Research on High-Performance Explicit Model Predictive Control Algorithm for Permanent Magnet Synchronous Motors
Liu Zhongyong1,2, Fan Tao1,2, He Guolin2, Wen Xuhui1,2
1. University of Chinese Academy of Sciences Beijing 100049 China; 2. Institute of Electrical Engineering Chinese Academy of Sciences Beijing 100190 China
Abstract Since the 1970s, model predictive control (MPC) algorithms have proven to be effective control strategies for multi-input and multi-output nonlinear dynamic systems with complex constraints. However, due to the significant computational demands associated with optimization problems, applying MPC to control objects with fast response time requirements, such as motor systems, presents challenges in achieving iterative solutions for constrained problems within short control cycles. This paper proposes a high-performance control strategy for permanent magnet synchronous motors based on the explicit model predictive control (EMPC) concept. The strategy involves the establishment of linearized models for current and speed control using multiparametric programming to eliminate coupling effects and nonlinear influences between states. The offline solution yields optimal control actions under effective constraint conditions, stored as piecewise-affine functions. During operation, the corresponding optimal control actions are obtained by querying the partition containing the current state combination. The paper comprehensively analyzes model mismatch, digital delay, and dead-zone effects in EMPC applications and provides corresponding solutions. A fully automated dyno test platform verifies the proposed algorithm's efficacy. The paper introduces the theoretical foundations of multiparametric programming and presents a comprehensive design process for explicit model predictive control. It establishes linearized models for controlling current and speed in permanent magnet synchronous motors while linearizing voltage and current constraints. The effects of parameter mismatch, digital delay, and inverter nonlinearity on EMPC are analyzed, and respective compensatory measures are proposed. The EMPC problem definition and optimal control law are solved using the MPT3 toolbox, displaying critical partitions and optimal cost functions under different state combinations. The simulation verifies the algorithm and the preceding analysis of various non-ideal factors. Experimental validation is conducted on a motor dyno test platform, comparing the performance of EMPC with a proportional-integral (PI) control algorithm. In the current control scenario, when given a 30 A current step command, the PI algorithm exhibits a response time of 0.1 s, while the EMPC algorithm responds in 0.001 4 s. In speed control, with a 600 r/min speed step command, the PI algorithm takes 1 s to respond, whereas the EMPC algorithm responds in 0.3 s. When subjected to load disturbances, the PI algorithm reaches a steady state after 0.5 s, while the EMPC algorithm reaches a steady state after 0.1 s. The experimental results demonstrate that EMPC effectively reduces coupling effects without overshooting because each control is optimized under constraints, exhibiting superior harmonic current suppression capabilities. Based on the theoretical analysis and experimental results, the following conclusions can be drawn: (1) The EMPC algorithm incorporates models and various constraints into the control problem, which can encompass all dynamic characteristics during the control process, guarantee linear stability, and achieve better dynamic performance compared to anti-saturation strategies. (2) Due to the high bandwidth characteristic, the EMPC algorithm has faster dynamic response and harmonic suppression than PI control. The design approach based on multivariable control does not consider coupling effects between system states, and the optimal control action obtained through feasible region-solving meets global control requirements. Thus, it eliminates the need for cumbersome tuning based on operating conditions. Keywords：Permanent magnet synchronous motor (PMSM), explicit model predictive control, optimal control, speed prediction control, current prediction control
[1] Cui Kai, Wang Chenchen, Gou Lifeng, et al.Analysis and design of current regulators for PMSM drives based on DRGA[J]. IEEE Transactions on Trans- portation Electrification, 2020, 6(2): 659-667. [2] Belda K, Vošmik D.Explicit generalized predictive control of speed and position of PMSM drives[J]. IEEE Transactions on Industrial Electronics, 2016, 63(6): 3889-3896. [3] Mariethoz S, Domahidi A, Morari M.High-bandwidth explicit model predictive control of electrical drives[J]. IEEE Transactions on Industry Applications, 2012, 48(6): 1980-1992. [4] De Doná J A, Goodwin G C, Seron M M. Anti-windup and model predictive control: reflections and con- nections[J]. European Journal of Control, 2000, 6(5): 467-477. [5] Richalet J, Rault A, Testud J L, et al.Model algorithmic control of industrial processes[J]. IFAC Proceedings Volumes, 1977, 10(16): 103-120. [6] Richalet J, Rault A, Testud J L, et al.Model predi- ctive heuristic control[J]. Automatica, 1978, 14(5): 413-428. [7] Clarke D W, Mohtadi C, Tuffs P S.Generalized predictive control-part I. the basic algorithm[J]. Automatica, 1987, 23(2): 137-148. [8] Clarke D W, Mohtadi C, Tuffs P S.Generalized predictive control-part II extensions and inter- pretations[J]. Automatica, 1987, 23(2): 149-160. [9] Rodriguez J, Cortes P.Predictive control of power converters and electrical drives[M]. Chichester, West Sussex, UK: John Wiley & Sons, 2012. [10] Karamanakos P, Liegmann E, Geyer T, et al.Model predictive control of power electronic systems: methods, results, and challenges[J]. IEEE Open Journal of Industry Applications, 2020, 1: 95-114. [11] Zhang Yongchang, Xie Wei, Li Zhengxi, et al.Low-complexity model predictive power control: double-vector-based approach[J]. IEEE Transactions on Industrial Electronics, 2014, 61(11): 5871-5880. [12] Zhang Yongchang, Xie Wei.Low complexity model predictive control-single vector-based approach[J]. IEEE Transactions on Power Electronics, 2014, 29(10): 5532-5541. [13] 陈荣, 翟凯淼, 舒胡平. 