基于μ理论的永磁直线同步电机鲁棒重复控制

Robust Repetitive Control for Permanent-magnet Linear Synchronous Motor Based on μ Theory

永磁直线同步电机(permanent-magnet linear synchronous motor,PMLSM)伺服系统具有高速、高响应和直接驱动等优点,但其端部效应引起的与位移相关的周期性推力波动、摩擦力及参数变化等不确定性降低了系统的伺服性能。为了削弱周期性扰动及参数变化不确定性的影响,将重复控制和结构奇异值理论(μ理论)相结合,利用线性分式变换(linear fractional transformation,LFT)将鲁棒重复控制问题转换成H∞最优控制问题,采用D-K迭代法设计鲁棒重复控制器(robust repetitive controller,RRC),实现系统的稳定性和鲁棒性,提高系统的跟踪特性。仿真结果表明,该控制方案有效抑制了PMLSM伺服系统的周期性扰动及不确定性,提高了系统的鲁棒性和跟踪特性。

Permanent-magnet linear synchronous motor （PMLSM） servo system has the merits of high speed, high response, and direct drive, but the servo performance is affected by the position-dependent periodic thrust ripple caused by ending effect, friction and parameters uncertainties. To weaken the influences of the position-dependent periodic disturbances and parameter uncertainties, the robust repetitive controller was designed, which associated structure singular value theory （μ theory） with the discrete-time repetitive control theory. The problem of robust repetitive control was transformed into one of H∞ optimal control using linear fractional transformation （LFT）. The robust repetitive controller （RRC） was achieved using D-K iteration procedure and made the servo system have stability, robustness and tracking performance. The simulation results show that the proposed scheme can efficaciously reduce the influence of the periodic disturbance and uncertainties of PMLSM servo system, and make the system have good robustness and tracking performance.