic capacitor” for <span class="html-italic">I</span> = 100 mA.</p>
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<p>Spatial distribution of the magnetic field <span class="html-italic">h</span><sub>y</sub> inside the “magnetic capacitor” for <span class="html-italic">I</span> = 100 mA and z = 0.</p>
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<p>Distribution of the magnetic field <span class="html-italic">h</span><sub>y</sub> along the length inside the “magnetic capacitor” for <span class="html-italic">I</span> = 100 mA and <span class="html-italic">z</span> = 0.</p>
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<p>Distribution of the magnetic field <span class="html-italic">h</span><sub>y</sub> along the width inside the “magnetic capacitor” for <span class="html-italic">I</span> = 100 mA and <span class="html-italic">z</span> = 0.</p>
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<p>Current density distribution over the width of the Cu electrode for different current frequencies <span class="html-italic">f</span> from 1 MHz to 100 MHz.</p>
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<p>Current density distribution over the thickness of the Cu electrode for different current frequencies <span class="html-italic">f</span> from 1 MHz to 100 MHz.</p>
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<p>The block diagram of the experimental set-up for the ME effect investigation under coil-free excitation.</p>
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<p>Schematic view of the Metglas/PZT heterostructure excited by a strip with ac current <span class="html-italic">I</span>. The arrows show directions of electric <span class="html-italic">E</span> and magnetic <span class="html-italic">H</span> fields.</p>
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<p>Dependence of ME voltage <span class="html-italic">u</span> on the frequency <span class="html-italic">f</span> upon excitation of a Metglas/PZT structure by a strip with a current (1) and by a volumetric coil (2) at <span class="html-italic">H</span> = 5 Oe.</p>
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<p>Dependence of ME voltage <span class="html-italic">u</span><sub>1</sub> on the field <span class="html-italic">H</span> under the structure excitation at resonance frequency by a strip with a current (1) and a volumetric coil (2).</p>
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<p>Schematic view of a Metglas/PZT/Metglas heterostructure placed inside the “magnetic capacitor”. The arrows show directions of electric <span class="html-italic">E</span> and magnetic <span class="html-italic">H</span> fields.</p>
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<p>Measured distributions of excitation field <span class="html-italic">h</span><sub>y</sub> along and across the direction of the current in a “magnetic capacitor” for <span class="html-italic">I</span> = 80 mA. Curve along “<span class="html-italic">x</span>” is for <span class="html-italic">y</span> = 0 and <span class="html-italic">z</span> = 0, and curve along “<span class="html-italic">y</span>” is for <span class="html-italic">x</span> = 0 and <span class="html-italic">z</span> = 0.</p>
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<p>Dependence of ME voltage u on the frequency <span class="html-italic">f</span> of the excitation current for the Metglas/PZT/Metglas heterostructure, placed in a “magnetic capacitor”.</p>
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<p>Dependence of ME voltage <span class="html-italic">u</span> on the magnetic field <span class="html-italic">H</span> for the Metglas/PZT/Metglas heterostructure placed in a “magnetic capacitor”.</p>
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<p>Schematic view of a Cu/Metglas-PZT-Metglas/Cu heterostructure with integrated “magnetic capacitor” excitation system. The arrows show directions of electric <span class="html-italic">E</span> and magnetic <span class="html-italic">H</span> fields.</p>
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<p>Characteristics of a monolithic Cu-Metglas/PZT/Metglas-Cu structure with integrated excitation system at <span class="html-italic">H</span> ┴ <span class="html-italic">I</span>; (<b>a</b>) ME voltage <span class="html-italic">u</span> vs. frequency <span class="html-italic">f</span> for <span class="html-italic">H</span> = 134 Oe; (<b>b</b>) ME voltage <span class="html-italic">u</span><sub>1</sub> vs. field <span class="html-italic">H</span> for <span class="html-italic">f</span> = 73.3 kHz.</p>
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<p>Characteristics of a monolithic Cu-Metglas/PZT/Metglas-Cu structure with integrated excitation system at <span class="html-italic">H</span>//<span class="html-italic">I</span>; (<b>a</b>) ME voltage <span class="html-italic">u</span> vs. frequency <span class="html-italic">f</span> for <span class="html-italic">H</span> = 20 Oe; (<b>b</b>) ME voltage <span class="html-italic">u</span> vs. field <span class="html-italic">H</span> for <span class="html-italic">f</span> = 73.3 kHz.</p>
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<p>Schematic view of a monolithic Cu/Metglas-PZT-Metglas/Cu heterostructure with an integrated “magnetic capacitor” excitation system. The arrows show directions of electric <span class="html-italic">E</span> and magnetic <span class="html-italic">H</span> fields.</p>
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<p>Dependence of the ME voltage <span class="html-italic">u</span> on the excitation current frequency <span class="html-italic">f</span> for the Cu/Metglas-PZT-Metglas/Cu heterostructure at <span class="html-italic">H</span> = 25 Oe.</p>
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<p>Dependence of the ME voltage <span class="html-italic">u</span><sub>1</sub> on the field <span class="html-italic">H</span> for the Cu/Metglas-PZT-Metglas/Cu heterostructure at frequency <span class="html-italic">f</span><sub>1</sub>.</p>
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<p>Schematic view of a Cu/NZFO/Cu-PZT heterostructure with integrated excitation system. The arrows show directions of electric <span class="html-italic">E</span> and magnetic <span class="html-italic">H</span> fields.</p>
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<p>Dependence of ME voltage <span class="html-italic">u</span> on the current frequency <span class="html-italic">f</span> for a monolithic Cu/NZFO/Cu-PZT heterostructure with an integrated excitation system at <span class="html-italic">I</span> = 0.1 A and <span class="html-italic">H</span> = 95 Oe.</p>
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<p>Dependence of ME voltage <span class="html-italic">u</span> on the field <span class="html-italic">H</span> for a monolithic Cu/NZFO/Cu-PZT heterostructure with integrated excitation system at a frequency <span class="html-italic">f</span><sub>1</sub>.</p>
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<p>Schematic view of a FeBSiC/PZT heterostructure upon excitation of the ME effect by alternating current flowing through the FM layer. The arrows show directions of electric <span class="html-italic">E</span> and magnetic <span class="html-italic">H</span> fields.</p>
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<p>Dependence of ME voltage <span class="html-italic">u</span> on the current frequency <span class="html-italic">f</span> for the Metglas/PZT heterostructure excited by a current flowing through the Metglas layer.</p>
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<p>Dependences of ME voltage <span class="html-italic">u</span> on the field <span class="html-italic">H</span> and excitation field <span class="html-italic">h</span> for the Metglas/PZT heterostructure excited by a current flowing through the Metglas layer.</p>
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22 pages, 2093 KiB  
Article
Interval Type-2 Fuzzy Dynamic High Type Control of Permanent Magnet Synchronous Motor with Vector Decoupling Method
by Xinglong Chen, Wei Tong, Yao Mao and Tao Zhao
Actuators 2021, 10(11), 293; https://doi.org/10.3390/act10110293 - 2 Nov 2021
Cited by 4 | Viewed by 2431
Abstract
This paper presents an interval type-2 fuzzy dynamic high type (IT2FDHT) control based on vector decoupling method for permanent magnet synchronous motor (PMSM) to improve the dynamic characteristics of the system. Firstly, to address the shortcomings of the traditional PI regulator used in [...] Read more.
