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Search Results (235)

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Keywords = sensorless speed

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24 pages, 7299 KiB  
Article
An Anti-Disturbance Extended State Observer-Based Control of a PMa-SynRM for Fast Dynamic Response
by Dongyang Li, Shuo Wang, Chunyang Gu, Yuli Bao, Xiaochen Zhang, Chris Gerada and He Zhang
Energies 2024, 17(17), 4260; https://doi.org/10.3390/en17174260 - 26 Aug 2024
Viewed by 338
Abstract
The control system of PMa-SynRMs (Permanent Magnet-assisted Synchronous Reluctance Machines) exhibit susceptibility to external disturbances, thereby emphasizing the utmost significance of employing an observer to effectively observe and suppress system disturbances. Meanwhile, disturbances in load are sensitive to control system noise, which may [...] Read more.
The control system of PMa-SynRMs (Permanent Magnet-assisted Synchronous Reluctance Machines) exhibit susceptibility to external disturbances, thereby emphasizing the utmost significance of employing an observer to effectively observe and suppress system disturbances. Meanwhile, disturbances in load are sensitive to control system noise, which may be introduced from current sensors, hardware circuit board systems, sensor-less control, and analog position sensors. To tackle these problems, this paper proposes an A-DESO (anti-disturbance extended state observer) to improve the dynamic performance, noise suppression, and robustness of PMa-SynRMs in both the constant torque and FW (flux weakening) regions. With the proposed A-DESO, lumped disturbance in torque could be detected, and speed could be extracted in position with unmeasurable noise. Thanks to the merits of the small observation error in the low-frequency region and the excellent anti-disturbance performance in the high-frequency region of the proposed A-DESO, the control of the PMa-SynRM features the advantages of a fast response and good noise immunity ability within the same observation error range. The proposed A-DESO presents a shorter convergence time and a better noise suppression ability, which leads to a better dynamic response of the PMa-SynRM when encountering an unknown load disturbance compared to the traditional ESO-based control, according to simulations and experiments. Full article
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Figure 1

Figure 1
<p>Flux characteristics of the PMa-SynRM: (<b>a</b>) <span class="html-italic">d-</span> and <span class="html-italic">q-</span>axis flux with different <span class="html-italic">d-</span> and <span class="html-italic">q</span>-axis currents; (<b>b</b>) <span class="html-italic">d-</span> and <span class="html-italic">q-</span>axis inductance with different <span class="html-italic">d-</span> and <span class="html-italic">q-</span>axis currents; and (<b>c</b>) permanent magnet flux with different <span class="html-italic">d-</span> and <span class="html-italic">q-</span>axis currents.</p>
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<p>Voltage and current restriction of PMa-SynRM.</p>
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<p>Relationship between maximum error and frequency.</p>
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<p>Error dynamics diagram of the ESO.</p>
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<p>Frequency responses of the ESO error.</p>
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<p>Noise suppression performance.</p>
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<p>Error dynamics diagram of A-DESO.</p>
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<p>Frequency responses of disturbance estimation error for the A-DESO and ESO.</p>
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<p>Comparison for noise suppression performance of ESO and A-DESO.</p>
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<p>Error dynamic response for speed of ESO and A-DESO.</p>
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<p>Error suppression response for position observation of ESO and A-DESO.</p>
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<p>Frequency responses of load torque estimation with different <span class="html-italic">k</span> and <span class="html-italic">τ</span>.</p>
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<p>Frequency responses of noise suppression with different <span class="html-italic">k</span> and <span class="html-italic">τ</span>.</p>
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<p>Parameter calculation process of A-DESO based on the PMa-SynRM.</p>
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<p>Observation error with <span class="html-italic">d-</span> and <span class="html-italic">q-</span>axis inductance mismatch: (<b>a</b>) observation error in rated-load condition; (<b>b</b>) observation error in half-load condition.</p>
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<p>Overall control diagram.</p>
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<p>Overall control diagram of <span class="html-italic">i</span><sub>d</sub> and <span class="html-italic">i</span><sub>q</sub> generation.</p>
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<p>Hardware testbench of PMa-SynRM.</p>
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<p>Simulation results on step load response in MTPA region: (<b>a</b>) speed fluctuation when load step; (<b>b</b>) observed lumped disturbance and given load disturbance; (<b>c</b>) comparison of the different speed calculation method.</p>
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<p>Simulation results on step load response in FW region: (<b>a</b>) observed lumped disturbance and given load disturbance; (<b>b</b>) speed fluctuation when increasing load under flux weakening control; (<b>c</b>) comparison of different speed calculation method in FW condition.</p>
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<p>Experiments’ results in MTPA region: speed fluctuation with A-DESO and without ESO; current fluctuation with A-DESO and without ESO; load torque and observed disturbance.</p>
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<p>Experiments’ results in FW region: speed fluctuation with A-DESO and without ESO; current fluctuation with A-DESO and without ESO; load torque and observed disturbance.</p>
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<p>Experiments’ results in repeating step-load response in MTPA working condition: speed fluctuation with A-DESO and without ESO; load torque and observed disturbance.</p>
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<p>Experiments’ results in repeating step-load response in FW working condition: speed fluctuation with A-DESO and without ESO; load torque and observed disturbance.</p>
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<p>Experiments’ results in ramp load response in the whole working condition: speed fluctuation with ESO and without ESO; load torque and observed disturbance.</p>
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22 pages, 16164 KiB  
Article
Reducing Noise and Impact of High-Frequency Torque Ripple Caused by Injection Voltages by Using Self-Regulating Random Model Algorithm for SynRMs Sensorless Speed Control
by Yibo Guo, Lingyun Pan, Yang Yang, Yimin Gong and Xiaolei Che
Electronics 2024, 13(16), 3327; https://doi.org/10.3390/electronics13163327 - 22 Aug 2024
Viewed by 471
Abstract
For the sensorless control in a low-speed range of synchronous reluctance motors (SynRMs), injecting random high-frequency (HF) square-wave-type voltages has become a widely used and technologically mature method. It can solve the noise problem of traditional injection signal methods. However, all injection signal [...] Read more.
