基于LMI 的永磁同步电机鲁棒H∞自补偿滑模控制
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第 49 卷 第 5 期 2021 年 3 月 1 日
DOI: 10.19783/spc.200357
电力系统保护与控制
Power System Protection and Control
Vol.49 No.5 Mar. 1, 2021
基于 LMI 的永磁同步电机鲁棒 H∞自补偿滑模控制
Robust H∞ self-compensation sliding mode control of a permanent magnet synchronous motor based on linear matrix inequality
WANG Yuhong, ZHANG Wei, HAN Bing, FU Hua (Faculty of Electrical and Control Engineering, Liaoning Technical University, Huludao 125105, China)
0 引言
永磁同步电机(Permanent Magnet Synchronous Motor, PMSM)因具有转矩纹波系数小、结构简单， 而且在运行过程中效率高并性能可靠等特点，逐渐 开始取代传统的直流电机与异步电机，同时在诸如
基金项目：国家自然科学基金项目资助(51974151)；辽宁省 自然基金指导计划项目资助(20180550438)
器械生产、机床加工等许多工业领域及日常的生活活 动中应用广泛[1-2]。在电机运行时，随着温度等环境因 素的变化，会出现参数摄动现象，使调速系统性能受 到影响。另外，负载扰动等不确定因素的存在会进一 步对调速系统的鲁棒性造成负面影响。针对上述问 题，传统 PID 控制已经很难满足电机控制越来越高的 性能要求。故而探索与调速系统更好契合且具有优越 性能的控制策略将对生产实践大有裨益[3]。
This work is supported by the National Natural Science Foundation of China (No. 51974151) and Guiding Program of Liaoning Natural Science Foundation (No. 20180550438). Key words: H∞ robust control; PMSM; LMI; adaptive compensation; sliding mode gain
Abstract: The conventional vector control method is vulnerable to the influence of uncertainties such as load disturbance and parameters perturbation due to conservative selection of sliding mode gain. Thus a robust H∞ sliding mode speed controller and current controller based on Linear Matrix Inequality (LMI) are designed. When designing the speed controller, the solution of the H∞-state feedback controller gain is transformed into the solution of the LMI with constraints, so that the H∞-state feedback controller gain is obtained, and the sliding mode surface is formed. Furthermore, a sliding mode control law based on being norm-bounded is designed. This enables the state of the system to reach the required sliding mode surface within a limited time. When designing the current controller, the sliding mode surface and sliding mode control law are designed in the same way. The composite term in the sliding mode control law is estimated by an adaptive method which eliminates the conservative selection of sliding mode switch gain. Finally, the effectiveness of the proposed control strategy is verified by simulation and experiment.
王雨虹，张 威，韩 冰，付 华
(辽宁工程技术大学电气与控制工程学院，辽宁 葫芦岛 125105)
摘要：针对传统矢量控制方案由滑模增益选择保守造成抗负载扰动与参数摄动等不确定因素的鲁棒性差的问题， 设计了基于线性矩阵不等式(LMI)的鲁棒H∞滑模速度控制器和电流控制器。在速度控制器设计中，将求解 H∞状态 反馈控制器增益问题转化为求解具有约束条件的 LMI 问题，从而求出 H∞状态反馈控制器增益，构成滑模面。在 此基础上，设计出基于范数有界的滑模控制律，使系统状态可以实现有限时间内到达所需滑模面。在电流控制器 设计中，同理设计出滑模面与滑模控制律，对于滑模控制律中的复合项采用自适应方式进行估计，消除了滑模开 关增益选择的保守性。仿真与实验验证了所提控制策略的有效性。 关键词：H∞滑模控制；永磁同步电机；线性矩阵不等式；自适应补偿；滑模增益
DOI: 10.19783/spc.200357
电力系统保护与控制
Power System Protection and Control
Vol.49 No.5 Mar. 1, 2021
基于 LMI 的永磁同步电机鲁棒 H∞自补偿滑模控制
Robust H∞ self-compensation sliding mode control of a permanent magnet synchronous motor based on linear matrix inequality
WANG Yuhong, ZHANG Wei, HAN Bing, FU Hua (Faculty of Electrical and Control Engineering, Liaoning Technical University, Huludao 125105, China)
0 引言
永磁同步电机(Permanent Magnet Synchronous Motor, PMSM)因具有转矩纹波系数小、结构简单， 而且在运行过程中效率高并性能可靠等特点，逐渐 开始取代传统的直流电机与异步电机，同时在诸如
基金项目：国家自然科学基金项目资助(51974151)；辽宁省 自然基金指导计划项目资助(20180550438)
器械生产、机床加工等许多工业领域及日常的生活活 动中应用广泛[1-2]。在电机运行时，随着温度等环境因 素的变化，会出现参数摄动现象，使调速系统性能受 到影响。另外，负载扰动等不确定因素的存在会进一 步对调速系统的鲁棒性造成负面影响。针对上述问 题，传统 PID 控制已经很难满足电机控制越来越高的 性能要求。故而探索与调速系统更好契合且具有优越 性能的控制策略将对生产实践大有裨益[3]。
This work is supported by the National Natural Science Foundation of China (No. 51974151) and Guiding Program of Liaoning Natural Science Foundation (No. 20180550438). Key words: H∞ robust control; PMSM; LMI; adaptive compensation; sliding mode gain
Abstract: The conventional vector control method is vulnerable to the influence of uncertainties such as load disturbance and parameters perturbation due to conservative selection of sliding mode gain. Thus a robust H∞ sliding mode speed controller and current controller based on Linear Matrix Inequality (LMI) are designed. When designing the speed controller, the solution of the H∞-state feedback controller gain is transformed into the solution of the LMI with constraints, so that the H∞-state feedback controller gain is obtained, and the sliding mode surface is formed. Furthermore, a sliding mode control law based on being norm-bounded is designed. This enables the state of the system to reach the required sliding mode surface within a limited time. When designing the current controller, the sliding mode surface and sliding mode control law are designed in the same way. The composite term in the sliding mode control law is estimated by an adaptive method which eliminates the conservative selection of sliding mode switch gain. Finally, the effectiveness of the proposed control strategy is verified by simulation and experiment.
王雨虹，张 威，韩 冰，付 华
(辽宁工程技术大学电气与控制工程学院，辽宁 葫芦岛 125105)
摘要：针对传统矢量控制方案由滑模增益选择保守造成抗负载扰动与参数摄动等不确定因素的鲁棒性差的问题， 设计了基于线性矩阵不等式(LMI)的鲁棒H∞滑模速度控制器和电流控制器。在速度控制器设计中，将求解 H∞状态 反馈控制器增益问题转化为求解具有约束条件的 LMI 问题，从而求出 H∞状态反馈控制器增益，构成滑模面。在 此基础上，设计出基于范数有界的滑模控制律，使系统状态可以实现有限时间内到达所需滑模面。在电流控制器 设计中，同理设计出滑模面与滑模控制律，对于滑模控制律中的复合项采用自适应方式进行估计，消除了滑模开 关增益选择的保守性。仿真与实验验证了所提控制策略的有效性。 关键词：H∞滑模控制；永磁同步电机；线性矩阵不等式；自适应补偿；滑模增益