压电微操作器的混合灵敏度H∞控制

Mixed Sensitivity H∞Control for Piezoelectric Micromanipulator

针对压电微操作器的迟滞非线性补偿问题,采用Prandtl-Ishlinskii(PI)法建立了描述微操作器迟滞非线性特性的迟滞模型,并设计其前馈控制器。首先通过将系统逆补偿输出线性化,设计混合灵敏度H∞控制器,使系统具有较好的动静态特性。其次搭建了由多自由度微动平台和末端柔性操作臂构成的压电微操作器系统,并进行一系列测控实验。结果表明,基于PI逆模型的前馈控制可以较好地补偿压电微操作器的迟滞非线性,在最大输出位移125μm的情况下,最大迟滞非线性率由21.7%降低至7.4%。同时混合灵敏度H∞控制能以较小的相对控制误差实现对不同类型和频率的参考轨迹跟踪,甚至微操作器动力学参数发生变化时,仍然具有较好的控制效果,证实了所提出控制器的可行性。

Aiming at the nonlinear hysteresis compensation of piezoelectric micromanipulators,a hysteresis model describing the nonlinear hysteresis characteristics of the micromanipulator is established by using the Prandtl-Ishlinskii method and its feedforward controller is designed.Firstly,by linearizing the inverse compensation output of the system,the mixed sensitivity H∞controller is designed to make the system have better dynamic and static characteristics.Secondly,a piezoelectric micromanipulator system consisting of a multi-degree-of-freedom micro-motion stage and a flexible end-of-manipulator is set up,and a series of measurement and control experiments are carried out.The results show that the feedforward control based on the PI inverse model can compensate the hysteresis nonlinearity of the piezoelectric micromanipulator well.The maximum hysteresis nonlinearity rate is reduced from 21.7%to 7.4%with the maximum output displacement of 125μm.Meanwhile,the mixed sensitivity H∞control can realize the reference trajectory tracking of different types and frequencies with a small relative control error,even when the dynamic parameters of the micromanipulator change,it still has a good control effect,which verifies the feasibility of the proposed controller.