A Cost-Effective Integrated Methodology for Electromagnetic Actuation via Visual Feedback
<p>Novel set-up for electromagnetic actuation proposed in this paper: (<b>a</b>) system overview, (<b>b</b>) zoomed-in view of the actuator and moving object, and (<b>c</b>) simplified view of the moving object with its free-body diagram.</p> "> Figure 2
<p>Block diagram showing the structure of the experimental set-up.</p> "> Figure 3
<p>Representative results for motion tracking of the oscillating pendulum: (<b>a</b>) displacement time-series, (<b>b</b>) detailed view of displacement time-series, (<b>c</b>) displacement normalized histogram, (<b>d</b>) displacement power spectrum (PSD).</p> "> Figure 4
<p>Electromagnet experimental characterization at 24 V supply voltage: (<b>a</b>) axial magnetic flux, (<b>b</b>) radial magnetic flux, (<b>c</b>) axial magnetic flux measured in the presence of the ball, (<b>d</b>) radial magnetic flux measured in the presence of the ball. The black circle in panels (<b>c</b>,<b>d</b>) represents the ball, while the coordinate system is placed on the electromagnet surface with its origin on the geometrical center of the core.</p> "> Figure 5
<p>(<b>a</b>) Magnetic force measurements at various distances between the electromagnet surface and the ball center for different electromagnet supply voltages (4, 8, 12, 16, 20, and 24 V): the discrete data points are the measured values, while the continuous lines are the predictions of the fitting relation in Equation (7); (<b>b</b>) parity plot with comparison between magnetic force predictions from Equation (7) and measurements (the dashed lines are ±20% error bounds).</p> "> Figure 6
<p>Measured (<math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>) and simulated (<math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>P</mi> <mi>r</mi> <mi>e</mi> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math>) trends of the damped free oscillations in (<b>a</b>) air, (<b>b</b>) water, and (<b>c</b>) glycol. The ball is in contact with the electromagnet surface at the beginning of the tests and is released with a step command that removes the applied voltage at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> </mrow> </semantics></math> 0 s. The plots use a different time scale for better visualization.</p> "> Figure 7
<p>Block diagram of the proposed closed-loop position control algorithm used to generate the voltage applied to the electromagnet.</p> "> Figure 8
<p>Closed-loop motion control of the ball surrounded by air with a constant-frequency position command (<a href="#app1-sensors-24-02760" class="html-app">Video S1</a> and control parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>P</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 2.2 V/mm, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>I</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 1.8 V/mm/s, and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>x</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 7 Hz): (<b>a</b>) ball position (commanded position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and filtered measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>F</mi> <mi>i</mi> <mi>l</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>), (<b>b</b>) position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and (<b>c</b>) voltage command.</p> "> Figure 9
<p>Closed-loop control of the ball in air with a variable-frequency command (<a href="#app1-sensors-24-02760" class="html-app">Video S2</a> and control parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1, <math display="inline"><semantics> <mrow> <msubsup> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> </mrow> </semantics></math> 0.05/30 1/s, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>P</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 1.5 V/mm, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>I</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 1.05 V/mm/s, and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>x</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 15 Hz): (<b>a</b>) ball position (commanded position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and filtered measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>F</mi> <mi>i</mi> <mi>l</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>), (<b>b</b>) position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>c</b>) voltage command, and (<b>d</b>) input frequency.</p> "> Figure 10
<p>Closed-loop motion control of the ball surrounded by water with a constant-frequency command (<a href="#app1-sensors-24-02760" class="html-app">Video S3</a> and control parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>P</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 1.8 V/mm, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>I</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 1.2 V/mm/s, and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>x</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 25 Hz): (<b>a</b>) ball position (commanded position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and filtered measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>F</mi> <mi>i</mi> <mi>l</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>), (<b>b</b>) position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and (<b>c</b>) voltage command.</p> "> Figure 11
<p>Closed-loop control of the ball in water with a variable-frequency position command (<a href="#app1-sensors-24-02760" class="html-app">Video S4</a> and control parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1, <math display="inline"><semantics> <mrow> <msubsup> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> </mrow> </semantics></math> 0.005 1/s, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>P</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 1.05 V/mm, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>I</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 0.7 V/mm/s, and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>x</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 30 Hz): (<b>a</b>) ball position (commanded position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and filtered measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>F</mi> <mi>i</mi> <mi>l</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>), (<b>b</b>) position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>c</b>) and voltage command.</p> "> Figure 12