For the sensorless control in a low-speed range of synchronous reluctance motors (SynRMs), injecting random high-frequency (HF) square-wave-type voltages has become a widely used and technologically mature method. It can solve the noise problem of traditional injection signal methods. However, all injection signal methods will cause problems such as torque ripple, which causes speed fluctuations. This article proposes a self-regulating random model algorithm for the random injection signal method, which includes a quantity adaptive module for adding additional random processes, an evaluation module for evaluating torque deviation degree, and an updated model module that is used to receive signals from the other two modules and complete model changes and output random model elements. The main function of this algorithm is to create a model that updates to suppress the evaluation value deviation based on the evaluation situation and outputs an optimal sequence of random numbers, thereby limiting speed bias always in a small range; this can reduce unnecessary changes in the output value of the speed regulator. The feasibility and effectiveness of the proposed algorithm and control method have been demonstrated in experiments based on a 5-kW synchronous reluctance motor. Full article
(This article belongs to the Special Issue Power Electronics in Renewable Systems)
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Figure 1

Figure 1
<p>The schematic diagram of the injection voltage of the <span class="html-italic">d</span>-axis.</p>
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<p>Configuration of adaptive speed estimator.</p>
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<p>PLL for calculating electrical angle.</p>
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<p>Using adaptive velocity estimator and PLL to obtain motor speed and electrical angle.</p>
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<p>The schematic diagram of the eight basic injection voltages and corresponding induced currents in <span class="html-italic">d</span>-axis. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>45</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>90</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>135</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>180</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>225</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>270</mn> <mo>°</mo> </mrow> </semantics></math>. (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mn>315</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Reference diagram for calculating the impact of injected voltage on speed. (<b>a</b>) No.1. (<b>b</b>) No.2.</p>
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<p>The variation in SynRM <span class="html-italic">dq</span>-axis inductance due to saturation effect.</p>
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<p>The summed-up value of the speed bias of using RVIM according to <a href="#electronics-13-03327-t002" class="html-table">Table 2</a>.</p>
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<p>Overall diagram of self-regulating random model algorithm.</p>
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<p>Principle diagram of the quantity adaptive module.</p>
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<p>Update Model Module. (<b>a</b>) Overall logic diagram. (<b>b</b>) Schematic diagram of model state changes.</p>
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<p>Flowchart of using the self-regulating random model algorithm to output injection voltage.</p>
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<p>Block diagram of speed sensorless control system for SynRMs using self-regulating random model algorithm.</p>
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<p>PSD results of the induced current of three different control methods.</p>
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<p>Experimental platform display diagram.</p>
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<p>The output signal from quantity adaptive module and the number of active elements.</p>
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<p>The evaluation result value and the injection voltage number.</p>
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<p>Sampling results of current, speed, and torque during motor running at 100 rpm. (<b>a</b>) SRRMM with no load. (<b>b</b>) RVIM with no load. (<b>c</b>) SRRMM with 50% rated load. (<b>d</b>) RVIM with 50% rated load. (<b>e</b>) SRRMM with rated load. (<b>f</b>) RVIM with rated load.</p>
Full article ">Figure 19
<p>Sampling results of current and speed during motor start-up to 100 rpm. (<b>a</b>) SRRMM with no load. (<b>b</b>) RVIM with no load. (<b>c</b>) SRRMM with rated load. (<b>d</b>) RVIM with rated load.</p>
Full article ">Figure 20
<p>Sampling results of current and speed of the motor from −100 rpm to 100 rpm. (<b>a</b>) SRRMM with no load. (<b>b</b>) RVIM with no load. (<b>c</b>) SRRMM with rated load. (<b>d</b>) RVIM with rated load.</p>
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<p>Sampling results of current and speed during acceleration and deceleration of the motor between 100 rpm and 150 rpm. (<b>a</b>) SRRMM with no-load. (<b>b</b>) RVIM with no-load. (<b>c</b>) SRRMM with rated load. (<b>d</b>) RVIM with rated load.</p>
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<p>Collecting the noise level generated by the motor using Smart Sensor AS804B.</p>
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<p>Record of voltage injection times for each number.</p>
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<p>During steady state of the motor, phase current image, corresponding PSD calculation results, and Fourier transform results display diagram. (<b>a</b>) OVIM with 2.5 kHz injection voltage with no load. (<b>b</b>) OVIM with 1.25 kHz injection voltage with no load. (<b>c</b>) RVIM with no load. (<b>d</b>) SRRMM with no load. (<b>e</b>) OVIM with 2.5 kHz injection voltage with rated load. (<b>f</b>) OVIM with 1.25 kHz injection voltage with rated load. (<b>g</b>) RVIM with rated load. (<b>h</b>) SRRMM with rated load.</p>
Full article ">
17 pages, 8329 KiB  
Article
Research on Fourier Coefficient-Based Energy Capture for Direct-Drive Wave Energy Generation System Based on Position Sensorless Disturbance Suppression
by Shiquan Wu, Lei Huang, Jianlong Yang, Jiyu Zhang, Haitao Liu, Shixiang Wang and Zihao Mou
J. Mar. Sci. Eng. 2024, 12(8), 1358; https://doi.org/10.3390/jmse12081358 - 9 Aug 2024
Viewed by 403
Abstract
In order to improve the energy capture efficiency of direct-drive wave power generation (DDWEG) systems and enhance the robustness of the reference power tracking control, a Fourier coefficient-based energy capture (FCBEC) and a position sensorless disturbance suppression (PSDS) control strategy are proposed. For [...] Read more.
In order to improve the energy capture efficiency of direct-drive wave power generation (DDWEG) systems and enhance the robustness of the reference power tracking control, a Fourier coefficient-based energy capture (FCBEC) and a position sensorless disturbance suppression (PSDS) control strategy are proposed. For energy capture, FCBEC is proposed to construct the objective function by maximizing the average power over a period of time and expanding the variables in the Fourier basis when the maximum power is captured, which is used as the basis for obtaining the reference trajectory. To address the limitations of the mechanical encoder, the position sensorless technique, based on a sliding mode observer (SMO), is used in the power tracking control, and the position information is obtained through an inverse tangent function. The perturbation caused by the inverse electromotive force error in the system is theoretically analyzed. A full-order terminal sliding mode approach is employed to design a current controller that suppresses the perturbation and ensures accurate tracking of the reference current. Simulation results show that the ocean-wave energy capture strategy proposed in this paper can make the energy captured by the PTO reach the optimal value under the impedance matching condition, and that the response speed and robustness of the full-order terminal sliding mode are better than the traditional PI control. Full article
(This article belongs to the Section Coastal Engineering)
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Figure 1
<p>Schematic diagram of the forces on the cylinder float.</p>
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<p>Equivalent circuit diagram of DDWEG.</p>
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<p>Schematic diagram of interval time domain optimization.</p>
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<p>Flowchart of FCBEC control strategy.</p>
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<p>SMO-based position sensorless control block diagram.</p>
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<p>Control block diagram of a DDWEG system.</p>
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<p>Excitation force and calculated PTO force.</p>
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<p>Reference displacement and reference velocity.</p>
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<p>Energy capture effect under optimal solution conditions.</p>
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<p>Energy capture effect under amplitude control strategy.</p>
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<p>Actuator position estimation and error variation curves.</p>
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<p><span class="html-italic">d</span>- and <span class="html-italic">q</span>-axis current tracking.</p>
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24 pages, 3349 KiB  
Article
Adaptive QSMO-Based Sensorless Drive for IPM Motor with NN-Based Transient Position Error Compensation
by Linfeng Sun, Jiawei Guo, Xiongwen Jiang, Takahiro Kawaguchi, Seiji Hashimoto and Wei Jiang
Electronics 2024, 13(15), 3085; https://doi.org/10.3390/electronics13153085 - 4 Aug 2024
Viewed by 602
Abstract
In commercial electrical equipment, the popular sensorless drive scheme for the interior permanent magnet synchronous motor, based on the quasi-sliding mode observer (QSMO) and phase-locked loop (PLL), still faces challenges such as position errors and limited applicability across a wide speed range. To [...] Read more.
