基于率相关迟滞模型的压电微动平台前馈控制

为了降低压电微动平台的动态迟滞误差对平台定位精度的影响，该文设计了基于率相关迟滞逆模型的前馈控制器对其进行迟滞补偿。首先，在对平台受力分析和运动分析的基础上建立平台的动力学模型；其次，在经典Prandtl-Ishilinskii(PI)模型的基础上加以改造，得到Modified Prandtl-Ishilinskii(MPI)模型，并将MPI模型与平台的线性动力学模型串联，得到分离式率相关MPI模型，进而基于率相关MPI逆模型建立平台的前馈控制器；最后，对所设计的控制器进行阶跃响应和正弦轨迹跟踪实验。实验结果表明，所设计的控制器具有较好的定位精度与跟踪性能，可以有效地补偿压电微动平台的动态迟滞误差。

Feedforward Control of Piezoelectric Micro-positioning Stage Based onRate-dependent Hysteresis Model

In order to reduce the influence of the dynamic hysteresis characteristics of the piezoelectric micro-positioning stage on the positioning accuracy, a feedforward controller based on the rate-dependent inverse hysteresis model is designed to compensate the hysteresis. Firstly, the dynamic model of the stage is established on the basis of force analysis and motion analysis. Secondly, the Modified Prandtl-Ishilinskii(MPI) model is obtained by improving the classical Prandtl-Ishilinskii(PI) model, and the separated rate-dependent MPI model is obtained by connecting the MPI model in series with the linear dynamic model of the stage, and then the feedforward controller of the stage is established based on the rate-dependent MPI inverse model. Finally, the step response experiments and sinusoidal trajectory tracking experiments on the designed controller are carried out. The experimental results show that the designed controller has good positioning accuracy and tracking performance, and can effectively compensate the dynamic hysteresis errors of the piezoelectric micro-positioning stage.