为了提高空间天文望远镜精密稳像系统中大口径压电快摆镜机构(Fast Steering Mirror, FSM)的控制精度, 采用迟滞前馈补偿和最优PID控制算法相结合的复合控制策略。针对基于广义Play算子的Prandtl-Ishlinskii (PI)模型可逆性受约束条件限制以及求逆过程中模型参数估计误差累加的问题, 提出了一种基于广义Stop算子的PI逆模型进行压电执行器(Piezoelectric Actuator, PZT)迟滞补偿。针对逆迟滞模型的不确定性和直接前馈控制抗干扰能力差的问题, 在控制系统中加入最优PID闭环控制器。采用自适应差分进化算法(Adaptive Differential Evolution, ADE)对迟滞逆模型参数和PID控制器参数进行寻优并引入混沌搜索机制来提高ADE算法的性能。实验结果表明: 与传统PI模型解析求逆方法相比, 基于广义Stop算子的PI逆模型能够更好描述逆迟滞曲线, 拟合频率为1 Hz的迟滞曲线, 拟合精度提高78.04%;实时跟踪频率分别为1、10、20 Hz的大口径快摆机构目标摆动位移, 复合控制策略的跟踪精度相比于直接前馈控制分别提高了38.56%,22.92%和13.5%。

In order to improve the control accuracy of large-aperture piezoelectric fast steering mirror(FSM) in precision image stabilization system in space telescope, the compound control strategy combining hysteresis feed forward compensation with the optimal PID control algorithm was adopted. According to the problems that the reversibility of Prandtl-Ishlinskii (PI) model based on Play operator was limited by the constraint condition and the estimation error accumulation of model parameters in the inverse process, the PI inverse model based on the generalized Stop operator was proposed to compensate the PZT hysteresis. The optimal PID closed loop controller was added in the control system for the problems of the inverse hysteresis model uncertainty and the poor anti-interference ability of direct feed forward control. The adaptive differential evolution(ADE) was used to optimize the hysteresis inverse model and PID controller parameters and the chaos search mechanism was introduced to improve the performance of ADE. The experimental results show that, compared with the traditional analytic method to obtain the inverse model, the hysteresis inverse model based on the Stop operator can better describe the inverse hysteresis curve, and the fitting precision increases by 78.04% when fitting the hysteresis curve with 1 Hz frequency; the tracking accuracy of compound control algorithm increases by 38.56%,22.92% and 13.5% respectively compared with the direct feedforward control, in the real-time tracking for target swinging displacements of large-aperture piezoelectric fast steering mirror with 1 Hz,10 Hz and 20 Hz frequencies.