基于迟滞观测器的压电工作台自适应控制

Adaptive Control of Piezoelectric Stage Based on Hysteresis Observer

为提高压电陶瓷驱动的微定位工作台的精度和速度,设计了一种基于迟滞状态观测器的自适应控制系统.在分析压电陶瓷迟滞非线性特性和工作台结构的基础上,建立了压电工作台的动态迟滞模型.迟滞观测器用于估计由位移偏差、传递函数、迟滞变量和扰动而产生的不确定误差,对神经网络控制器的输出量进行补偿,使工作台的位移跟随参考值.基于李雅普诺夫稳定理论推导了迟滞观测器的自适应调节律.实验结果表明,采用带有迟滞观测器的自适应控制系统时,在30μm、1 Hz正弦信号作用下,工作台的平均定位误差从之前的0.39μm减小到了0.19μm,对迟滞特性的非对称拟合平均误差由0.42μm减小到0.22μm,在10μm阶跃输入时的平均定位误差从0.22μm减小到了0.13μm,稳定时间由0.19 s缩短为0.08 s,定位工作台的性能得到明显的改善,能够满足实验要求.

An adaptive control system based on a hysteresis observer was designed to enhance the precision and response speed of a micro-positioning stage actuated by piezoelectric ceramics.The dynamic hysteresis model of the piezoelectric stage was established based on analysis of the nonlinear hysteresis characteristics of the piezoelectric ceramics and structure of the positioning stage.The hysteresis observer was applied to estimating the uncertain errors caused by displacement,transfer functions,hysteresis variables and disturbance.The output of the neural network controller was compensated to drive the stage to track the expected displacement.Adaptive law of the hysteresis observer was derived based on the Lyapunov stability theorem.Experimental results indicate that,with the application of the adaptive control system based on hysteresis observer,the mean positioning error of the stage for a reference sinusoid wave with the amplitude of 30 μm and the frequency of 1 Hz was reduced from 0.39 μm to 0.19 μm and the mean error of the unsymmetrical fitting to the hysteresis characteristics was reduced from 0.42 μm to 0.22 μm.The mean positioning error for a step input of 10 μm dropped from 0.22 μm to 0.13 μm,and the stability time was shortened from 0.19 s to 0.08 s.The performance of the positioning stage has been greatly improved so as to satisfy the requirement of experiment.