This paper presents an interval type-2 fuzzy dynamic high type (IT2FDHT) control based on vector decoupling method for permanent magnet synchronous motor (PMSM) to improve the dynamic characteristics of the system. Firstly, to address the shortcomings of the traditional PI regulator used in the current loop of PMSM, an improved PI regulator based on voltage feed-forward decoupling is used. Then, considering the characteristics that the higher the system type, the smaller the steady-state error and the shorter the regulation time, the high type control structure is added. However, a purely high type structure amplifies the oscillations of the system and is extremely sensitive to perturbations, which can easily lead to system divergence. Therefore, in order to solve the problems caused by high type structure, finally we designed dynamic high type control with the help of fuzzy logic systems (FLSs), which successfully achieved automatic switching of system type while improving response speed and steady-state accuracy. Meanwhile, quantum-behaved particle swarm optimization (QPSO) algorithm is employed to determine the parameters of FLSs. In summary, five methods including conventional PI, feed-forward decoupling PI (FDPI), FDPI high type (FDPI-HT), FDPI type-1 fuzzy dynamic high type (FDPI-T1FDHT), and FDPI-IT2FDHT, are compared to show the superiority of the proposed method. By means of simulations, the excellence of proposed FDPI-IT2FDHT is verified. Full article
(This article belongs to the Section Control Systems)
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<p>Structure of the PMSM vector control system.</p>
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<p>Current closed-loop control block diagram.</p>
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<p>Structure of the voltage feed-forward decoupling PI.</p>
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<p>Structure of HT based on feed-forward decoupling PI.</p>
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<p>Comparison of HT control effect.</p>
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<p>Structure diagram of a T1FLS.</p>
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<p>Structure of FDHT based on feed-forward decoupling PI.</p>
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<p>MFs of input and output variables. (<b>a</b>) MFs of input variable <span class="html-italic">E</span>; (<b>b</b>) MFs of input variable <math display="inline"><semantics> <mrow> <mi>E</mi> <mi>C</mi> </mrow> </semantics></math>; (<b>c</b>) MFs of output variable <span class="html-italic">U</span>.</p>
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<p>Structure diagram of an IT2FLS.</p>
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<p>MFs of input variables in the IT2FLS. (<b>a</b>) MFs of input variable <span class="html-italic">E</span>; (<b>b</b>) MFs of input variable <math display="inline"><semantics> <mrow> <mi>E</mi> <mi>C</mi> </mrow> </semantics></math>.</p>
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<p>Structure of the PMSM vector control system applying FDPI-FDHT.</p>
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<p>Motor speed tracking results under no-load situation.</p>
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<p>Electromagnetic torque response results in the no-load case.</p>
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<p>Motor speed tracking results under load situation.</p>
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<p>Electromagnetic torque response results in the load case.</p>
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<p>Voltage responses of <math display="inline"><semantics> <msub> <mi>u</mi> <mi>d</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>u</mi> <mi>q</mi> </msub> </semantics></math>. (<b>a</b>) PI; (<b>b</b>) FDPI; (<b>c</b>) FDPI-HT; (<b>d</b>) FDPI-T1FDHT; (<b>e</b>) FDPI-IT2FDHT.</p>
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<p>Three-phase current variation curves. (<b>a</b>) PI; (<b>b</b>) FDPI; (<b>c</b>) FDPI-HT; (<b>d</b>) FDPI-T1FDHT; (<b>e</b>) FDPI-IT2FDHT.</p>
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<p>Current variation of Ia, Ib and Ic. (<b>a</b>) Ia; (<b>b</b>) Ib; (<b>c</b>) Ic.</p>
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9 pages, 1951 KiB  
Communication
Design of Four-DoF Compliant Parallel Manipulators Considering Maximum Kinematic Decoupling for Fast Steering Mirrors
by Guangbo Hao, Haiyang Li, Yu-Hao Chang and Chien-Sheng Liu
Actuators 2021, 10(11), 292; https://doi.org/10.3390/act10110292 - 1 Nov 2021
Cited by 5 | Viewed by 2362
Abstract
Laser beams can fluctuate in four directions, which requires active compensation by a fast steering mirror (FSM) motion system. This paper deals with the design of four-degrees-of-freedom (DoF) compliant parallel manipulators, for responding to the requirements of the FSM. In order to simplify [...] Read more.
Laser beams can fluctuate in four directions, which requires active compensation by a fast steering mirror (FSM) motion system. This paper deals with the design of four-degrees-of-freedom (DoF) compliant parallel manipulators, for responding to the requirements of the FSM. In order to simplify high-precision control in parallel manipulators, maximum kinematic decoupling is always desired. A constraint map method is used to propose the four required DoF with the consideration of maximum kinematic decoupling. A specific compliant mechanism is presented based on the constraint map, and its kinematics is estimated analytically. Finite element analysis demonstrates the desired qualitative motion and provides some initial quantitative analysis. A normalization-based compliance matrix is finally derived to verify and demonstrate the mobility of the system clearly. In a case study, the results of normalization-based compliance matrix modelling show that the diagonal entries corresponding to the four DoF directions are about 10 times larger than those corresponding to the two-constraint directions, validating the desired mobility. Full article
(This article belongs to the Special Issue Design and Application of Actuators with Multi-DOF Movement)
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<p>A basic constraint map considering maximum kinematic decoupling.</p>
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<p>Interconnection of input stages.</p>
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<p>Two examples of interconnection constraints.</p>
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<p>A 4-DoF compliant parallel manipulator.</p>
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<p>Simulation results and the prototype of the proposed 4-DoF compliant parallel manipulator: (<b>a</b>) translational case: <span class="html-italic">X</span><sub>I</sub> = <span class="html-italic">X</span><sub>II</sub> = 1mm, <span class="html-italic">Y</span><sub>I</sub> = <span class="html-italic">Y</span><sub>II</sub> = 0, (<b>b</b>) rotational case: <span class="html-italic">X</span><sub>I</sub> = 1mm, <span class="html-italic">X</span><sub>II</sub> = <span class="html-italic">Y</span><sub>I</sub> = <span class="html-italic">Y</span><sub>II</sub> = 0, and (<b>c</b>) 3D-printed prototype.</p>
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<p>Simulation results and the prototype of the proposed 4-DoF compliant parallel manipulator: (<b>a</b>) translational case: <span class="html-italic">X</span><sub>I</sub> = <span class="html-italic">X</span><sub>II</sub> = 1mm, <span class="html-italic">Y</span><sub>I</sub> = <span class="html-italic">Y</span><sub>II</sub> = 0, (<b>b</b>) rotational case: <span class="html-italic">X</span><sub>I</sub> = 1mm, <span class="html-italic">X</span><sub>II</sub> = <span class="html-italic">Y</span><sub>I</sub> = <span class="html-italic">Y</span><sub>II</sub> = 0, and (<b>c</b>) 3D-printed prototype.</p>
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20 pages, 11019 KiB  
Article
An Extended Model for Ripple Analysis of 2–4 Phase Resonant Electrostatic Induction Motors
by Fernando Carneiro, Guangwei Zhang, Masahiko Osada, Shunsuke Yoshimoto and Akio Yamamoto
Actuators 2021, 10(11), 291; https://doi.org/10.3390/act10110291 - 29 Oct 2021
Cited by 2 | Viewed by 2361
Abstract
Electrostatic motors are promising forms of actuation for future robotic devices. The study of their different implementations should accelerate their adoption. Current models for resonant electrostatic induction motors were found not to be able to properly describe their behavior, namely, with regard to [...] Read more.
Electrostatic motors are promising forms of actuation for future robotic devices. The study of their different implementations should accelerate their adoption. Current models for resonant electrostatic induction motors were found not to be able to properly describe their behavior, namely, with regard to changes with position. This paper reports a new analytical model for these motors, aiming to address this issue. The model is based on identification of all capacitance harmonics, through a simplified method. Using these, equations for different motor parameters, notably, thrust force, were obtained and compared to previous literature. The new equations model position dependent properties, such as force ripple. The outputs of this model were validated through experimentation with a prototype, with the results confirming the new model better describes motor behavior. An analysis into how to decrease this ripple was also discussed and tested. We concluded that the use of a higher number of harmonics resulted in a much more accurate model, capable of adequately characterizing motor outputs with changes in position. Full article
(This article belongs to the Section Precision Actuators)
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<p>Schematic images of the 2–4 phase resonant electrostatic induction motor: (<b>a</b>) the general layout of the films; (<b>b</b>) their typical arrangement, external circuit components and working principle; and (<b>c</b>) a more detailed section view with identification of the discrete capacitive elements (designations are the ones introduced in this paper).</p>
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<p>Capacitance versus displacement, for different elements of the capacitance matrix (indices indicate position within the matrix).</p>
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<p>Comparison of the voltage amplitude output, as a function of displacement, between the newly proposed equation and the one reported in [<a href="#B28-actuators-10-00291" class="html-bibr">28</a>].</p>
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<p>Comparison of the thrust force output, as a function of displacement, between the newly proposed equation and the one reported in [<a href="#B28-actuators-10-00291" class="html-bibr">28</a>].</p>
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<p>Model thrust force output throughout one displacement period, considering different force harmonic components. The coefficient <math display="inline"><semantics> <msub> <mi>k</mi> <mi>n</mi> </msub> </semantics></math> represents the amplitude of each harmonic, as per (<a href="#FD25-actuators-10-00291" class="html-disp-formula">25</a>). The average value of <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo form="prefix">sin</mo> <mfenced separators="" open="(" close=")"> <msub> <mi>ϕ</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>x</mi> </msub> <mo>)</mo> </mrow> </mfenced> </mrow> </semantics></math> is defined as <math display="inline"><semantics> <msub> <mi>F</mi> <mn>0</mn> </msub> </semantics></math>, which is equal to <math display="inline"><semantics> <msub> <mi>k</mi> <mn>1</mn> </msub> </semantics></math> and is approximately 1.4 N.</p>
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<p>Voltage amplitude ratio and <math display="inline"><semantics> <mrow> <mo>%</mo> <msub> <mi>F</mi> <mrow> <mi>r</mi> <mi>p</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> as a function of resistance with resistance (in the range of 10 to 5000 Ω), for the considered model parameters. <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>s</mi> <mi>l</mi> </mrow> </msub> </semantics></math> was calculated for <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>x</mi> </msub> <mo>=</mo> <mi>π</mi> <mspace width="-1.111pt"/> <mo>/</mo> <mspace width="-0.55542pt"/> <mn>8</mn> </mrow> </semantics></math>, for which its value is maximum.</p>
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<p>Experimental setup used for force measurement. (<b>a</b>) Prototype motor and load cell assembly. (<b>b</b>) Pictures of the used films, highlighting the electrode structure.</p>
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<p>Main force and voltage measurement results and comparison to the two model implementations: (i), using measured inductance values and (ii), using “optimized” inductance values. (<b>a</b>) Using only the inductor (R ≈ 305 Ω). (<b>b</b>) With external resistance connected in series (R ≈ 804 Ω). (<b>c</b>) With external resistance connected in series (R ≈ 1918 Ω). Model (ii) was not generated for this set of results. Results using past model included for comparison.</p>
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<p>Main force and voltage measurement results and comparison to the two model implementations: (i), using measured inductance values and (ii), using “optimized” inductance values. (<b>a</b>) Using only the inductor (R ≈ 305 Ω). (<b>b</b>) With external resistance connected in series (R ≈ 804 Ω). (<b>c</b>) With external resistance connected in series (R ≈ 1918 Ω). Model (ii) was not generated for this set of results. Results using past model included for comparison.</p>
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<p>Force ripple measurements compared to values obtained from the model under different conditions.</p>
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<p>Relative error for both model parameter sets on the performed experiments. Error relative to past model also presented for experiment (c). Cyan-colored lines indicate <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>5</mn> <mo>%</mo> </mrow> </semantics></math> error.</p>
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<p>Comparison of mean force output against inductance, considering different sets of model parameters.</p>
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19 pages, 46634 KiB  
Article
Design and Assist-as-Needed Control of Flexible Elbow Exoskeleton Actuated by Nonlinear Series Elastic Cable Driven Mechanism
by Bingshan Hu, Fuchao Zhang, Hongrun Lu, Huaiwu Zou, Jiantao Yang and Hongliu Yu
Actuators 2021, 10(11), 290; https://doi.org/10.3390/act10110290 - 29 Oct 2021
Cited by 15 | Viewed by 3917
Abstract
Exoskeletons can assist the daily life activities of the elderly with weakened muscle strength, but traditional rigid exoskeletons bring parasitic torque to the human joints and easily disturbs the natural movement of the wearer’s upper limbs. Flexible exoskeletons have more natural human-machine interaction, [...] Read more.
