American Institute of Mathematical Sciences

doi: 10.3934/jimo.2019136

An adaptive dynamic programming method for torque ripple minimization of PMSM

 1 School of Automation and engineering, University of Electronic Science and Technology of China, China 2 The Shenzhen Energy Storage Power Generation Co., Ltd. of China Southern Power Grid, China

* Corresponding author: Qunying Liu

Received  May 2019 Revised  July 2019 Published  November 2019

The imperfect sinusoidal flux distribution, cogging torque, and current measurement errors can cause periodic torque ripple in the permanent magnet synchronous motor (PMSM). These ripples are reflected in the periodic oscillation of the motor speed and torque, causing vibration at low speeds and noise at high speeds. As a high-precision tracking application, ripple degrades the application performance of PMSM. In this paper, an adaptive dynamic programming (ADP) scheme is proposed to reduce the periodic torque ripples. An optimal controller is designed by iterative control algorithm using robust adaptive dynamic programming theory and strategic iterative technique. ADP is combined with the existing Proportional-Integral (PI) current controller and generates compensated reference current iteratively from cycle to cycle so as to minimize the mean square torque error. As a result, an optimization problem is constructed and an optimal controller is obtained. The simulation results show that the robust adaptive dynamic programming achieves lower torque ripple and shorter dynamic adjustment time during steady-state operation, thus meeting the requirements of steady speed state and the dynamic performance of the regulation system.

Citation: Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li, Bowen Li. An adaptive dynamic programming method for torque ripple minimization of PMSM. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019136
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References:
Configuration of an ADP-based control system
The controller block diagram of PMSM
The controller block diagram of PMSM
Speed response with ADP controller at 500r/min
Speed response Fourier analysis with ADP controller at 500r/min
Speed response with ADP controller at 50r/min
Speed response Fourier analysis with ADP controller at 50r/min
Torque response with ADP and PI controller at 1.6Nm
Torque response with ADP and PI controller at 9.0Nm
parameters of PMSM
 Characteristic Symbol Value Stator phase resistance R 2.875Ω d and q-axes ${L_d} = {L_q}$ 8.5mH Number of pole pairs ${p_n}$ 4 viscous damping B 0.008 N. m. s Torque constant ${K_t}$ 1.05 N. m Rotational inertia J 0.003kg.m2
 Characteristic Symbol Value Stator phase resistance R 2.875Ω d and q-axes ${L_d} = {L_q}$ 8.5mH Number of pole pairs ${p_n}$ 4 viscous damping B 0.008 N. m. s Torque constant ${K_t}$ 1.05 N. m Rotational inertia J 0.003kg.m2
response at different reference speed
 Speed at 500r/min Speed range(r/min) Fluctuation error ADP controller 499.8802-500.1253 0.2451 PI controller 495.6341-502.8779 7.2438 Speed at 50r/min Speed range(r/min) Fluctuation error ADP controller 49.7712-50.2942 0.5230 PI controller 46.3281-53.5526 7.2279
 Speed at 500r/min Speed range(r/min) Fluctuation error ADP controller 499.8802-500.1253 0.2451 PI controller 495.6341-502.8779 7.2438 Speed at 50r/min Speed range(r/min) Fluctuation error ADP controller 49.7712-50.2942 0.5230 PI controller 46.3281-53.5526 7.2279
response at different load torque
 Load torque at 1.6Nm Torque range(Nm) Fluctuation error ADP controller 1.5603-1.6428 0.0825 PI controller 0.3482-3.0570 2.7088 Load torque at 9.0Nm Torque range(Nm) Fluctuation error ADP controller 8.9603-9.1562 0.1959 PI controller 6.9523-12.1328 5.1805
 Load torque at 1.6Nm Torque range(Nm) Fluctuation error ADP controller 1.5603-1.6428 0.0825 PI controller 0.3482-3.0570 2.7088 Load torque at 9.0Nm Torque range(Nm) Fluctuation error ADP controller 8.9603-9.1562 0.1959 PI controller 6.9523-12.1328 5.1805
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