An adaptive dynamic programming method for torque ripple minimization of PMSM

Tengfei Yan; Qunying Liu; Bowen Dou; Qing Li; Bowen Li

doi:10.3934/jimo.2019136

Article Contents

2021, Volume 17, Issue 2: 827-839. Doi: 10.3934/jimo.2019136

This issue Previous Article An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information Next Article Optimal stop-loss reinsurance with joint utility constraints

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
^* Corresponding author: Qunying Liu

Received: May 2019

Revised: July 2019

Early access: November 2019

Published: March 2021

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Abstract

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.

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Mathematics Subject Classification: Primary: 93C40, 93A30; Secondary: 93C73.

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Figure 1. Configuration of an ADP-based control system

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Figure 2. The controller block diagram of PMSM

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Figure 3. The controller block diagram of PMSM

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Figure 4. Speed response with ADP controller at 500r/min

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Figure 5. Speed response Fourier analysis with ADP controller at 500r/min

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Figure 6. Speed response with ADP controller at 50r/min

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Figure 7. Speed response Fourier analysis with ADP controller at 50r/min

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Figure 8.

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Figure 9.

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Figure 10. Torque response with ADP and PI controller at 1.6Nm

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Figure 11. Torque response with ADP and PI controller at 9.0Nm

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Table 1. 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

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Table 2. 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

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Table 3. 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

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