Exoskeletons can assist the daily life activities of the elderly with weakened muscle strength, but traditional rigid exoskeletons bring parasitic torque to the human joints and easily disturbs the natural movement of the wearer’s upper limbs. Flexible exoskeletons have more natural human-machine interaction, lower weight and cost, and have great application potential. Applying assist force according to the patient’s needs can give full play to the wearer’s remaining muscle strength, which is more conducive to muscle strength training and motor function recovery. In this paper, a design scheme of an elbow exoskeleton driven by flexible antagonistic cable actuators is proposed. The cable actuator is driven by a nonlinear series elastic mechanism, in which the elastic elements simulate the passive elastic properties of human skeletal muscle. Based on an improved elbow musculoskeletal model, the assist torque of exoskeleton is predicted. An assist-as-needed (AAN) control algorithm is proposed for the exoskeleton and experiments are carried out. The experimental results on the experimental platform show that the root mean square error between the predicted assist torque and the actual assist torque is 0.00226 Nm. The wearing experimental results also show that the AAN control method designed in this paper can reduce the activation of biceps brachii effectively when the exoskeleton assist level increases. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Schematic diagram of cable driven flexible exoskeleton. (<b>a</b>) Overall structure diagram. (<b>b</b>) Schematic diagram of actuating control box.</p>
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<p>Schematic diagram of cable driven flexible exoskeleton. (<b>a</b>) Overall structure diagram. (<b>b</b>) Schematic diagram of actuating control box.</p>
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<p>Nonlinear series elastic cable drive mechanism. (<b>a</b>) Physical drawing. (<b>b</b>) Sectional drawing.</p>
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<p>Passive contraction force of skeletal muscle (Long head of biceps brachii) and its fitting. Muscle fiber contraction length = 0 means that the muscle is at rest (that is, the elbow flexion is about 60 degrees).</p>
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<p>Force analysis of cable SEA mechanism.</p>
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<p>Assist-as-needed control system block diagram.</p>
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<p>Schematic diagram of improved elbow joint musculoskeletal model.</p>
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<p>Prediction of elbow muscle torque based on musculoskeletal model.</p>
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<p>The geometric analysis diagram of flexible exoskeleton.</p>
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<p>Force arm and force of flexion assist cable actuator. (<b>a</b>) Force arm. (<b>b</b>) Force on the flexion cable actuator.</p>
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<p>Tension control block diagram. (<b>a</b>) Cascade controller of the nonlinear cable SEA. (<b>b</b>) Motor control block diagram.</p>
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<p>Schematic diagram of experimental platform. 1, extension side cable SEA; 2, flexion side cable SEA; 3, signal converter of tension sensor; 4, tension sensor; 5, cable sheath; 6, cable at drive end; 7, angle sensor; 8, rotating disk; 9, torque sensor; 10, load arm; 11, motor driver.</p>
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<p>Design of rotating disk for simulating flexion and extension assist force arm.</p>
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<p>The sinusoidal force command following experimental results. (<b>a</b>) Sinusoidal command tracking curve. (<b>b</b>) Sinusoidal command tracking error curve.</p>
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<p>The related muscle activation obtained by OpenSim.</p>
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<p>Predicted elbow muscle torque.</p>
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<p>Exoskeleton assist torque control of elbow joint.</p>
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<p>Assist force control experiment of antagonistic cable actuator. (<b>a</b>) Flexion side. (<b>b</b>) Extension side.</p>
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<p>Assist force control experiment of antagonistic cable actuator. (<b>a</b>) Flexion side. (<b>b</b>) Extension side.</p>
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<p>Flexible exoskeleton wearing experiment. (<b>a</b>) Extension state. (<b>b</b>) Flexion state.</p>
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<p>Comparison of activation of surface EMG signal of biceps brachii activation.</p>
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<p>Hill muscle model.</p>
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19 pages, 50723 KiB  
Article
SMARCOS: Off-the-Shelf Smart Compliant Actuators for Human–Robot Applications
by Vincent Ducastel, Kevin Langlois, Marco Rossini, Victor Grosu, Bram Vanderborght, Dirk Lefeber, Tom Verstraten and Joost Geeroms
Actuators 2021, 10(11), 289; https://doi.org/10.3390/act10110289 - 27 Oct 2021
Cited by 4 | Viewed by 4012
Abstract
With the growing popularity of Human–Robot Interactions, a series of robotic assistive devices have been created over the last decades. However, due to the lack of easily integrable resources, the development of these custom made devices turns out to be long and expensive. [...] Read more.
With the growing popularity of Human–Robot Interactions, a series of robotic assistive devices have been created over the last decades. However, due to the lack of easily integrable resources, the development of these custom made devices turns out to be long and expensive. Therefore, the SMARCOS, a novel off-the-shelf Smart Variable Stiffness Actuator for human-centered robotic applications is proposed in this paper. This modular actuator combines compliant elements and sensors as well as low-level controller and high-bandwidth communication. The characterisation of the actuator is presented in this manuscript, followed by two use-cases wherein the benefits of such technology can be truly exploited. The actuator provides a lightweight design that can serve as the building blocks to facilitate the development of robotic applications. Full article
(This article belongs to the Special Issue Advanced Robots: Design, Control and Application)
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<p>Schematic drawing of the spindle-driven MACCEPA principle with its parameters. The input link (grey) is usually the fixed one and therefore serves as a reference for the angular positions of the output arm (blue) and lever arm (orange), <math display="inline"><semantics> <mi>ϑ</mi> </semantics></math> and <math display="inline"><semantics> <mi>φ</mi> </semantics></math>, respectively. The latter two are connected through an elastic element (spring <span class="html-italic">K</span>). The motor actuates the lever arm through a spindle drive, therefore creating a deflection angle (<math display="inline"><semantics> <mi>α</mi> </semantics></math>) between the lever arm and the output arm. As a result, the spring is compressed, generating a torque around the output link rotation axis. Such a torque pulls the output arm back to its new equilibrium position, aligned with the lever arm (<math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>). The stiffness of the actuator can be tuned by adjusting the pre-compression of the spring <span class="html-italic">P</span>.</p>
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<p>(<b>a</b>) Front view of the SMARCOS (at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>). In this position, the hard stop 1 pushes on the motor cage to prevent the lever arm to run into the spindle and the ball-screw nut to run into the motor-spindle combination. (<b>b</b>) Top view of the SMARCOS (at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>). (<b>c</b>) Front view of the SMARCOS. Without electronics and cover, the actuator weighs 1.4 kg.</p>
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<p>Cross-section view of the SMARCOS presenting the two pre-tension mechanisms of the <span class="html-italic">Dyneema</span> rope (in orange). A first pre-tension screw, situated in the output connector, is used to tension the rope during the assembly, and for the rough tensioning of the cable. Next to this, a second pre-tension screw, which acts on the rope by pulling it with a barrel nut, is used for fine pretension changes.</p>
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<p>(<b>a</b>) Front view of the SMARCOS with cover (at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>104</mn> </mrow> </semantics></math>°). In this position, the hard stop 2 pushes on the input arms to prevent the lever arms from exceeding their operating range of motion. The cover shutter is pulled by the output arm covers to isolate the ball-screw from the external world. The height (<span class="html-italic">h</span>) of the actuator is increased by its cover due to the included electronics. Electronics and covers included, the actuator weighs 1.7 kg. (<b>b</b>) Isometric view of the SMARCOS with cover (at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>). The output arm covers push on the cover shutter to retract it in the input arm covers. (<b>c</b>) Top view of the SMARCOS with cover (at <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>). With a size of 70 × 55 mm, the electronics can be stored under the actuator without increasing the overall width, which is therefore the same as the one without covers (cf. <a href="#actuators-10-00289-f002" class="html-fig">Figure 2</a>).</p>
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<p>Cross-section view of the SMARCOS presenting the disposition of the encoders. For sake of compactness, the encoders are situated in the heart of the actuator. The rotation joint is split into two axes. On one side the axis is rotating together with the output arm, whereas on the other side, it is attached to the lever arm.</p>
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<p>Calibration of the strain gauges used to estimate the output torque generated by the SMARCOS. A linear regression (in orange) was applied to the gathered data (in grey). A coefficient of determination (<math display="inline"><semantics> <msup> <mi>R</mi> <mn>2</mn> </msup> </semantics></math>) of 0.995 suggests a good match between the model and the data. For sake of validation, the distribution of the residuals was also analysed. The symmetry around the origin and the absence of extreme value points confirm the validity of the model.</p>