In commercial electrical equipment, the popular sensorless drive scheme for the interior permanent magnet synchronous motor, based on the quasi-sliding mode observer (QSMO) and phase-locked loop (PLL), still faces challenges such as position errors and limited applicability across a wide speed range. To address these problems, this paper analyzes the frequency domain model of the QSMO. A QSMO-based parameter adaptation method is proposed to adjust the boundary layer and widen the speed operating range, considering the QSMO bandwidth. A QSMO-based phase lag compensation method is proposed to mitigate steady-state position errors, considering the QSMO phase lag. Then, the PLL model is analyzed to select the estimated speed difference for transient position error compensation. Specifically, a transient position error compensator based on a feedback time delay neural network (FB-TDNN) is proposed. Based on the back propagation learning algorithm, the specific structure and optimal parameters of the FB-TDNN are determined during the offline training process. The proposed parameter adaptation method and two position error compensation methods were validated through simulations in simulated wide-speed operation scenarios, including sudden speed changes. Overall, the proposed scheme fully mitigates steady-state position errors, substantially mitigates transient position errors, and exhibits good stability across a wide speed range. Full article
(This article belongs to the Special Issue New Horizons and Recent Advances of Power Electronics)
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Figure 1
<p>Block diagram of the EEMF-based QSMO.</p>
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<p>Block diagram of the conventional QSMO-based position and speed estimation method.</p>
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<p>Block diagram of the conventional QSMO-based sensorless drive scheme of an IPM motor used for FOC using <math display="inline"><semantics> <mrow> <msup> <mrow> <msub> <mi>i</mi> <mi mathvariant="normal">d</mi> </msub> </mrow> <mo>*</mo> </msup> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> control.</p>
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<p>Frequency domain analysis results of the EEMF-based QSMO: (<b>a</b>) With different speed values <math display="inline"><semantics> <msub> <mi>ω</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math> and fixed boundary layer <math display="inline"><semantics> <msup> <mrow> <msub> <mi>m</mi> <mi mathvariant="normal">f</mi> </msub> </mrow> <mo>*</mo> </msup> </semantics></math>. (<b>b</b>) With fixed bandwidth <math display="inline"><semantics> <msup> <mrow> <msub> <mi>ω</mi> <mi>QSMO</mi> </msub> </mrow> <mo>*</mo> </msup> </semantics></math>.</p>
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<p>Block diagram of the PLL with a speed LPF.</p>
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<p>Block diagram of the proposed NN-based transient position error compensator.</p>
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<p>Structure of the proposed FB-TDNN.</p>
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<p>Estimated rotational speed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and speed difference <math display="inline"><semantics> <mrow> <mo>−</mo> <mo>Δ</mo> <msub> <mover accent="true"> <mi>ω</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">e</mi> </msub> </mrow> </semantics></math> in the selected offline training scenario.</p>
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<p>MSE-epoch curves of the FB-TDNN during offline training: (<b>a</b>) With 1 IDT and 0 FDTs. (<b>b</b>) With 2 IDTs and 0 FDTs. (<b>c</b>) With 3 IDTs and 0 FDTs. (<b>d</b>) With 3 IDTs and 1 FDT. (<b>e</b>) With 3 IDTs and 2 FDTs. (<b>f</b>) With 3 IDTs and 3 FDTs.</p>
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<p>Transient position error compensation <math display="inline"><semantics> <msub> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mrow> <mi>comp</mi> <mn>2</mn> </mrow> </mrow> </msub> </semantics></math> estimated by the FB-TDNN: (<b>a</b>) With 1 IDT and 0 FDTs. (<b>b</b>) With 2 IDTs and 0 FDTs. (<b>c</b>) With 3 IDTs and 0 FDTs. (<b>d</b>) With 3 IDTs and 1 FDT. (<b>e</b>) With 3 IDTs and 2 FDTs. (<b>f</b>) With 3 IDTs and 3 FDTs.</p>
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<p>Determination of the optimal model parameters: (<b>a</b>) MSE-epoch curves including the training MSE, training set MSE, and validation set MSE. (<b>b</b>) Position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, estimated compensation <math display="inline"><semantics> <msub> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mrow> <mi>comp</mi> <mn>2</mn> </mrow> </mrow> </msub> </semantics></math>, and position error after offline compensation using the selected parameters.</p>
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<p>A simulation platform for the proposed QSMO-based sensorless drive scheme.</p>
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<p>Test results of the proposed QSMO-based parameter adaptation method: (<b>a</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated speed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, actual speed <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>. (<b>b</b>) Boundary layer <math display="inline"><semantics> <msub> <mi>m</mi> <mi mathvariant="normal">f</mi> </msub> </semantics></math>, sliding mode gain <math display="inline"><semantics> <msub> <mi>k</mi> <mi mathvariant="normal">s</mi> </msub> </semantics></math>, estimated EEMF <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>α</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>β</mi> </msub> </semantics></math>, and QSMO bandwidth <math display="inline"><semantics> <msub> <mi>ω</mi> <mi>QSMO</mi> </msub> </semantics></math>.</p>
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<p>Test results of the proposed QSMO-based phase lag compensation method: (<b>a</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated speed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, actual speed <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math> at a constant speed of 1500 rpm. (<b>b</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated and actual speeds <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math> at a constant speed of 2000 rpm.</p>
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<p>Test results of the proposed NN-based transient position error compensation method: (<b>a</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated speed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, actual speed <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math> before transient position error compensation. (<b>b</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated and actual speeds <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math> after the compensation. (<b>c</b>) Estimated EEMF <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>α</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>β</mi> </msub> </semantics></math> after the compensation.</p>
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<p>Test results in a simulated wide-speed application scenario for the air compressor: (<b>a</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated speed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, actual speed <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math> before transient position error compensation. (<b>b</b>) Torque <math display="inline"><semantics> <msub> <mi>T</mi> <mi mathvariant="normal">e</mi> </msub> </semantics></math>, estimated and actual speeds <math display="inline"><semantics> <msub> <mover accent="true"> <mi>N</mi> <mo stretchy="false">^</mo> </mover> <mi mathvariant="normal">r</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">r</mi> </msub> </semantics></math>, speed error <math display="inline"><semantics> <msub> <mi>N</mi> <mrow> <mi mathvariant="normal">r</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math>, and position error <math display="inline"><semantics> <msub> <mi>θ</mi> <mrow> <mi mathvariant="normal">e</mi> <mo>_</mo> <mi>err</mi> </mrow> </msub> </semantics></math> after the compensation. (<b>c</b>) Estimated EEMF <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>α</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mover accent="true"> <mi>e</mi> <mo stretchy="false">^</mo> </mover> <mi>β</mi> </msub> </semantics></math> after the compensation.</p>
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15 pages, 3109 KiB  
Article
Sensorless Control for a Permanent Magnet Synchronous Motor Based on a Sliding Mode Observer
by Jinfa Liang, Jun Wu, Yong Wang, Zhihong Zhong and Xinxin Bai
Eng 2024, 5(3), 1737-1751; https://doi.org/10.3390/eng5030091 - 2 Aug 2024
Viewed by 507
Abstract
This paper proposes a sensorless control strategy for permanent magnet synchronous motors (PMSMs) based on a sliding mode observer (SMO), and high-speed PMSM sensorless velocity control is realized. To solve the serious chattering and phase lag problems of conventional SMOs, the continuous function [...] Read more.
This paper proposes a sensorless control strategy for permanent magnet synchronous motors (PMSMs) based on a sliding mode observer (SMO), and high-speed PMSM sensorless velocity control is realized. To solve the serious chattering and phase lag problems of conventional SMOs, the continuous function is used as the control function, and the low-pass filter is improved into a back electromotive force (EMF) observer with an adaptive structure. In addition, the phase-locked loop is combined to perform the SMO-based sensorless control. The simulations and experiments prove the effectiveness of the proposed strategy. Full article
(This article belongs to the Section Electrical and Electronic Engineering)
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<p>Conventional SMO.</p>
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<p>Saturation function.</p>
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<p>Continuous function.</p>
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<p>Block diagram of SMO based on PLL.</p>
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<p>Equivalent block diagram of PLL.</p>
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<p>Improved SMO.</p>
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<p>Block diagram of a PMSM sensorless control system based on the improved SMO.</p>
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<p>Schematic diagram of the experimental platform for a PMSM based on the Myway system.</p>
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<p>Pictures of the experimental platform for a PMSM based on the Myway system.</p>
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<p>Experimental result of closed-loop control with speed change without load torque.</p>
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<p>Experimental result of closed-loop control with a constant speed and load torque change.</p>
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18 pages, 8389 KiB  
Article
Sensorless Capability Expansion for SPMSM Based on Inductance Parameter Identification
by Peng Chen, Ruiqing Ma, Shoujun Song and Zhe Chen
Energies 2024, 17(13), 3219; https://doi.org/10.3390/en17133219 - 30 Jun 2024
Viewed by 569
Abstract
Pulsating high-frequency voltage injection can be used for the sensorless control of a surface-mounted permanent magnet synchronous motor (SPMSM) at zero- and low-speed ranges. However, the sensorless capability still faces challenges to the requirements of industrial application, especially at heavy load status. Aiming [...] Read more.