永磁同步电机双矢量固定开关频率模型预测控制研究[J]. 电工技术学报, 2023, 38(14): 3812-3823. Chen Rong, Zhai Kaimiao, Shu Huping.Predictive control of dual vector fixed switching frequency model for permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2023, 38(14): 3812-3823. [14] 李祥林, 薛志伟, 阎学雨, 等. 基于电压矢量快速筛选的永磁同步电机三矢量模型预测转矩控制[J]. 电工技术学报, 2022, 37(7): 1666-1678. Li Xianglin, Xue Zhiwei, Yan Xueyu, et al.Voltage vector rapid screening-based three-vector model predictive torque control for permanent magnet syn- chronous motor[J]. Transactions of China Elec- trotechnical Society, 2022, 37(7): 1666-1678. [15] 张珍睿, 刘彦呈, 陈九霖, 等. 永磁同步电机幅值控制集模型预测控制策略[J]. 电工技术学报, 2022, 37(23): 6126-6134. Zhang Zhenrui, Liu Yancheng, Chen Jiulin, et al.Amplitude control set model predictive control strategy for permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2022, 37(23): 6126-6134. [16] 郑长明, 阳佳峰, 高昂, 等. 永磁同步电机长线变频驱动系统定频滑模预测电流控制[J]. 电工技术学报, 2023, 38(4): 915-924. Zheng Changming, Yang Jiafeng, Gao Ang, et al.Fixed switching frequency sliding-mode predictive current control of a PMSM variable-frequency drive system with long cables[J]. Transactions of China Electrotechnical Society, 2023, 38(4): 915-924. [17] 周奇勋, 刘帆, 吴紫辉, 等. 永磁同步电机转矩与定子磁链模型预测控制预测误差补偿方法[J]. 电工技术学报, 2022, 37(22): 5728-5739. Zhou Qixun, Liu Fan, Wu Zihui, et al.Model predictive torque and stator flux control method for PMSMs with prediction error compensation[J]. Transactions of China Electrotechnical Society, 2022, 37(22): 5728-5739. [18] Geyer T, Quevedo D E.Performance of multistep finite control set model predictive control for power electronics[J]. IEEE Transactions on Power Elec- tronics, 2015, 30(3): 1633-1644. [19] Scoltock J, Geyer T, Madawala U K.A comparison of model predictive control schemes for MV induction motor drives[J]. IEEE Transactions on Industrial Informatics, 2013, 9(2): 909-919. [20] Borrelli F, Bemporad A, Morari M.Predictive control for linear and hybrid systems[M]. New York: Cambridge University Press, 2017. [21] Bemporad A, Morari M, Dua V, et al.The explicit linear quadratic regulator for constrained systems[J]. Automatica, 2002, 38(1): 3-20. [22] Boyd S, Vandenberghe L.Convex optimization[M]. Cambridge, UK: Cambridge University Press, 2004. [23] Springob L, Holtz J.High-bandwidth current control for torque-ripple compensation in PM synchronous machines[J]. IEEE Transactions on Industrial Elec- tronics, 1998, 45(5): 713-721. [24] Abdel-Rady I M Y, El-Saadany E F. An improved deadbeat current control scheme with a novel adaptive self-tuning load model for a three-phase PWM voltage-source inverter[J]. IEEE Transactions on Industrial Electronics, 2007, 54(2): 747-759. [25] 国敬, 范涛, 章回炫, 等. 高速低载波比下永磁同步电机电流环稳定性分析[J]. 中国电机工程学报, 2019, 39(24): 7336-7346, 7506. Guo Jing, Fan Tao, Zhang Huixuan, et al.Stability analysis of permanent magnet synchronous motor current loop control at high speed and low carrier ratio[J]. Proceedings of the CSEE, 2019, 39(24): 7336-7346, 7506. [26] Chen Jiahao, Mei Jie, Yuan Xin, et al.Online adapta- tion of two-parameter inverter model in sensorless motor drives[J]. IEEE Transactions on Industrial Electronics, 2022, 69(10): 9860-9871. [27] Choi J W, Sul S K.Inverter output voltage synthesis using novel dead time compensation[J]. IEEE Transa- ctions on Power Electronics, 1996, 11(2): 221-227. [28] Park Y, Sul S K.A novel method utilizing trapezoidal voltage to compensate for inverter nonlinearity[J]. IEEE Transactions on Power Electronics, 2012, 27(12): 4837-4846. [29] Hwang S H, Kim J M.Dead time compensation method for voltage-fed PWM inverter[J]. IEEE Transa- ctions on Energy Conversion, 2010, 25(1): 1-10. [30] Young H A, Perez M A, Rodriguez J.Analysis of finite-control-set model predictive current control with model parameter mismatch in a three-phase inverter[J]. IEEE Transactions on Industrial Elec- tronics, 2016, 63(5): 3100-3107. [31] Wipasuramonton P, Zhu Z Q, Howe D.Predictive current control with current-error correction for PM brushless AC drives[J]. IEEE Transactions on Industry Applications, 2006, 42(4): 1071-1079. [32] Muske K R, Badgwell T A.Disturbance modeling for offset-free linear model predictive control[J]. Journal of Process Control, 2002, 12(5): 617-632. [33] Faanes A, Skogestad S.Offset-free tracking of model predictive control with model mismatch: experi- mental results[J]. Industrial & Engineering Chemistry Research, 2005, 44(11): 3966-3972. [34] Herceg M, Kvasnica M, Jones C N, et al.Multi- parametric toolbox 3.0[C]//2013 European Control Conference (ECC), Zurich, Switzerland, 2013: 502-510.
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