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<p>Comparison of the output torque obtained from the strain gauges and from the current with the one measured by the torque sensor. The results obtained from the current tend to overestimate the output torque generated, since it does not include the losses of the actuator. A linear regression can be applied to it, to have a better match with the torques measured by the sensor and by the strain gauges.</p>
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<p>Low-level control module included in SMARCOS. The board allows connection to a wide variety of sensors/encoders through the different communication ports listed in the Figure. The control of a (BL)DC motor is possible with the optional interfacing of a Maxon ESCON 50/5 power module. For more versatility, the board is EtherCAT compatible.</p>
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<p>Test-bench used for the characterisation of the SMARCOS. For the quasi-static experiments, the output arm of the actuator is mechanically grounded to the aluminium cage through a torque sensor. The position encoders and the strain gauges are read by the SMARCOS electronics board.</p>
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<p>Torque-deflection characteristics of the SMARCOS. The points correspond to the experimental data collected for different levels of spring pre-compression (light blue represents low pre-compression, dark blue is for higher pre-compression). The corresponding theoretical curves of the MACCEPA model are represented by the dotted lines. There is a good match between the data points and the model lines, except for the hysteresis phenomenon, which is not present in the model.</p>
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<p>Quasi-stiffness characteristics of the SMARCOS obtained by numerical differentiation of the curves shown in <a href="#actuators-10-00289-f010" class="html-fig">Figure 10</a>. At maximal deflection, the torque value drops when passing from loading to unloading, whereas the deflection angle remains locally constant. This causes infinite slopes in the quasi-stiffness curves, which are represented by the vertical lines at maximal deflection. The full lines correspond to 2nd order regression fitted on the experimental data.</p>
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<p>Position step responses for different spring pre-compression levels in no-load conditions. This test is realised in order to estimate the maximum speed of the actuator. This is done through numerical derivation, and leads to a value of 500°/s for each curve.</p>
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<p>Upper-limb rehabilitation prototype built with two SMARCOS. The device can provide assistance with a variable stiffness configuration to adapt to the needs of the subject. The device is easy to assemble/disassemble to facilitate transportation. The system only requires a table to be clamped to, and a computer to acquire the data, as pictured in <a href="#actuators-10-00289-f014" class="html-fig">Figure 14</a>.</p>
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<p>Picture of the upper-body rehabilitation device in use. The user is performing his exercises by playing a game in which he has to pick up apples in a tree and drop them in a basket. The cursor on the computer is controlled by the rotation of the links measured by the encoders inside the SMARCOS. For the sake of clarity, a screen capture of the game is shown in this Figure. During this test, the subject was looking at a projection on a wall, as can be seen in the video of the experiment.</p>
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<p>Menu of the game where the user can choose among four different game scenarios. The possible game modes are “vertical motion”, “horizontal motion”, ’limited time” and “evaluation”. The level corresponds to the number of objects the patient will have to catch. The size of the targets can be chosen between “small”, “medium” and “large”.</p>
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<p>Block-diagram of the cascade controller used for the SMARCOS prototypes. The output torque is measured by the strain gauges and the torque error is fed into a PID controller, which converts it into a motor velocity reference for the inner loop. The latter is a low-level velocity control available within the Maxon ESCON module plug in the SMARCOS LLC.</p>
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<p>Zero-torque controller realised with the SMARCOS. The output arm is actuated over the whole range of motion while the output torque remains contained between [−1;1] Nm. The controller helps the user to overcome the back-driving torque of the actuator given in <a href="#actuators-10-00289-t002" class="html-table">Table 2</a>.</p>
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<p>Force-field controller realised with the SMARCOS. This corresponds to a variant of the zero-torque controller shown in <a href="#actuators-10-00289-f017" class="html-fig">Figure 17</a>, where an offset is applied. The output torque oscillates around the targeted value of −2 Nm.</p>
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<p>Impedance controller realised with the SMARCOS. The controller simulates a spring of stiffness 0.4 Nm/deg, acting around the centre point of the ball-screw axis, which corresponds to approximately <math display="inline"><semantics> <mrow> <mi>ϑ</mi> <mo>=</mo> <mn>50</mn> </mrow> </semantics></math>°.</p>
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<p>Prototype of an assistive knee orthosis developed with the SMARCOS. The actuator is rigidly interfaced with two generic cuffs in order to be attached to the human body.</p>
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24 pages, 3704 KiB  
Article
Chattering-Suppressed Sliding Mode Control for Flexible-Joint Robot Manipulators
by Xin Cheng, Huashan Liu and Wenke Lu
Actuators 2021, 10(11), 288; https://doi.org/10.3390/act10110288 - 27 Oct 2021
Cited by 29 | Viewed by 3338
Abstract
In this paper, sliding mode tracking control and its chattering suppression method are investigated for flexible-joint robot manipulators with only state measurements of joint actuators. First, within the framework of singular perturbation theory, the control objective of the system is decoupled into two [...] Read more.
In this paper, sliding mode tracking control and its chattering suppression method are investigated for flexible-joint robot manipulators with only state measurements of joint actuators. First, within the framework of singular perturbation theory, the control objective of the system is decoupled into two typical tracking aims of a slow subsystem and a fast subsystem. Then, considering lumped uncertainties (including dynamics uncertainties and external disturbances), a composite chattering-suppressed sliding mode controller is proposed, where a smooth-saturation-function-contained reaching law with adjustable saturation factor is designed to alleviate the inherent chattering phenomenon, and a radial basis function neural network (RBFNN)-based soft computing strategy is applied to avoid the high switching gain that leads to chattering amplification. Simultaneously, an efficient extended Kalman filter (EKF) with respect to a new state variable is presented to enable the closed-loop tracking control with neither position nor velocity measurements of links. In addition, an overall analysis on the asymptotic stability of the whole control system is given. Finally, numerical examples verify the superiority of the dynamic performance of the proposed control approach, which is well qualified to suppress the chattering and can effectively eliminate the undesirable effects of the lumped uncertainties with a smaller switching gain reduced by 80% in comparison to that in the controller without RBFNN. The computational efficiency of the proposed EKF increased by about 26%. Full article
(This article belongs to the Section Actuators for Robotics)
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<p>Online operational structure of the RBFNN.</p>
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<p>Block diagram of the proposed controller.</p>
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<p>Model of the flexible-joint robot manipulator.</p>
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<p>Trajectory tracking error <math display="inline"><semantics> <mi mathvariant="bold-italic">e</mi> </semantics></math>.</p>
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<p>Time history of the slow sliding surface <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mrow> <mo>_</mo> <mi mathvariant="normal">s</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Time history of the fast sliding surface <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mrow> <mo>_</mo> <mi mathvariant="normal">f</mi> </mrow> </msub> </semantics></math>.</p>
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<p>RBF compensation of torque input.</p>
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<p>Position estimated by EKF of link 1.</p>
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<p>Position estimated by EKF of link 2.</p>
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<p>Trajectory tracking error <math display="inline"><semantics> <mi mathvariant="bold-italic">e</mi> </semantics></math>.</p>
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<p>Torque control input.</p>
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<p>Trajectory tracking error <math display="inline"><semantics> <mi mathvariant="bold-italic">e</mi> </semantics></math>.</p>
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<p>Time history of the slow sliding surface <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mrow> <mo>_</mo> <mi mathvariant="normal">s</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Time history of the fast sliding surface <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">s</mi> <mrow> <mo>_</mo> <mi mathvariant="normal">f</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Torque control inputs.</p>
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20 pages, 5527 KiB  
Article
A Novel Double Redundant Brake-by-Wire System for High Automation Driving Safety: Design, Optimization and Experimental Validation
by Chao Li, Junzhi Zhang, Xiaohui Hou, Yuan Ji, Jinheng Han, Chengkun He and Jiangmai Hao
Actuators 2021, 10(11), 287; https://doi.org/10.3390/act10110287 - 26 Oct 2021
Cited by 8 | Viewed by 4431
Abstract
The high redundant brake-by-wire system reveals vehicular safety handling ability and rarely emerges in the automotive area at the present time. This paper presents a novel brake-by-wire system, DREHB (Double Redundant Electro-Hydraulic Brake), with extensible fail-safe operations for high-automation autonomous driving vehicles. The [...] Read more.