Pulsating high-frequency voltage injection can be used for the sensorless control of a surface-mounted permanent magnet synchronous motor (SPMSM) at zero- and low-speed ranges. However, the sensorless capability still faces challenges to the requirements of industrial application, especially at heavy load status. Aiming at this issue, this article proposes a sensorless capability expansion method for an SPMSM based on inductance parameter identification. Firstly, incremental inductances at the d-q-axis and cross-coupling inductance are identified offline by three steps combining the rotating high-frequency voltage injection and pulsating high-frequency voltage injection. Using a polynomial curve fitting algorithm, apparent inductances are calculated. Secondly, positive DC current injection at the d-axis is proposed to enhance the saliency ratio based on the analysis of parameter identification results. Compared with the conventional id = 0 or id < 0 method, the saliency ratio is enhanced obviously when a positive DC current is injected at the d-axis. Then, the convergence region of the sensorless control method at heavy load status is expanded and the accuracy of rotor position estimation is improved using the proposed method. Finally, the experimental results validate that the sensorless capability of the SPMSM is expanded. Full article
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<p>Incremental inductance and apparent inductance.</p>
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<p>Equivalent circuit on the <span class="html-italic">d-q</span>-axis: (<b>a</b>) <span class="html-italic">d-axis</span>; (<b>b</b>) <span class="html-italic">q-axis</span>.</p>
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<p>Reference frame and rotor position estimation.</p>
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<p>Conventional pulsating high-frequency voltage injection method.</p>
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<p>The proposed sensorless capability expansion method for SPMSM.</p>
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<p>Experiment platform.</p>
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<p>Incremental inductance identification: (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mi>d</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mi>q</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>d</mi> <mi>q</mi> <mi>h</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) −<math display="inline"><semantics> <mrow> <mn>0.5</mn> <msub> <mi>θ</mi> <mi>m</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Incremental inductance identification: (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mi>d</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mi>q</mi> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi>L</mi> <mrow> <mi>d</mi> <mi>q</mi> <mi>h</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>d</b>) −<math display="inline"><semantics> <mrow> <mn>0.5</mn> <msub> <mi>θ</mi> <mi>m</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Sum of squares (SOS) approximation error as the function of the polynomial order m for <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>d</mi> <mo>_</mo> <mi>a</mi> <mi>d</mi> <mi>j</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math> and order n for <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>q</mi> <mo>_</mo> <mi>a</mi> <mi>d</mi> <mi>j</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>d</mi> <mo>_</mo> <mi>a</mi> <mi>d</mi> <mi>j</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>q</mi> <mo>_</mo> <mi>a</mi> <mi>d</mi> <mi>j</mi> </mrow> <mrow> <mi>i</mi> <mi>n</mi> <mi>c</mi> </mrow> </msubsup> </mrow> </semantics></math>.</p>
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<p>Apparent inductance identification result: (<b>a</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mi>d</mi> <mrow> <mi>a</mi> <mi>p</mi> <mi>p</mi> </mrow> </msubsup> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msubsup> <mi>L</mi> <mi>q</mi> <mrow> <mi>a</mi> <mi>p</mi> <mi>p</mi> </mrow> </msubsup> </mrow> </semantics></math>.</p>
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<p>Saliency ratio variation with <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>d</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>i</mi> <mi>q</mi> </msub> </mrow> </semantics></math>.</p>
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<p>Experimental results of convergence range comparison at 120 r/min: (<b>a</b>) conventional method; (<b>b</b>) zoom in of the conventional method in which sensorless control of the SPMSM fails when the load is increased to a 130% rated value; (<b>c</b>) proposed method without compensation for the position estimation error due to the cross-coupling effect; (<b>d</b>) proposed method with compensation for the position estimation error due to the cross-coupling effect.</p>
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<p>Comparison of rotor position estimation during starting process (from 0 to 120 r/min with rated load): (<b>a</b>) conventional method; (<b>b</b>) proposed method.</p>
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<p>Rotor position estimation at 120 r/min with rated load: (<b>a</b>) conventional method; (<b>b</b>) proposed method.</p>
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<p>Rotor position estimation during the dynamic process of speed reversal test with rated load (rotor speed changes from −120 r/min to 120 r/min, then back to −120 r/min): (<b>a</b>) conventional method; (<b>b</b>) proposed method.</p>
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<p>Rotor position estimation during the loading and unloading process at 120 r/min (load increases from 0 to rated value, then back to 0): (<b>a</b>) conventional method; (<b>b</b>) proposed method.</p>
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<p>Rotor position estimation at 120 r/min with a 200% rated load: (<b>a</b>) without compensation for the error due to cross-coupling effect; (<b>b</b>) with compensation for the error due to cross-coupling effect.</p>
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15 pages, 3142 KiB  
Article
Sensorless Control of Surface-Mount Permanent-Magnet Synchronous Motors Based on an Adaptive Super-Twisting Sliding Mode Observer
by Hengqiang Wang, Guangming Zhang and Xiaojun Liu
Mathematics 2024, 12(13), 2029; https://doi.org/10.3390/math12132029 - 29 Jun 2024
Cited by 1 | Viewed by 488
Abstract
The Sliding Mode Observer (SMO) is widely used for the sensorless control of Permanent-Magnet Synchronous Motors (PMSMs) due to its simple structure and strong parameter robustness. However, traditional SMOs have a limited speed range and suffer from chattering issues, which affect the accuracy [...] Read more.
The Sliding Mode Observer (SMO) is widely used for the sensorless control of Permanent-Magnet Synchronous Motors (PMSMs) due to its simple structure and strong parameter robustness. However, traditional SMOs have a limited speed range and suffer from chattering issues, which affect the accuracy of rotor position estimation. To address these problems, this paper proposes an Adaptive Super-Twisting SMO (AST-SMO) method. First, a fast super-twisting function is designed to resolve the step problem that occurs at the zero-crossing of the traditional sign function. Next, an adaptive-tracking high-order Sliding Mode Observer is constructed to extend the speed range of the SMO. The stability of the system is proven using the Lyapunov theorem. Finally, a sensorless control system for PMSMs is implemented and validated in MATLAB/SIMULINK. The results indicate that, compared to the traditional SMO, the AST-SMO reduces the back EMF THD from 20.03% to 14.2%. Additionally, the rotor estimation error across all speed ranges is less than 0.01. Therefore, AST-SMO offers a higher tracking accuracy, a wider speed range, and effectively suppresses sliding mode chattering and harmonic interference. Full article
(This article belongs to the Section Dynamical Systems)
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<p>Image of the sign function.</p>
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<p>Image of the hyperbolic function under <span class="html-italic">α</span> = 2.</p>
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<p>Block diagram of the PLL.</p>
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<p>Block diagram of the AST-SMO.</p>
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<p>Simulated dynamic response under HSMO.</p>
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<p>Simulated dynamic response under AST-SMO.</p>
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<p>The steady-state simulation results of the HSMO for (<b>a</b>) 500 r/min and (<b>b</b>) 800 r/min.</p>
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<p>The steady−state simulation results of the AST−SMO for (<b>a</b>) 500 r/min and (<b>b</b>) 800 r/min.</p>
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<p>The steady−state simulation results of the AST−SMO for (<b>a</b>) 500 r/min and (<b>b</b>) 800 r/min.</p>
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<p>The estimated back EMF results at 800 rpm for (<b>a</b>) the HSMO and (<b>b</b>) the AST−SMO.</p>
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<p>The estimated back EMF results at 800 rpm for (<b>a</b>) the HSMO and (<b>b</b>) the AST−SMO.</p>
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<p>The FFT analysis results at 800 rpm for (<b>a</b>) the HSMO and (<b>b</b>) the AST-SMO.</p>
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20 pages, 14884 KiB  
Article
Current Sensor Fault-Tolerant Control Strategy for Speed-Sensorless Control of Induction Motors Based on Sequential Probability Ratio Test
by Feige Zhang, Shesheng Gao, Wenjuan Zhang, Guo Li and Chao Zhang
Electronics 2024, 13(13), 2476; https://doi.org/10.3390/electronics13132476 - 25 Jun 2024
Viewed by 593
Abstract
In the speed-sensorless vector control of induction motors (IMs), the speed estimation accuracy suffers from the deteriorated current measurement caused by the current sensor faults, such as open circuit in one phase, DC bias, and odd harmonics. In this paper, a novel speed [...] Read more.