<p>Closed-loop control of the ball in glycol with a constant-frequency position command (<a href="#app1-sensors-24-02760" class="html-app">Video S5</a> and control parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>P</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 3 V/mm, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>I</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 2.5 V/mm/s, and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>x</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 25 Hz): (<b>a</b>) ball position (commanded position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and filtered measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>F</mi> <mi>i</mi> <mi>l</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>), (<b>b</b>) position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and (<b>c</b>) voltage command.</p> "> Figure 13
<p>Closed-loop motion control of the ball in glycol with a variable-frequency position command (<a href="#app1-sensors-24-02760" class="html-app">Video S6</a> and control parameters <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 1, <math display="inline"><semantics> <mrow> <msubsup> <mi>k</mi> <mrow> <mi>F</mi> <mi>F</mi> </mrow> <mo>*</mo> </msubsup> <mo>=</mo> </mrow> </semantics></math> 0.1/30 1/s, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>P</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 0.8 V/mm, <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mi>I</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 0.7 V/mm/s, and <math display="inline"><semantics> <mrow> <msub> <mi>ω</mi> <mi>x</mi> </msub> <mo>=</mo> </mrow> </semantics></math> 30 Hz): (<b>a</b>) ball position (commanded position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>, measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, and filtered measured position <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mrow> <mi>F</mi> <mi>i</mi> <mi>l</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>), (<b>b</b>) position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>, (<b>c</b>) voltage command.</p> "> Figure 14
<p>Comparison of the actual position error <math display="inline"><semantics> <mrow> <msubsup> <mi>e</mi> <mi>z</mi> <mo>*</mo> </msubsup> <mo>=</mo> <msub> <mi>z</mi> <mrow> <mi>S</mi> <mi>e</mi> <mi>t</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>z</mi> <mrow> <mi>M</mi> <mi>e</mi> <mi>a</mi> <mi>s</mi> </mrow> </msub> <mo> </mo> </mrow> </semantics></math> resulting from the tests reported above and performed in different conditions (air, water, and glycol): (<b>a</b>) constant-frequency position command, and (<b>b</b>) variable-frequency position command.</p> ">
Abstract
:1. Introduction
2. Experimental Set-Up
2.1. Overall System
2.1.1. System Description
2.1.2. System Implementation
2.2. Motion Tracking Methodology
2.3. Magnetic Flux and Force
2.4. Viscous Friction Force
2.5. Closed-Loop Position Control
3. Experiments
3.1. Case 1: Motion in Air
3.2. Case 2: Motion in Water
3.3. Case 3: Motion in Glycol
3.4. System Comparison
4. Conclusions
- We have proposed a user-friendly set-up that relies on cost-effective, off-the-shelf components. This set-up combines three main subsystems: actuation, motion tracking, and feedback control. Our approach has minimum complexity since we have chosen a plug-and-play webcam for optical tracking and developed an intuitive, model-based control law.
- We have gained significant insight into the distribution of the magnetic flux/magnetic force of electromagnets. We have shown that the magnetic flux is highly nonlinear and severely changes when a ferromagnetic object is nearby. We have also done an accurate and experimentally validated fitting of the electromagnetic force by creating an invertible function to be used for the control design.
- We have used an off-the-shelf webcam to implement motion tracking via visual feedback. The camera samples images in the range of 85 ± 2 fps. Our conservative estimate for the sensing accuracy of the ball centroid’s location is about ±300 microns. We have validated this approach with an oscillating pendulum whose power spectrum presents one dominant peak that closely matches its theoretical oscillation frequency.
- We have deliberately designed a control algorithm for closed-loop, position control of the actuated object with minimum complexity. This law combines a model-based feedforward term (it predicts the electromagnet’s voltage command based on the desired motion) and a feedback term (it corrects the voltage command by applying proportional-integrative control on the position error).
- We have performed closed-loop position tracking (1D vertical motion) with a 10 mm steel ball hanging from a low-stiffness spring and surrounded by diverse fluids (air, water, and glycol). Despite the different conditions, our set-up can consistently perform well when proper control settings are chosen. When commanded by a sinusoidal position with constant frequency, the tracking error stays within ±0.5 mm with a negligible phase delay.
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Test | (-) | (-) | (V/mm) | (V/mm/s) | (Hz) |
---|---|---|---|---|---|
Air (constant frequency) | 1 | 0 | 2.2 | 1.8 | 7 |
Air (variable frequency) | 1 | 0.05/30 | 1.5 | 1.05 | 15 |
Water (constant frequency) | 1 | 0 | 1.8 | 1.2 | 25 |
Water (variable frequency) | 1 | 0.005 | 1.05 | 0.7 | 30 |
Glycol (constant frequency) | 1 | 0 | 3 | 2.5 | 25 |
Glycol (variable frequency) | 1 | 0.1/30 | 0.8 | 0.7 | 30 |
Test | RMS Value | Test | RMS Value |
---|---|---|---|
Air (constant frequency) | 0.1884 | Air (variable frequency) | 0.3857 |
Water (constant frequency) | 0.1612 | Water (variable frequency) | 0.3471 |
Glycol (constant frequency) | 0.1491 | Glycol (variable frequency) | 0.2896 |
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Chen, S.; Padovani, D.; Cioncolini, A.; Alessandri, A. A Cost-Effective Integrated Methodology for Electromagnetic Actuation via Visual Feedback. Sensors 2024, 24, 2760. https://doi.org/10.3390/s24092760
Chen S, Padovani D, Cioncolini A, Alessandri A. A Cost-Effective Integrated Methodology for Electromagnetic Actuation via Visual Feedback. Sensors. 2024; 24(9):2760. https://doi.org/10.3390/s24092760
Chicago/Turabian StyleChen, Shuwan, Damiano Padovani, Andrea Cioncolini, and Angelo Alessandri. 2024. "A Cost-Effective Integrated Methodology for Electromagnetic Actuation via Visual Feedback" Sensors 24, no. 9: 2760. https://doi.org/10.3390/s24092760