The high redundant brake-by-wire system reveals vehicular safety handling ability and rarely emerges in the automotive area at the present time. This paper presents a novel brake-by-wire system, DREHB (Double Redundant Electro-Hydraulic Brake), with extensible fail-safe operations for high-automation autonomous driving vehicles. The DREHB is designed as a decoupled-architecture system containing three-layer cascaded modules, including a hydraulic power provider, a hydraulic flow switcher, and a hydraulic pressure modulator, and each of the modules can share dual redundancy. The operating principles of the DREHB in normal and degraded initiative braking modes are introduced, especially for the consideration of fail-safe and fail-operational functions. The matching and optimization of selected key parameters of the electric boost master cylinder and the linear solenoid valve were conducted using computer-aided batched simulations with a DREHB system modeled in MATLAB/Simulink and AMESim. The prototype of the DREHB was tested in hardware-in-the-loop experiments. The test results of typical braking scenarios verify the feasibility and effectiveness of the DREHB system, and the hydraulic pressure response as 28.0 MPa/s and tracking error within 0.15 MPa and the desirable fail-safe braking ability fully meets the requirements of higher braking safety and efficiency. Full article
(This article belongs to the Section Actuators for Land Transport)
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<p>Schematic configuration diagram of the DREHB system.</p>
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<p>Normal initiative braking modes. (<b>a</b>) Braking with a sole EBMC as the hydraulic power source; (<b>b</b>) Braking with a sole EHPA as the hydraulic power source; (<b>c</b>) Braking with both an EBMC and an EHPA as the hydraulic power sources.</p>
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<p>Degraded initiative braking F1 modes. F1 represents for the braking failure type 1 in hydraulic power provider layer. (<b>a</b>) Braking with EBMC failure; (<b>b</b>) Braking with EHPA failure.</p>
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<p>Degraded initiative braking F2 modes. F2 represents for the braking failure type 2 in hydraulic flow switcher layer. (<b>a</b>) Braking with TwV failure; (<b>b</b>) Braking with FwV failure.</p>
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<p>Degraded initiative braking F3 modes. F3 represents for the braking failure type 3 in hydraulic pressure modulator layer. (<b>a</b>) Braking with CV failure; (<b>b</b>) Braking with OV failure.</p>
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<p>Dynamic model of the EBMC in AMESim.</p>
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<p>Hydraulic pressure responses on batched mechanical parameter sets of the EBMC.</p>
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<p>Coordinate system of solenoid valve.</p>
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<p>Dynamic Model of LSV in Simulink.</p>
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<p>Hydraulic pressure responses of LSVs with batched mechanical parameter sets.</p>
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<p>Electromagnetic dynamic model of the LSV.</p>
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<p>Dynamic current responses of coil in an LSV.</p>
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<p>Prototype of manufactured DREHB and HIL test platform.</p>
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<p>The test results of step wave input for the piston position.</p>
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<p>The test results of sinusoidal pressure target tracking of LSVs.</p>
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<p>The test results of comparative validation of fail-safe braking.</p>
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22 pages, 4151 KiB  
Article
Learning-Based Cooperative Adaptive Cruise Control
by Jonas Mirwald, Johannes Ultsch, Ricardo de Castro and Jonathan Brembeck
Actuators 2021, 10(11), 286; https://doi.org/10.3390/act10110286 - 26 Oct 2021
Cited by 7 | Viewed by 4147
Abstract
Traffic congestion and the occurrence of traffic accidents are problems that can be mitigated by applying cooperative adaptive cruise control (CACC). In this work, we used deep reinforcement learning for CACC and assessed its potential to outperform model-based methods. The trade-off between distance-error [...] Read more.
Traffic congestion and the occurrence of traffic accidents are problems that can be mitigated by applying cooperative adaptive cruise control (CACC). In this work, we used deep reinforcement learning for CACC and assessed its potential to outperform model-based methods. The trade-off between distance-error minimization and energy consumption minimization whilst still ensuring operational safety was investigated. Alongside a string stability condition, robustness against burst errors in communication also was incorporated, and the effect of preview information was assessed. The controllers were trained using the proximal policy optimization algorithm. A validation by comparison with a model-based controller was performed. The performance of the trained controllers was verified with respect to the mean energy consumption and the root mean squared distance error. In our evaluation scenarios, the learning-based controllers reduced energy consumption in comparison to the model-based controller by 17.9% on average. Full article
(This article belongs to the Special Issue Vehicle Modeling and Control)
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<p>Platooning linear model with information flow [<a href="#B26-actuators-10-00286" class="html-bibr">26</a>].</p>
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<p>Block diagram of the environment.</p>
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<p>Agent-environment interaction in a Markov decision process [<a href="#B5-actuators-10-00286" class="html-bibr">5</a>].</p>
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<p>Average return and standard error for multiple runs of the EM-RL (<b>a</b>) and PM-RL (<b>b</b>) reward function parametrization.</p>
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<p>Velocity <math display="inline"><semantics> <mi>v</mi> </semantics></math> of the leader vehicle, as well as the follower vehicle (<b>a</b>). The velocity of the latter was created by mb-PDFF, P-EM-RL, and P-PM-RL; the respective distance errors <math display="inline"><semantics> <mrow> <mi>e</mi> <mo>=</mo> <msub> <mi>e</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </semantics></math> are shown in (<b>b</b>).</p>
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<p>Control value <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>=</mo> <msub> <mi>u</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </semantics></math> with respective string-stability limit, created by mb-PDFF, P-EM-RL, and P-PM-RL. The time interval from 60 s to 80 s of the simulation with a total length of 120 s is shown.</p>
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<p>Platoon consisting of three agent-controlled vehicles and a leader vehicle. (<b>a</b>,<b>b</b>) show the velocities <math display="inline"><semantics> <mi>v</mi> </semantics></math> and the respective distance errors <math display="inline"><semantics> <mi>e</mi> </semantics></math> in case the follower vehicles were P-EM-RL-controlled; (<b>c</b>,<b>d</b>) show <math display="inline"><semantics> <mi>v</mi> </semantics></math> and <math display="inline"><semantics> <mi>e</mi> </semantics></math> in case the follower vehicles were P-PM-RL-controlled.</p>
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0 pages, 3359 KiB  
Article
RETRACTED: A Closed-Loop Control Mathematical Model for Photovoltaic-Electrostatic Hybrid Actuator with a Slant Lower Electrode Based on PLZT Ceramic
by Zhen Lv, Muhammad Uzair, Xinjie Wang and Yafeng Liu
Actuators 2021, 10(11), 285; https://doi.org/10.3390/act10110285 - 25 Oct 2021
Cited by 3 | Viewed by 2272 | Retraction
Abstract
In this paper, a novel photovoltaic-electrostatic hybrid actuator with a slant lower electrode based on the PLZT ceramic is proposed. The mathematical model of photovoltaic-electrostatic hybrid actuator is established. Then, based on the mathematical model of photovoltaic-electrostatic hybrid actuator and the parameters identified, [...] Read more.
In this paper, a novel photovoltaic-electrostatic hybrid actuator with a slant lower electrode based on the PLZT ceramic is proposed. The mathematical model of photovoltaic-electrostatic hybrid actuator is established. Then, based on the mathematical model of photovoltaic-electrostatic hybrid actuator and the parameters identified, the mathematical simulation of the closed-loop displacement control for the photovoltaic-electrostatic hybrid actuator based on the PLZT ceramic is carried out. The results show that the displacement of the actuator can be controlled successfully at a particular value within the pull-in displacement by the light source. Furthermore, the response speed of the output displacement for photovoltaic-electrostatic hybrid actuator with a slant lower electrode is faster than that with a parallel lower electrode, offering a good potential to advance the current applications on micro-electro-mechanical system. Full article
(This article belongs to the Special Issue Miniature and Micro-Actuators)
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<p>Schematic diagram of the photovoltaic-electrostatic hybrid actuator with a slant lower electrode. (<b>a</b>) The structure parameters of the actuator. (<b>b</b>) Force condition of the actuator.</p>
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<p>The coupling relationship of opto-electric-thermo-mechanic fields of PLZT ceramic.</p>
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<p>Time history of the photovoltage of PLZT under irradiation of different light intensities.</p>
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<p>The experimental and fitting curves of the photovoltage of PLZT ceramic under irradiation of different light intensities. (<b>a</b>) Light intensity is 20 mW/cm<sup>2</sup>. (<b>b</b>) Light intensity is 40 mW/cm<sup>2</sup>. (<b>c</b>) Light intensity is 60 mW/cm<sup>2</sup>.</p>
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<p>The flow sheet for the closed-loop displacement control of the hybrid actuator.</p>
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<p>Relation between displacement of upper electrode tip and torque under different driving voltage.</p>
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<p>The closed-loop control simulation curve of photovoltaic-electrostatic hybrid actuator illuminated by light intensity of 20 mW/cm<sup>2</sup>. (<b>a</b>) Time history of displacement. (<b>b</b>) Time history of photovoltage.</p>
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<p>The closed-loop control simulation curve of photovoltaic-electrostatic hybrid actuator illuminated by light intensity of 40 mW/cm<sup>2</sup>. (<b>a</b>) Time history of displacement. (<b>b</b>) Time history of photovoltage.</p>
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<p>The closed-loop control simulation curve of photovoltaic-electrostatic hybrid actuator illuminated by light intensity of 60 mW/cm<sup>2</sup>. (<b>a</b>) Time history of displacement. (<b>b</b>) Time history of photovoltage.</p>
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14 pages, 7382 KiB  
Article
Adaptive Control of Chaotic Signals: Investigated by Simulation Software and Real Electronic Circuits
by Cheng-Hsiung Yang, Che-Lun Chang and Shih-Yu Li
Actuators 2021, 10(11), 284; https://doi.org/10.3390/act10110284 - 25 Oct 2021
Cited by 1 | Viewed by 2194
Abstract
Chaotic behavior is complicated, sensitive, and has the feature of great variety, which are the most potential signals to be applied in data encryption, secure communication, medical information protection, etc. As a consequence, in this paper, we try to propose three different ways [...] Read more.