In the speed-sensorless vector control of induction motors (IMs), the speed estimation accuracy suffers from the deteriorated current measurement caused by the current sensor faults, such as open circuit in one phase, DC bias, and odd harmonics. In this paper, a novel speed estimation strategy based on the current sensor fault-tolerant control is proposed to improve the speed estimation accuracy under the current sensor faults. First, to detect the current sensor faults in real time, the sequential probability ratio test is introduced to the system by using the innovations of the extended Kalman filter (EKF). Second, to ensure speed estimation accuracy, a double-cascading second-order generalized integrator (DSOGI) is employed to reconstruct the faulty current information when a fault is identified. Finally, the reconstructed current information is fed back to the sequential probability extended Kalman filter (SPEKF), which estimates the rotor speed of the IM, and high-accuracy speed estimation under the condition of current sensor faults is achieved. The effectiveness of the proposed strategy is validated by a series of experiments, which were conducted on a 3 kW induction motor drive platform. Full article
(This article belongs to the Special Issue New Insights Into Smart and Intelligent Sensors)
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<p>The flowchart for diagnosing a current sensor fault based on the SPRT.</p>
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<p>Scheme of reconstructing current signal of <math display="inline"><semantics> <mi mathvariant="sans-serif">β</mi> </semantics></math> axis.</p>
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<p>Bode plots of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mn>1</mn> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mn>2</mn> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math>.</p>
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<p>Improved scheme of reconstructing current signal of β axis.</p>
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<p>Bode plots of <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mn>3</mn> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> (red) and <math display="inline"><semantics> <mrow> <msub> <mi>G</mi> <mn>4</mn> </msub> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </semantics></math> (blue).</p>
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<p>Block diagram of proposed current sensor fault-tolerant control strategy for speed-sensorless IM drive system based on EKF.</p>
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<p>Induction motor experiment platform.</p>
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<p>Rotor speed estimation of SPEKF-DSOGI under no load.</p>
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<p>Results of dynamic tracking performance test during sudden increase or decrease in load.</p>
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<p>Experimental results of fault-tolerant strategy obtained under open-circuit fault in A-phase: (<b>a</b>) open-circuit fault occurred in A-phase, (<b>b</b>) SPEKF-SOGI estimated motor speed, and (<b>c</b>) SPEKF-DSOGI estimated motor speed.</p>
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<p>Experimental results of fault-tolerant strategy obtained under DC bias fault in A-phase: (<b>a</b>) DC bias fault occurs in A-phase, (<b>b</b>) SPEKF-SOGI estimated motor speed, and (<b>c</b>) SPEKF-DSOGI estimated motor speed.</p>
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<p>Experimental results of fault tolerance strategy obtained when odd harmonics were added to A-phase current: (<b>a</b>) odd harmonics were added to A-phase current, (<b>b</b>) SPEKF-SOGI estimated motor speed, and (<b>c</b>) SPEKF-DSOGI estimated motor speed.</p>
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<p>The open-circuit fault in the A-phase current sensor of the IM drives: (<b>a</b>) performance comparison between SPEKF-DSOGI, SEPLL, and the conventional current reconstruction scheme, and (<b>b</b>) estimated motor speed for the three schemes.</p>
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<p>The DC bias fault in the A-phase current sensor of the IM drives: (<b>a</b>) performance comparison between SPEKF-DSOGI, SEPLL, and the conventional current reconstruction scheme and (<b>b</b>) estimated motor speed for the three schemes.</p>
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<p>The gain fault in the A-phase current sensor of the IM drives: (<b>a</b>) performance comparison between SPEKF-DSOGI, SEPLL, and the conventional current reconstruction scheme and (<b>b</b>) estimated motor speed for the three schemes.</p>
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<p>The harmonic fault in the A-phase current sensor of the IM drives: (<b>a</b>) performance comparison between SPEKF-SOGI, SEPLL, and the conventional current reconstruction scheme and (<b>b</b>) estimated motor speed for the three schemes.</p>
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22 pages, 8574 KiB  
Article
Study on Mathematical Models for Precise Estimation of Tire–Road Friction Coefficient of Distributed Drive Electric Vehicles Based on Sensorless Control of the Permanent Magnet Synchronous Motor
by Binghao Yu, Yiming Hu and Dequan Zeng
Symmetry 2024, 16(7), 792; https://doi.org/10.3390/sym16070792 - 24 Jun 2024
Viewed by 838
Abstract
In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a [...] Read more.
In order to reduce the use of wheel angular velocity sensors and improve the estimation accuracy and robustness of the tire–road friction coefficient (TRFC) in non-Gaussian noise environments, this paper proposes a sensorless control-based distributed drive electric vehicle TRFC estimation algorithm using a permanent magnet synchronous motor (PMSM). The algorithm replaces the wheel angular velocity signal with the rotor speed signal obtained from the sensorless control of the PMSM. Firstly, a seven-degree-of-freedom vehicle dynamics model and a mathematical model of the PMSM are established, and the maximum correntropy singular value decomposition generalized high-degree cubature Kalman filter algorithm (MCSVDGHCKF) is derived. Secondly, a sensorless control system of a PMSM based on the MCSVDGHCKF algorithm is established to estimate the rotor speed and position of the PMSM, and its effectiveness is verified. Finally, the feasibility of the algorithm for TRFC estimation in non-Gaussian noise is demonstrated through simulation experiments, the Root Mean Square Error (RMSE) of TRFC estimates for the right front wheel and the left rear wheel were reduced by at least 41.36% and 40.63%, respectively. The results show that the MCSVDGHCKF has a higher accuracy and stronger robustness compared to the maximum correntropy high-degree cubature Kalman filter (MCHCKF), singular value decomposition generalized high-degree cubature Kalman filter (SVDGHCKF), and high-degree cubature Kalman filter (HCKF). Full article
(This article belongs to the Section Engineering and Materials)
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<p>Seven-degree-of-freedom vehicle dynamics model.</p>
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<p>Flowchart of MCSVDGHCKF algorithm.</p>
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<p>TRFC estimation scheme based on sensorless control of PMSM.</p>
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<p>Carsim drivetrain setup.</p>
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<p>PMSM velocity estimation and estimated error curve under serpentine conditions. (<b>a</b>) Rotor speed estimate; (<b>b</b>) rotor speed estimate error.</p>
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<p>PMSM rotor position estimation under serpentine conditions.</p>
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<p>PMSM velocity estimation and estimated error curve under step conditions. (<b>a</b>) Rotor speed estimate; (<b>b</b>) rotor speed estimate error.</p>
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<p>PMSM rotor position estimation under step conditions.</p>
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<p>The measured value of the sensor under serpentine conditions. (<b>a</b>) Longitudinal and lateral acceleration measurements; (<b>b</b>) yaw rate measurements.</p>
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<p>Estimated TRFC of the right front wheel and estimated error curve under serpentine conditions. (<b>a</b>) Right front wheel TRFC estimate; (<b>b</b>) right front wheel TRFC estimate error.</p>
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<p>Estimated TRFC of the left rear wheel and estimated error curve under serpentine conditions. (<b>a</b>) Left rear wheel TRFC estimate; (<b>b</b>) left rear wheel TRFC estimate error.</p>
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<p>Schematic diagram of the bisectional test path.</p>
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<p>Sensor measurement under step conditions. (<b>a</b>) Longitudinal and lateral acceleration measurements; (<b>b</b>) yaw rate measurements.</p>
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<p>Estimated TRFC of the right front wheel and estimated error curve under step conditions. (<b>a</b>) Right front wheel TRFC estimate; (<b>b</b>) right front wheel TRFC estimate error.</p>
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<p>Estimated TRFC of the left rear wheel and estimated error curve under step conditions. (<b>a</b>) Left rear wheel TRFC estimate; (<b>b</b>) left rear wheel TRFC estimate error.</p>
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19 pages, 5174 KiB  
Article
Finite Speed-Set Model Reference Adaptive System Based on Sensorless Control of Permanent Magnet Synchronous Generators for Wind Turbines
by Mohammed A. Hassan, Mahmoud M. Adel, Ahmed Farhan and Amr A. Saleh
Machines 2024, 12(7), 429; https://doi.org/10.3390/machines12070429 - 24 Jun 2024
Viewed by 568
Abstract
This paper proposes a novel finite speed-set model reference adaptive system (FSS-MRAS) based on the current predictive control (CPC) of a permanent magnet synchronous generator (PMSG) in wind energy turbine systems (WETSs). The mathematical models of wind energy systems (WESs) coupled with a [...] Read more.
