基于等价输入干扰补偿的永磁直线同步电机H∞预见重复控制

H∞preview repetitive control of PMLSM based on equivalent input disturbance compensation

中文关键词  永磁直线同步电机  预见控制  重复控制  等价输入干扰  线性矩阵不等式  二维连续/离散混合系统

英文关键词  permanent magnet linear synchronous motor  preview control  repetitive control  equivalent input distur bance  linear matrix inequality  two-dimensional continuous/discrete hybrid model

中文摘要

      永磁直线同步电机(PMLSM)应用在周期性高精度位置伺服时,容易受到以周期性端部效应推力波动和参 数摄动为主的不确定性因素的影响,因此提出一种基于等价输入干扰补偿的永磁直线同步电机H∞预见重复控制 的方法.首先在前馈补偿环节中引入预见补偿器和误差补偿项,用于减小重复控制器在第1个控制周期内正反馈延 迟环节不作用引起的跟踪误差;然后基于滑模观测器设计了等价输入干扰(SMO-RCEID)补偿器对PMLSM的端部 效应推力波动以及参数摄动等不确定性进行补偿;最后通过李雅普诺夫稳定性理论结合线性矩阵不等式(LMI)导 出二维连续/离散混合模型描述的H∞预见重复控制系统和SMO-RCEID补偿器稳定的条件,并且求解出系统的控制 器增益和观测器的增益.仿真结果表明该方法具有良好的跟踪性能和干扰抑制能力.

英文摘要

      The application of permanent magnet linear synchronous motor (PMLSM) in periodic high-precision po sition servo is susceptible to uncertainties, which is primarily caused by periodic end effects thrust ripple and parameter perturbations. Therefore, a method for H∞ preview repetitive control of PMLSM based on an equivalent input disturbance compensation is proposed. Firstly, a preview compensator and an error compensation term are introduced into the feed forward compensation loop, which are used to minimize the tracking error caused by the ineffectiveness of the positive feedback delay link in the first control cycle of the repetitive controller. Then, an equivalent input disturbance compensator equivalent input disturbance compensator based on the sliding mode observer (SMO-RCEID) is designed based on the sliding mode observer to compensate for the end effects thrust ripple and parameter perturbations of the PMLSM. Finally, the conditions for the stability of the SMO-RCEID compensator and the H∞ preview repetitive control system described by the two-dimensional continuous/discrete hybrid model are derived by means of the Lyapunov stability theory combined with the linear matrix inequality (LMI), and the controller gain and observer gain of the system are obtained. Simulation results demonstrate that this method has excellent tracking performance and disturbance rejection capability.