Chaotic behavior is complicated, sensitive, and has the feature of great variety, which are the most potential signals to be applied in data encryption, secure communication, medical information protection, etc. As a consequence, in this paper, we try to propose three different ways to show our data generating results step by step, which means it can be proved effectively and used in practice: (1) Chaotic solutions simulated by MATLAB, (2) chaotic motion drawn via electronic circuits software Multisim, and (3) chaotic signal implemented on real electronic circuits with breadboard. In advance, following the same design principal, the adaptive chaotic signal is also designed and presented in the end of this article for further study, which provides a more flexible and variable chaotic signal to enhance the encryption effectiveness. The experimental results are extremely close to the two simulation results and can definitely be technically transferred to real encryption application. Full article
(This article belongs to the Special Issue Actuators in Robotic Control)
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<p>A comprehensive reveal: 3-D phase portrait and its 3-axis projections of the four-dimensional Chen–Lee system.</p>
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<p>This 2-D phase portraits of the four-dimensional Chen–Lee system simulated by MATLAB: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane; (<b>e</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane; (<b>f</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane.</p>
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<p>Circuit configuration of the four-dimensional Chen–Lee system designed on Multisim.</p>
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<p>2-D phase portraits of the four-dimensional Chen–Lee system simulated by electronic circuits software Multisim: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane; (<b>e</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane; (<b>f</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane.</p>
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<p>Experimental setup for realization of the four-dimensional Chen–Lee system.</p>
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<p>Hardware configurations: real circuit of the four-order Chen–Lee system.</p>
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<p>2-D phase portraits of the four-dimensional Chen–Lee system implemented on real electronic circuits: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </semantics></math> plane; (<b>b</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane; (<b>c</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane; (<b>d</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> plane; (<b>e</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane; (<b>f</b>) <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mi>x</mi> <mn>3</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> plane.</p>
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<p>Circuit configuration of the whole adaptive electronic circuits.</p>
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<p>Circuit configuration of the master system.</p>
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<p>Circuit configuration of the slave system.</p>
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<p>Circuit configuration of the parameters update law.</p>
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<p>Circuit configuration of the controllers <span class="html-italic">u</span><sub>1</sub>, <span class="html-italic">u</span><sub>2</sub>, <span class="html-italic">u</span><sub>3</sub>, and <span class="html-italic">u</span><sub>4</sub>: (<b>a</b>) controller <span class="html-italic">u</span><sub>1</sub>; (<b>b</b>) controller <span class="html-italic">u</span><sub>2</sub>; (<b>c</b>) controller <span class="html-italic">u</span><sub>3</sub>; (<b>d</b>) controller <span class="html-italic">u</span><sub>4</sub>.</p>
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<p>Circuit configuration of the controllers <span class="html-italic">u</span><sub>1</sub>, <span class="html-italic">u</span><sub>2</sub>, <span class="html-italic">u</span><sub>3</sub>, and <span class="html-italic">u</span><sub>4</sub>: (<b>a</b>) controller <span class="html-italic">u</span><sub>1</sub>; (<b>b</b>) controller <span class="html-italic">u</span><sub>2</sub>; (<b>c</b>) controller <span class="html-italic">u</span><sub>3</sub>; (<b>d</b>) controller <span class="html-italic">u</span><sub>4</sub>.</p>
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<p>Time histories of the error states.</p>
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<p>Time histories of the estimated parameters.</p>
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22 pages, 2330 KiB  
Article
Adaptive Cuckoo Search-Extreme Learning Machine Based Prognosis for Electric Scooter System under Intermittent Fault
by Ming Yu, Chenyu Xiao, Hai Wang, Wuhua Jiang and Rensheng Zhu
Actuators 2021, 10(11), 283; https://doi.org/10.3390/act10110283 - 22 Oct 2021
Cited by 5 | Viewed by 2036
Abstract
In this paper, an adaptive Cuckoo search extreme learning machine (ACS-ELM)-based prognosis method is developed for an electric scooter system with intermittent faults. Firstly, bond-graph-based fault detection and isolation is carried out to find possible faulty components in the electric scooter system. Secondly, [...] Read more.
In this paper, an adaptive Cuckoo search extreme learning machine (ACS-ELM)-based prognosis method is developed for an electric scooter system with intermittent faults. Firstly, bond-graph-based fault detection and isolation is carried out to find possible faulty components in the electric scooter system. Secondly, submodels are decomposed from the global model using structural model decomposition, followed by adaptive Cuckoo search (ACS)-based distributed fault estimation with less computational burden. Then, as the intermittent fault gradually deteriorates in magnitude, and possesses the characteristics of discontinuity and stochasticity, a set of fault features that can describe the intermittent fault’s evolutionary trend are captured with the aid of tumbling window. With the obtained dataset, which represents the fault features, the ACS-ELM is developed to model the intermittent fault degradation trend and predict the remaining useful life of the intermittently faulty component when the physical degradation model is unavailable. In the ACS-ELM, the ACS is employed to optimize the input weights and hidden layer biases of an extreme learning machine, to improve the algorithm performance. Finally, the proposed methodologies are validated by a series of simulation and experiment results based on the electric scooter system. Full article
(This article belongs to the Section Actuators for Land Transport)
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<p>Structure diagram of electric scooter.</p>
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<p>DBG model of electric scooter.</p>
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<p>Submodels of electric scooter.</p>
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<p>The framework of ACS-ELM based prognosis under intermittent fault.</p>
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<p>Residual responses under <math display="inline"><semantics> <msub> <mi>β</mi> <msub> <mi>U</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>f</mi> <mi>c</mi> </mrow> </msub> </semantics></math> faults.</p>
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<p>Estimation and prediction results of <math display="inline"><semantics> <msub> <mi>β</mi> <msub> <mi>U</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </msub> </semantics></math>.</p>
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<p>Estimation and prediction results of <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>f</mi> <mi>c</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Diagram of experimental platform workflow.</p>
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<p>Residual responses under <math display="inline"><semantics> <msub> <mi>β</mi> <msub> <mi>θ</mi> <mi>r</mi> </msub> </msub> </semantics></math> fault.</p>
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<p>Estimation and prediction results of <math display="inline"><semantics> <msub> <mi>β</mi> <msub> <mi>θ</mi> <mi>r</mi> </msub> </msub> </semantics></math>.</p>
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<p>Estimation and prediction results of <math display="inline"><semantics> <msub> <mi>β</mi> <msub> <mi>θ</mi> <mi>r</mi> </msub> </msub> </semantics></math>.</p>
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<p>Histogram of RUL prediction performance.</p>
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28 pages, 11152 KiB  
Article
Prescribed Performance Control with Sliding-Mode Dynamic Surface for a Glue Pump Motor Based on Extended State Observers
by Peiyu Wang, Liangkuan Zhu, Chunrui Zhang, Chengcheng Wang and Kangming Xiao
Actuators 2021, 10(11), 282; https://doi.org/10.3390/act10110282 - 22 Oct 2021
Cited by 7 | Viewed by 2184
Abstract
The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control [...] Read more.