This paper proposes a novel finite speed-set model reference adaptive system (FSS-MRAS) based on the current predictive control (CPC) of a permanent magnet synchronous generator (PMSG) in wind energy turbine systems (WETSs). The mathematical models of wind energy systems (WESs) coupled with a permanent magnet synchronous generator (PMSG) are presented in addition to the implementation of the CPC of PMSGs. The proposed FSS-MRAS is based on eliminating the tuning burden of the conventional MRAS by using a limited set of speeds of the PMSG rotor that are employed to predict the rotor speed of the generator. Consequently, the optimal speed of the rotor is the one resulting from the optimization of a proposed new cost function. Accordingly, the conventional MRAS controller is eliminated and the main disadvantage represented in the tuning burden of the constant-gain proportional-integral (PI) controller has been overcome. The proposed FSS-MRAS observer is validated using MATLAB/Simulink (R2023b) at different operating conditions. The results of the proposed FSS-MRAS have been compared with those of the conventional MRAS, which proved the high robustness and reliability of the proposed observer. Full article
(This article belongs to the Section Electrical Machines and Drives)
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<p><math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">C</mi> </mrow> <mrow> <mi mathvariant="normal">p</mi> </mrow> </msub> </mrow> </semantics></math> vs. <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">λ</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">β</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> [<a href="#B26-machines-12-00429" class="html-bibr">26</a>].</p>
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<p>Two-level three-phase inverter: (<b>a</b>) PMSG fed by a three-phase inverter, and (<b>b</b>) voltage space vectors [<a href="#B31-machines-12-00429" class="html-bibr">31</a>,<a href="#B32-machines-12-00429" class="html-bibr">32</a>].</p>
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<p>Traditional MRAS estimator block diagram.</p>
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<p>Block diagram for the proposed FSS-MRAS observer.</p>
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<p>The proposed sensor-less FSS-MRAS estimator of the PMSG for a wind turbine system.</p>
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<p>Simulation results of the proposed FSS-MRAS observer against the conventional MRAS at rated wind speed (15 m/s).</p>
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<p>Simulation results of the proposed FSS-MRAS observer against the conventional MRAS at low wind speed (5 m/s).</p>
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<p>Performance of the proposed FSS-MRAS against the conventional observer at wide dynamics in wind speed.</p>
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<p>Performance of a proposed FSS-MRAS and a classical one at step variations of PMSG resistance: (<b>a</b>) traditional MRAS; (<b>b</b>) FSS-MRAS estimator.</p>
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<p>Performance of the proposed FSS-MRAS and the classical one at step variations of PMSG inductance: (<b>a</b>) traditional MRAS; (<b>b</b>) FSS-MRAS estimator.</p>
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23 pages, 9346 KiB  
Article
PMSM Sensorless Control Based on Moving Horizon Estimation and Parameter Self-Adaptation
by Aoran Chen, Wenbo Chen and Heng Wan
Electronics 2024, 13(13), 2444; https://doi.org/10.3390/electronics13132444 - 21 Jun 2024
Viewed by 624
Abstract
The field of sensorless control of permanent magnet synchronous motor (PMSM) systems has been the subject of extensive research. The accuracy of sensorless controllers depends on the precise estimation of PMSM state quantities, including rotational speed and rotor position. In order to enhance [...] Read more.
The field of sensorless control of permanent magnet synchronous motor (PMSM) systems has been the subject of extensive research. The accuracy of sensorless controllers depends on the precise estimation of PMSM state quantities, including rotational speed and rotor position. In order to enhance state estimation accuracy, this paper proposes a moving horizon estimator that can be utilized in the sensorless control system of PMSM. Considering the parameter variations observed in PMSM, a nonlinear mathematical model of PMSM is established. A model reference adaptive system (MRAS) is employed to identify parameters such as resistance, inductance, and magnetic chain in real time. This approach can mitigate the impact of parameter fluctuations. Moving horizon estimation (MHE) is an estimation method based on optimization that can directly handle nonlinear system models. In order to eliminate the influence of external interference and improve the robustness of state estimation, a method based on MHE has been designed for PMSM, and a sensorless observer has been established. Considering the traditional MHE with large computation and high memory occupation, the calculation of MHE is optimized by utilizing a Hessian matrix and gradient vector. The speed and position of the PMSM are estimated within constraints during a single-step iteration. The results of the simulation demonstrate that in comparison to the traditional control structure, the estimation error of rotational speed and rotor position can be reduced by utilizing the proposed method. A more accurate estimation can be achieved with good adaptability and computational speed, which can enhance the robustness of the control system of PMSM. Full article
(This article belongs to the Special Issue Advances in Control for Permanent Magnet Synchronous Motor (PMSM))
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<p>Block diagram of parameter identification of MRAS.</p>
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<p>Schematic diagram of MHE method.</p>
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<p>SPMSM sensorless control scheme.</p>
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<p>Measurement of speed (SPMSM operates under Condition I with PI controller, EKF, and MHE use the same parameter initialization settings).</p>
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<p>Measurement of <span class="html-italic">i<sub>d</sub></span> and <span class="html-italic">i<sub>q</sub></span>, under condition I.</p>
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<p>Error of speed estimation, under condition I.</p>
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<p>Measurement of rotor position (under Condition I, in case of sudden torque change at 1.2 s).</p>
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<p>Error of rotor position estimation, under condition I.</p>
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<p>Measurement of speed under Condition II.</p>
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<p>Error of speed estimation, under Condition II.</p>
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<p>Measurement of <span class="html-italic">i<sub>d</sub></span> and <span class="html-italic">i<sub>q</sub></span>.</p>
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<p>Measurement of rotor position under Condition II.</p>
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<p>Error of rotor position estimation, under Condition II.</p>
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<p>Errors of speed estimation. (horizon chooses <span class="html-italic">N</span> = 3, 5, 10).</p>
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<p>Error of position estimation (horizon chooses <span class="html-italic">N</span> = 3, 5, 10).</p>
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<p>Error values of speed and rotor position with different <span class="html-italic">N</span>.</p>
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<p>The speed estimation and error of estimation of two approaches demonstrate the impact of MRAS on the accuracy of estimate findings.</p>
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<p>Position estimation of two MHE strategies.</p>
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<p>The impact of MRAS on the accuracy of estimation as demonstrated by the value of RMSE.</p>
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<p>Identification of flux, rotor resistance, and inductance by MRAS.</p>
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<p>Error of speed estimation, where red represents the general MHE and blue represents the optimized MHE calculated by the Hessian matrix and gradient vector.</p>
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<p>Error of rotor position estimation of the two schemes, in which blue represents the general MHE and red represents the optimized MHE calculated by the Hessian matrix and gradient vector.</p>
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17 pages, 2327 KiB  
Article
Observer-Based Suboptimal Controller Design for Permanent Magnet Synchronous Motors: State-Dependent Riccati Equation Controller and Impulsive Observer Approaches
by Nasrin Kalamian, Masoud Soltani, Fariba Bouzari Liavoli and Mona Faraji Niri
Computers 2024, 13(6), 142; https://doi.org/10.3390/computers13060142 - 4 Jun 2024
Viewed by 751
Abstract
Permanent Magnet Synchronous Motors (PMSMs) with high energy efficiency, reliable performance, and a relatively simple structure are widely utilised in various applications. In this paper, a suboptimal controller is proposed for PMSMs without sensors based on the state-dependent Riccati equation (SDRE) technique combined [...] Read more.
