# American Institute of Mathematical Sciences

March  2021, 17(2): 827-839. 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, 2021, 17 (2) : 827-839. doi: 10.3934/jimo.2019136
##### References:

show all references

##### 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
 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
 [1] Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semi-infinite programming. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021012 [2] Jian-Xin Guo, Xing-Long Qu. Robust control in green production management. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021011 [3] Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076 [4] Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021013 [5] Simone Fiori. Error-based control systems on Riemannian state manifolds: Properties of the principal pushforward map associated to parallel transport. Mathematical Control & Related Fields, 2021, 11 (1) : 143-167. doi: 10.3934/mcrf.2020031 [6] Duy Phan, Lassi Paunonen. Finite-dimensional controllers for robust regulation of boundary control systems. Mathematical Control & Related Fields, 2021, 11 (1) : 95-117. doi: 10.3934/mcrf.2020029 [7] Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $L^2-$norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077 [8] Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323 [9] Weinan E, Weiguo Gao. Orbital minimization with localization. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 249-264. doi: 10.3934/dcds.2009.23.249 [10] Manxue You, Shengjie Li. Perturbation of Image and conjugate duality for vector optimization. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020176 [11] Alberto Bressan, Wen Shen. A posteriori error estimates for self-similar solutions to the Euler equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 113-130. doi: 10.3934/dcds.2020168 [12] Elvio Accinelli, Humberto Muñiz. A dynamic for production economies with multiple equilibria. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021002 [13] Kha Van Huynh, Barbara Kaltenbacher. Some application examples of minimization based formulations of inverse problems and their regularization. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020074 [14] Ying Lin, Qi Ye. Support vector machine classifiers by non-Euclidean margins. Mathematical Foundations of Computing, 2020, 3 (4) : 279-300. doi: 10.3934/mfc.2020018 [15] Wen Li, Wei-Hui Liu, Seak Weng Vong. Perron vector analysis for irreducible nonnegative tensors and its applications. Journal of Industrial & Management Optimization, 2021, 17 (1) : 29-50. doi: 10.3934/jimo.2019097 [16] Liping Tang, Ying Gao. Some properties of nonconvex oriented distance function and applications to vector optimization problems. Journal of Industrial & Management Optimization, 2021, 17 (1) : 485-500. doi: 10.3934/jimo.2020117 [17] Meng Ding, Ting-Zhu Huang, Xi-Le Zhao, Michael K. Ng, Tian-Hui Ma. Tensor train rank minimization with nonlocal self-similarity for tensor completion. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021001 [18] Helin Guo, Huan-Song Zhou. Properties of the minimizers for a constrained minimization problem arising in Kirchhoff equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1023-1050. doi: 10.3934/dcds.2020308 [19] Yahia Zare Mehrjerdi. A new methodology for solving bi-criterion fractional stochastic programming. Numerical Algebra, Control & Optimization, 2020  doi: 10.3934/naco.2020054 [20] Yasmine Cherfaoui, Mustapha Moulaï. Biobjective optimization over the efficient set of multiobjective integer programming problem. Journal of Industrial & Management Optimization, 2021, 17 (1) : 117-131. doi: 10.3934/jimo.2019102

2019 Impact Factor: 1.366