The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control method is used to improve the transient behaviors, and the error of the glue flow tracking is guaranteed to converge to a preset range, as a result of the design of an appropriate performance function. Second, two extended state observers were designed to estimate the state vector and the disturbance, in order to improve the robustness of the controlled system. To further strengthen the steady-state performance of the system, the sliding-mode dynamic surface control method was introduced to compensate for uncertainties and disturbances. Finally, a Lyapunov stability analysis was conducted, in order to prove that all of the signals are bounded in a closed-loop system, and the effectiveness and feasibility of the proposed method were verified through numerical simulation. Full article
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<p>Glue preparation subprocess of the particleboard glue-dosing process: 1. curing agent; 2. waterproofing agent; 3. curing buffer agent; 4. water; 5. liquid level detector; 6. quantitative barrel; 7. electronically controlled throttle valve; 8. feeding tube; 9. cylinder; 10. ball valve; 11. blanking tube; 12. agitator; 13. glue mixing case.</p>
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<p>Glue-dosing subprocess of the particleboard glue-dosing process.</p>
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<p><span class="html-italic">GMD-A</span>-type particleboard glue-dosing simulation system.</p>
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<p>Glue pump motor.</p>
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<p>Schematic diagram of the glue-dosing process.</p>
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<p>Time response of the hyperbolic tangent function.</p>
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<p>The configuration of the compound controller.</p>
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<p>Time response of glue flow tracking.</p>
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<p>Time response of control input.</p>
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<p>Time response of the glue flow tracking.</p>
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<p>Time response of the performance function.</p>
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<p>Time response of the first-order filter.</p>
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<p>Time response of glue flow tracking.</p>
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<p>Time response of the 2 ESOs in the controller.</p>
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<p>Time response of the ESOs.</p>
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<p>Time response of the ESOs.</p>
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18 pages, 2406 KiB  
Article
Model-Based Observer Design Considering Unequal Measurement Delays
by Yousef Alipouri and Lexuan Zhong
Actuators 2021, 10(11), 281; https://doi.org/10.3390/act10110281 - 22 Oct 2021
Viewed by 1524
Abstract
State observers are essential components of a modern control system. It is often designed based on a mathematical model of the process, thus requiring detailed process knowledge. However, in the existing state estimation methods, equal delays are commonly assumed for all communication lines, [...] Read more.
State observers are essential components of a modern control system. It is often designed based on a mathematical model of the process, thus requiring detailed process knowledge. However, in the existing state estimation methods, equal delays are commonly assumed for all communication lines, which is unrealistic and poses problems such as instability and a degraded performance of observers when unequal time delays exist. In this paper, a design of observers considering the measurement delays is presented. To deal with this problem, a chain-based observer has been proposed in which each chain deals with one output delay, performs prediction for the unavailable output value, and passes it to the next chain. Convergence of each chain observer as well as overall state estimation were proven. To illustrate the performance of the proposed scheme, simulation studies were performed on a benchmark continuous stirred tank heater (CSTH) process. Full article
(This article belongs to the Section Control Systems)
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<p>Schematic showing the transmission lines with measurement delays.</p>
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<p>The proposed <span class="html-italic">m</span> chain–observer (<span class="html-italic">y<sub>i</sub></span> (1: <span class="html-italic">s</span>) is the output <span class="html-italic">i</span> from sample 1 to sample <span class="html-italic">s</span>).</p>
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<p>The state 1 estimation results of the three introduced observers.</p>
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<p>The state 2 estimation results of the three introduced observers.</p>
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<p>The state 3 estimation results of the three introduced observers.</p>
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<p>Shows inputs signals of the CSTH system.</p>
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13 pages, 6324 KiB  
Article
Hysteresis Modeling of a PAM System Using ANFIS
by Saad Abu Mohareb, Adham Alsharkawi and Moudar Zgoul
Actuators 2021, 10(11), 280; https://doi.org/10.3390/act10110280 - 21 Oct 2021
Cited by 5 | Viewed by 2701
Abstract
Pneumatic artificial muscles (PAMs) are excellent environmentally friendly actuators and springs that remain somewhat underutilized in the industry due to their hysteretic behavior, which makes predicting their behavior difficult. This paper presents a novel black-box approach that employs an adaptive-network-based fuzzy inference system [...] Read more.
Pneumatic artificial muscles (PAMs) are excellent environmentally friendly actuators and springs that remain somewhat underutilized in the industry due to their hysteretic behavior, which makes predicting their behavior difficult. This paper presents a novel black-box approach that employs an adaptive-network-based fuzzy inference system (ANFIS) to create pressure-contraction hysteresis models. The resulting models are simulated in a control system toolbox to test their controllability using a simple proportional-integral (PI) controller. The data showed that the models created based on fixed inputs had an average normalized root mean square error (RMSE) of 0.0327, and their generalized counterparts achieved an average normalized RMSE of 0.04087. The simulation results showed that the PI controller was able to achieve mean tracking errors of 8.1 µm and 18.3 µm when attempting to track a sinusoidal and step references, respectively. This work concludes that modeling using the ANFIS is limited to being able to know the derivative of the input pressure or its rate of change, but competently models hysteresis in PAMs across multiple operating ranges. This is the highlight of this work. Additionally, these ANFIS-created models lend themselves well to controller, but exploring more refined control schemes is necessary to fully utilize them. Full article
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<p>Schematic diagram for the experimental setup.</p>
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<p>Antagonistic experimental setup.</p>
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<p>Membership functions of the input pressure.</p>
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<p>Membership functions of the input pressure derivative.</p>
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<p>ANFIS multilayer architecture.</p>
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<p>Rule base surfaces of the ANFIS hysteresis model.</p>
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<p>PI control scheme.</p>
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<p>Single-step input voltage applied to the test muscle subplot.</p>
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<p>Experimental vs. ANFIS pressure-contraction using single input for the ANFIS.</p>
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<p>Experimental vs. ANFIS pressure-contraction using the two-input technique for the ANFIS.</p>
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<p>A portion of the generalized model that compares experimental data against the ANFIS model at two different input voltage amplitude–frequency combinations.</p>
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<p>Time vs. contraction for the experimental data against the ANFIS model output.</p>
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<p>PI-controlled PAM simulation against a reference: (<b>a</b>) sinusoidal reference; (<b>b</b>) step reference.</p>
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19 pages, 3820 KiB  
Article
System-Level Modelling and Simulation of a Multiphysical Kick and Catch Actuator System
by Arwed Schütz, Sönke Maeter and Tamara Bechtold
Actuators 2021, 10(11), 279; https://doi.org/10.3390/act10110279 - 21 Oct 2021
Cited by 6 | Viewed by 2312
Abstract
This paper presents a system-level model of a microsystem architecture deploying cooperating microactuators. An assembly of a piezoelectric kick-actuator and an electromagnetic catch-actuator manipulates a structurally unconnected, magnetized micromirror. The absence of mechanical connections allows for large deflections and multistability. Closed-loop feedback control [...] Read more.
This paper presents a system-level model of a microsystem architecture deploying cooperating microactuators. An assembly of a piezoelectric kick-actuator and an electromagnetic catch-actuator manipulates a structurally unconnected, magnetized micromirror. The absence of mechanical connections allows for large deflections and multistability. Closed-loop feedback control allows this setup to achieve high accuracy, but requires fast and precise system-level models of each component. Such models can be generated directly from large-scale finite element (FE) models via mathematical methods of model order reduction (MOR). A special challenge lies in reducing a nonlinear multiphysical FE model of a piezoelectric kick-actuator and its mechanical contact to a micromirror, which is modeled as a rigid body. We propose to separate the actuator–micromirror system into two single-body systems. This step allows us to apply the contact-induced forces as inputs to each sub-system and, thus, avoid the nonlinear FE model. Rather, we have the linear model with nonlinear input, to which established linear MOR methods can be applied. Comparisons between the reference FE model and the reduced order model demonstrate the feasibility of the proposed methodology. Finally, a system-level simulation of the whole assembly, including two actuators, a micromirror and a simple control circuitry, is presented. Full article
(This article belongs to the Special Issue Cooperative Microactuator Systems)
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<p>Working principle of the kick and catch actuator system: the kick-actuator launches the hemispherical micromirror into a flight phase. Subsequently, the electromagnetic catch-actuator controls the mirror’s flight. Finally, the catch-actuator decelerates the sphere and supports its smooth landing on the kick-actuator. This sequence achieves a small rotation of the hemisphere and may be repeated periodically to achieve large deflections. Please note the symbolic nature of this illustration. Later versions of the catch-actuator may, for example, contain a three-dimensional Helmholtz-coil configuration. Furthermore, this work focuses on further developing and applying the mathematical methodology of model order reduction (MOR). For this reason, the system is simplified to vertical motion.</p>
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<p>Sectional three-dimensional view of the simplified actuator system with labeled components. This setup deploys a piezoelectric chip actuator for kick-actuation and an assembly of two coils and a ring magnet for electromagnetic interaction. Additionally, the micromirror is included as a magnetic sphere. The setup is designed for preliminary studies. This basis will be extended by more complex assemblies to precisely manipulate the micromirror.</p>