Permanent Magnet Synchronous Motors (PMSMs) with high energy efficiency, reliable performance, and a relatively simple structure are widely utilised in various applications. In this paper, a suboptimal controller is proposed for PMSMs without sensors based on the state-dependent Riccati equation (SDRE) technique combined with customised impulsive observers (IOs). Here, the SDRE technique facilitates a pseudo-linearised display of the motor with state-dependent coefficients (SDCs) while preserving all its nonlinear features. Considering the risk of non-available/non-measurable states in the motor due to sensor and instrumentation costs, the SDRE is combined with IOs to estimate the PMSM speed and position states. Customised IOs are proven to be capable of obtaining quality, continuous estimates of the motor states despite the discrete format of the output signals. The simulation results in this work illustrate an accurate state estimation and control mechanism for the speed of the PMSM in the presence of load torque disturbances and reference speed changes. It is clearly shown that the SDRE-IO design is superior compared to the most popular existing regulators in the literature for sensorless speed control. Full article
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<p>Block control diagram of the proposed method.</p>
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<p>Speed profiles of the PMSM, the state estimation, the tracking error, and the speed impulses, together with the zoomed-in areas.</p>
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<p>Current on the d-axis of the PMSM, the estimated states, the errors, and the impulses.</p>
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<p>Current on the q-axis of the PMSM, the estimated states, the errors, and the impulses.</p>
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<p>Voltage along the <span class="html-italic">d</span>-axis and <span class="html-italic">q</span>-axis of the PMSM, along with the <span class="html-italic">d</span>–<span class="html-italic">q</span> axis.</p>
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<p>Impulsive observer gains over the course of estimation and control.</p>
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<p>Load torque impulsive observer gains, speed tracking and estimation with load torque, speed tracking error with load torque, and speed estimation error with load torque.</p>
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<p>Comparison of PMSM parameters between the SDRE and the LQR.</p>
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16 pages, 4909 KiB  
Article
Research on Sliding Mode Variable Structure Model Reference Adaptive System Speed Identification of Bearingless Induction Motor
by Wenshao Bu, Wenqing Tao and Youpeng Chen
Energies 2024, 17(11), 2615; https://doi.org/10.3390/en17112615 - 29 May 2024
Viewed by 457
Abstract
To improve the speed observation accuracy of the bearingless induction motor (BL-IM) and achieve its high-performance speed sensorless control, an improved sliding mode variable structure model reference adaptive system speed identification method based on sigmoid function (sigmoid-VS-MRAS) is proposed. Firstly, to overcome the [...] Read more.
To improve the speed observation accuracy of the bearingless induction motor (BL-IM) and achieve its high-performance speed sensorless control, an improved sliding mode variable structure model reference adaptive system speed identification method based on sigmoid function (sigmoid-VS-MRAS) is proposed. Firstly, to overcome the problem of initial values and cumulative errors in the pure integration link of the reference flux-linkage voltage model, the rotor flux-linkage reference voltage model has been improved by using an equivalent integrator instead of the pure integration link. Then, in order to improve the rapidity and robustness of speed identification, the sliding mode variable structure adaptive law is adopted instead of the PI adaptive law. In addition, in order to optimize the sliding mode variable structure adaptive law and overcome the sliding mode chattering problem, a sigmoid function with smooth continuity characteristics is used instead of the sign function. Finally, on the basis of the inverse system decoupling control of a BL-IM, simulation experiments were conducted to verify the sigmoid-VS-MRAS speed identification method. The research results indicate that when the proposed speed identification method is adopted, not only higher identification accuracy and rapidity can be achieved than traditional PI-MRAS methods, but it can also eliminate the problem of high-frequency vibration (with an amplitude of about 3.0 r/min) when using the sign-VS-MRAS method; meanwhile, the steady-state tracking speed with zero deviation can still be maintained after loading. Full article
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<p>Schematic diagram of research method flow.</p>
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<p>Schematic diagram of improved rotor flux-linkage voltage model.</p>
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<p>Structure diagram of VS-MRAS rotor flux-linkage observation and speed identification.</p>
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<p>Speed sensorless inverse decoupling control system structure of a BL-IM based on VS-MRAS speed identification.</p>
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<p>Motor speed response waveform on non-load starting: (<b>a</b>) speed response waveform; (<b>b</b>) identification error of motor speed.</p>
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<p>Rotor flux-linkage waveform at no load: (<b>a</b>) <span class="html-italic">α</span>-axis and <span class="html-italic">β</span>-axis rotor flux-linkage components; (<b>b</b>) error between the amplitude and given value of rotor flux-linkage.</p>
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<p>Seed response waveform during loading and speed regulation: (<b>a</b>) response waveform of motor speed; (<b>b</b>) identification error of motor speed.</p>
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<p>Response waveforms of rotor flux-linkage during loading and speed regulation: (<b>a</b>) waveforms of α-axis and β-axis rotor flux-linkage components; (<b>b</b>) error waveform between the amplitude of the rotor flux-linkage and its given value.</p>
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<p>Response waveforms of α-axis and β-axis displacements.</p>
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17 pages, 4242 KiB  
Article
A Reliable and Efficient I-f Startup Method of Sensorless Ultra-High-Speed SPMSM for Fuel Cell Air Compressors
by Jilei Xing, Yao Xu, Junzhi Zhang, Yongshen Li and Xiongwei Jiang
Actuators 2024, 13(6), 203; https://doi.org/10.3390/act13060203 - 29 May 2024
Viewed by 635
Abstract
Extended back electromotive force (EEMF)-based position sensorless field-oriented control (FOC) is widely utilized for ultra-high-speed surface-mounted permanent magnet synchronous motors (UHS-SPMSMs) driven fuel cell air compressors in medium-high speed applications. Unfortunately, the estimated position is imprecise due to too small EEMF under low [...] Read more.
Extended back electromotive force (EEMF)-based position sensorless field-oriented control (FOC) is widely utilized for ultra-high-speed surface-mounted permanent magnet synchronous motors (UHS-SPMSMs) driven fuel cell air compressors in medium-high speed applications. Unfortunately, the estimated position is imprecise due to too small EEMF under low speed operation. Hence, current-to-frequency (I-f) control is more suitable for startup. Conventional I-f methods rarely achieve the tradeoff between startup acceleration and load capacity, and the transition to sensorless FOC is mostly realized in the constant-speed stage, which is unacceptable for UHS-SPMSM considering the critical requirement of startup time. In this article, a new closed-loop I-f control approach is proposed to achieve fast and efficient startup. The frequency of reference current vector is corrected automatically based on the active power and the real-time motor torque, which contributes to damping effect for startup reliability. Moreover, an amplitude compensator of reference current vector is designed based on the reactive power, ensuring the maximum torque per ampere operation and higher efficiency. Furthermore, the speed PI controller is enhanced by variable bandwidth design for smoother sensorless transition. These theoretical advantages are validated through experiments with a 550 V, 35 kW UHS-SPMSM. The experimental results demonstrated the enhanced startup performance compared with conventional I-f control. Full article
(This article belongs to the Special Issue Power Electronics and Actuators)
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<p>Vector diagram including <span class="html-italic">d-q</span> and <span class="html-italic">γ-δ</span> frames for UHS-SPMSM.</p>
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<p>Current vector amplitude and frequency of conventional I-f control.</p>
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<p>Small signal model of UHS-SPMSM under conventional I-f control.</p>
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<p>The variation between <span class="html-italic">T<sub>e</sub></span> and <span class="html-italic">θ<sub>err</sub></span>.</p>
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<p>Amplitude compensation design.</p>
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<p>The overall schematic diagram of the proposed I-f startup method, including transition to FOC. The two switches (<span class="html-italic">S</span><sub>1</sub> and <span class="html-italic">S</span><sub>2</sub>) are connected to terminal 1 for the proposed I-f control and 2 for sensorless FOC (where MTPA denotes maximum torque per ampere and SVPWM denotes space vector pulse width modulation, and EEMF-based position and speed estimation can be found in our previous research [<a href="#B35-actuators-13-00203" class="html-bibr">35</a>]).</p>
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<p>Overall experimental system test bench.</p>
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<p>Startup performance from standstill to 7000 r/min. (<b>a</b>) Conventional I-f control. (<b>b</b>) Proposed closed-loop I-f control.</p>
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<p>Startup performance from standstill to 30,000 r/min with transition from I–f control to sensorless FOC at 12,000 r/min. (<b>a</b>) Conventional I-f control with fixed-gain speed PI controller. (<b>b</b>) Proposed closed-loop I-f control with fixed-gain speed PI controller. (<b>c</b>) Proposed closed-loop I-f control with variable bandwidth speed PI controller.</p>
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19 pages, 7939 KiB  
Article
Inductance Estimation Based on Wavelet-GMDH for Sensorless Control of PMSM
by Gwangmin Park and Junhyung Bae
Appl. Sci. 2024, 14(11), 4386; https://doi.org/10.3390/app14114386 - 22 May 2024
Viewed by 569
Abstract
In permanent magnet synchronous motor (PMSM) sensorless drive systems, the motor inductance is a crucial parameter for rotor position estimation. Variations in the motor current induce changes in the inductance, leading to core magnetic saturation and degradation in the accuracy of rotor position [...] Read more.
In permanent magnet synchronous motor (PMSM) sensorless drive systems, the motor inductance is a crucial parameter for rotor position estimation. Variations in the motor current induce changes in the inductance, leading to core magnetic saturation and degradation in the accuracy of rotor position estimation. In systems with constant load torque, the saturated inductance remains constant. This inductance error causes a consistent error in rotor position estimation and some performance degradation, but it does not result in speed estimation errors. However, in systems with periodic load torque, the error in the saturated inductance varies, consequently causing fluctuations in both the estimated position and speed errors. Periodic speed errors complicate speed control and degrade the torque compensation performance. In this paper, we propose a wavelet denoising-group method of data handling (GMDH) based method for accurate inductance estimation in PMSM sensorless control systems with periodic load torque compensation. We present a method to analyze and filter the collected three-phase current signals of the PMSM using wavelet transformation and utilize the filtered results as inputs to GMDH for training. Additionally, a method for magnetic saturation compensation using the inductance parameter estimator is proposed to minimize periodic speed fluctuations and improve control accuracy. To replicate the load conditions and parameter variations equivalent to the actual system, experiments were conducted to measure the speed ripples, inductance variations, and torque component of the current. Finally, software simulation was performed to confirm the inductance estimation results and verify the proposed method by simulating load conditions equivalent to the experimental results. Full article
(This article belongs to the Special Issue Advanced Control Systems and Applications)
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<p>Block diagram of extended EMF based sensorless control algorithm.</p>
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<p>Comparison of estimated position errors (<b>a</b>) without extended back EMF errors, (<b>b</b>) with <math display="inline"><semantics> <mrow> <mi>γ</mi> </mrow> </semantics></math>-axis extended back EMF error (<math display="inline"><semantics> <mrow> <msub> <mrow> <mo>∆</mo> <mi>e</mi> </mrow> <mrow> <mi>γ</mi> </mrow> </msub> </mrow> </semantics></math>), and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>δ</mi> </mrow> </semantics></math>-axis extended back EMF error <math display="inline"><semantics> <mrow> <msub> <mrow> <mo>(</mo> <mo>∆</mo> <mi>e</mi> </mrow> <mrow> <mi>δ</mi> </mrow> </msub> </mrow> </semantics></math>).</p>
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<p>Comparison of <math display="inline"><semantics> <mrow> <mi>ω</mi> <msub> <mrow> <mover accent="true"> <mrow> <mi>L</mi> </mrow> <mo>^</mo> </mover> </mrow> <mrow> <mi>q</mi> </mrow> </msub> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mi>δ</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>p</mi> <msub> <mrow> <mover accent="true"> <mrow> <mi>L</mi> </mrow> <mo>^</mo> </mover> </mrow> <mrow> <mi>d</mi> </mrow> </msub> <msub> <mrow> <mi>i</mi> </mrow> <mrow> <mi>γ</mi> </mrow> </msub> </mrow> </semantics></math>, where <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1000</mn> <mo> </mo> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>L</mi> </mrow> <mo>^</mo> </mover> </mrow> <mrow> <mi>d</mi> </mrow> </msub> </mrow> </semantics></math> = 1.5 <math display="inline"><semantics> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">H</mi> <mo>,</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>L</mi> </mrow> <mo>^</mo> </mover> </mrow> <mrow> <mi>q</mi> </mrow> </msub> </mrow> </semantics></math> = 2 <math display="inline"><semantics> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">H</mi> </mrow> </semantics></math>.</p>
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<p>Comparison of three-phase current signals. (<b>a</b>) Raw signals without a wavelet filter; (<b>b</b>) denoised signals with a wavelet filter.</p>
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<p>Comparisons of evaluation metrics (RMSE, MSE, MAE) for all cases.</p>
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<p>Wavelet-GMDH based training results. (<b>a</b>) Linear regression result; (<b>b</b>) histogram of estimation errors; (<b>c</b>) estimation errors.</p>
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<p>Block diagram of the sensorless compensation control system based on wavelet-GMDH.</p>
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<p>Simulation model for magnetic saturation compensation of sensorless control system.</p>
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<p>Experimental results when the motor operated at 1000 rpm with a periodic load torque for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>δ</mi> </mrow> </semantics></math>-axis current, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> </mrow> </semantics></math>-axis inductance, (<b>c</b>) speed error, and (<b>d</b>) theta error.</p>
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<p>Experimental results when the motor operated at 1000 rpm with a periodic load torque for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>δ</mi> </mrow> </semantics></math>-axis current, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> </mrow> </semantics></math>-axis inductance, (<b>c</b>) speed error, and (<b>d</b>) theta error.</p>
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<p>Simulation results when the motor operated at 1000 rpm with a periodic load torque for (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>δ</mi> </mrow> </semantics></math>-axis current, (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>q</mi> </mrow> </semantics></math>-axis inductance, and (<b>c</b>) estimated speed.</p>
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<p>Comparison of estimated speed between no compensation, GMDH based compensation, and wavelet-GMDH based compensation in time domain.</p>
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<p>Comparison of estimated speed between no compensation, GMDH based compensation, and wavelet-GMDH based compensation in frequency domain.</p>
Full article ">Figure 13
<p>Comparison of torque ripple between no compensation and wavelet-GMDH based compensation.</p>
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