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<p>Considerations for the FEM model of the piezoelectric kick-actuator: (<b>a</b>) Symmetry allows to simulate only one quarter of the model, saving computational effort. (<b>b</b>) A mapped mesh of concentric circles around the location of contact results in equal vertical nodal forces per ring. The center node and the five rings are enumerated from <math display="inline"><semantics> <msub> <mi>R</mi> <mn>0</mn> </msub> </semantics></math> to <math display="inline"><semantics> <msub> <mi>R</mi> <mn>5</mn> </msub> </semantics></math>. (<b>c</b>) Contact-induced forces on the kick-actuator are equal per ring. Black arrows indicate the vertical force distribution for a single ring. Separately modelling the sphere and the kick-actuator provides access to the MOR methodology proposed in [<a href="#B40-actuators-10-00279" class="html-bibr">40</a>].</p>
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<p>Schematic workflow of MOR, illustrated for the Thorlabs PA3JEAW piezoelectric chip actuator: first, a physical problem to be investigated is chosen and subsequently modeled based on the FEM. The FEM spatially discretizes the computational domain, creating a large set of ODEs. MOR projects these ODEs onto a low-dimensional subspace, reducing the number of equations by several orders of magnitude. Finally, the resulting ROM is ready to use for commercial system-level simulation software. The picture of the actuator is adapted from [<a href="#B45-actuators-10-00279" class="html-bibr">45</a>] with the friendly permission of Thorlabs GmbH.</p>
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<p>Schematic diagram of the kick and catch actuator system at system-level, extended by a PID-based position control of the sphere. The four grey areas indicate the system’s major components: the controller, the electromagnetic catch-actuator, the piezoelectric kick-actuator, and the sphere (clockwise from top left). The catch-actuator is modelled as an equivalent circuit, the kick-actuator as an ROM and the micromirror as a point mass.</p>
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<p>The vertical electromagnetic force acting on the spherical magnet, plotted over its position. Each combination of coil currents is shown as a single line. The catch-actuator’s vertical symmetry induces a symmetric force for equal but opposed currents.</p>
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<p>(<b>a</b>) Comparison of the center node’s harmonic displacement amplitude obtained by the original FEM model and the ROM in a frequency range of 0 kHz to 500 kHz. (<b>b</b>) The harmonic relative error of the ROM’s solution for all seven outputs, demonstrating its accuracy. The ROM approximates the original transfer function at an expansion point of 0 Hz. Consequently, all errors are the lowest at this frequency and increase with higher frequencies. Extending the reduced basis with vectors for higher frequencies enhances accuracy if needed. The error plots for the remaining six inputs are provided by <a href="#app2-actuators-10-00279" class="html-app">Appendix B</a>.</p>
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<p>Static force opposing the sphere’s displacement into the kick-actuator. The sphere starts just in contact with the actuator’s top surface and is displaced 50 μm into the surface in increments of −0.2 μm. (<b>a</b>) Solutions of the reference FEM model and the ROM. Note that the force is one quarter of the full contact force. (<b>b</b>) The ROM’s relative error, demonstrating its accuracy.</p>
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<p>The sphere’s vertical position during impact measured from its lowest point. (<b>a</b>) The solutions of the reference FE model and the ROM. (<b>b</b>) The ROM’s relative error increases in time as deviations accumulate. The sphere leaves contact after 11 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math>, causing a high error at this point in time. Note that, due to limitations of commercial software, different methods are used for time integration.</p>
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<p>The kick and catch actuation at system-level. (<b>a</b>) The sphere’s vertical position over time for the full duration of 5 <math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math>, showing a clear catch at <math display="inline"><semantics> <mrow> <mn>2.5</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">m</mi> </semantics></math>. (<b>b</b>) Vertical position of the center node for 450 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math>–600 <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math><math display="inline"><semantics> <mi mathvariant="normal">s</mi> </semantics></math>, illustrating the kick actuation.</p>
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<p>Harmonic relative error of each of the ROM’s outputs for a single input each. (<b>a</b>) Unit force at <math display="inline"><semantics> <msub> <mi>R</mi> <mn>1</mn> </msub> </semantics></math> (<b>b</b>) Unit force at <math display="inline"><semantics> <msub> <mi>R</mi> <mn>2</mn> </msub> </semantics></math> (<b>c</b>) Unit force at <math display="inline"><semantics> <msub> <mi>R</mi> <mn>3</mn> </msub> </semantics></math> (<b>d</b>) Unit force at <math display="inline"><semantics> <msub> <mi>R</mi> <mn>4</mn> </msub> </semantics></math> (<b>e</b>) Unit force at <math display="inline"><semantics> <msub> <mi>R</mi> <mn>5</mn> </msub> </semantics></math> (<b>f</b>) Unit charge at the anode.</p>
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19 pages, 8184 KiB  
Article
Robust Control Design Based on Perturbation Cancellation for Micro-Positioning Design with Hysteresis
by Yung-Yue Chen, Yu-Jen Lan and Yi-Qing Zhang
Actuators 2021, 10(11), 278; https://doi.org/10.3390/act10110278 - 21 Oct 2021
Cited by 2 | Viewed by 1710
Abstract
Based on the superiority of the piezoelectric elements, including lightweight, high electric mechanical transformation efficiency and a quick response time, a piezoelectric-based micro-positioning actuator is developed in this investigation. For eliminating the effects of hysteresis and modeling uncertainties that appeared in this micro-positioning [...] Read more.
Based on the superiority of the piezoelectric elements, including lightweight, high electric mechanical transformation efficiency and a quick response time, a piezoelectric-based micro-positioning actuator is developed in this investigation. For eliminating the effects of hysteresis and modeling uncertainties that appeared in this micro-positioning actuator, a nonlinear adaptive fuzzy robust control design with a perturbation cancellation ability is proposed for this micro-positioning design to achieve a positioning resolution of 1 μm. Structurally, this proposed robust control methodology contains two particular parts: a universal fuzzy approximator and a robust compensator, which are employed to cancel the modeling uncertainties caused by the perturbed parts of the micro-positioning actuator and mitigate the approximation error between the modeling uncertainties and the universal fuzzy approximator, respectively. From both the numerical simulations and real validations, this proposed micro-positioning design performs a promising positioning performance in the micrometer level. Full article
(This article belongs to the Special Issue Ferroelectric Materials and Piezoelectric Actuators)
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<p>Illustration of the hysteresis loop.</p>
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<p>Schematics of a micro-positioning actuator with a piezoelectric element, a fastener, and two electrodes.</p>
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<p>The equivalent illustration of a piezoelectric-based micro-positioning actuator.</p>
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<p>Micro-positioning results of output displacement <span class="html-italic">z</span> based on the proposed method (green line) and feedback linearization method (blue dash line) with respect to a desired trapezoid trajectory (red dotted line).</p>
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<p>Histories of positioning errors for the proposed method (green line) and feedback linearization method (blue dash line) with respect to a desired trapezoid trajectory.</p>
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<p>Histories of the overall control commands of the proposed method and feedback linearization method.</p>
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<p>A time-varying positive perturbation (20% of <math display="inline"><semantics> <mover accent="true"> <mi>m</mi> <mo>¯</mo> </mover> </semantics></math>) is added for <math display="inline"><semantics> <mi>m</mi> </semantics></math> during 0–5 s and 10–19 s (red dotted line) in Scenario 1.</p>
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<p>Comparisons of model functions <math display="inline"><semantics> <mi>F</mi> </semantics></math> and <math display="inline"><semantics> <mi>G</mi> </semantics></math> (green line) with <math display="inline"><semantics> <mover accent="true"> <mi>F</mi> <mo>¯</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>G</mi> <mo>¯</mo> </mover> </semantics></math> (red dotted line) in Scenario 1. (<b>a</b>) <math display="inline"><semantics> <mi>F</mi> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>F</mi> <mo>¯</mo> </mover> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mi>G</mi> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>G</mi> <mo>¯</mo> </mover> </semantics></math>.</p>
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<p>Micro-positioning results of output displacement <span class="html-italic">z</span> based on the proposed method (green line) and feedback linearization method (blue dash line) with respect to a desired sinusoidal trajectory.</p>
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<p>Histories of positioning errors for the proposed method (green line) and feedback linearization method (blue dash line) with respect to a desired sinusoidal trajectory.</p>
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<p>Histories of the overall control commands of the proposed method and feedback linearization method.</p>
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<p>A fixed positive perturbation (20% of <math display="inline"><semantics> <mover accent="true"> <mi>m</mi> <mo>¯</mo> </mover> </semantics></math>) is added for <math display="inline"><semantics> <mi>m</mi> </semantics></math> in Scenario 2.</p>
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<p>Comparisons of model functions <math display="inline"><semantics> <mi>F</mi> </semantics></math> and <math display="inline"><semantics> <mi>G</mi> </semantics></math> (green line) with <math display="inline"><semantics> <mover accent="true"> <mi>F</mi> <mo>¯</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>G</mi> <mo>¯</mo> </mover> </semantics></math> (red dotted line) in Scenario 2. (<b>a</b>) <math display="inline"><semantics> <mi>F</mi> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>F</mi> <mo>¯</mo> </mover> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mi>G</mi> </semantics></math> and <math display="inline"><semantics> <mover accent="true"> <mi>G</mi> <mo>¯</mo> </mover> </semantics></math>.</p>
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<p>Experimental installation of the proposed micro-positioning design: (<b>a</b>) a piezoelectric-based actuator and (<b>b</b>) the overall micro-positioning system with a position measuring system, a piezoelectric-based actuator, and the proposed adaptive fuzzy robust control law carried out in the desktop.</p>
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<p>History of the proposed micro-positioning actuator for a desired stair-type trajectory.</p>
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<p>Micro-positioning error for a desired stair-type trajectory.</p>
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<p>History of the proposed micro-positioning actuator for a desired trapezoidal-type trajectory.</p>
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<p>Micro-positioning error for a desired trapezoidal-type trajectory.</p>
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<p>History of the proposed micro-positioning actuator for a desired sinusoidal-type trajectory.</p>
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<p>Micro-positioning error for a desired sinusoidal-type trajectory.</p>
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