压电定位台RBF非奇异快速终端滑模跟踪控制

RBF Nonsingular Fast Terminal Sliding Mode Tracking Control for Piezoelectric Positioning Platform

为了实现对具有强非线性压电定位台的精确位置跟踪,提出了一种基于径向基函数(RBF)神经网络和非奇异快速终端滑模面的自适应控制方法。对压电定位台进行了自适应控制建模,设计了非奇异快速终端滑模控制器。结合RBF神经网络实现了控制器的改进,提出了RBF非奇异快速终端滑模控制器及其参数更新规律,采用李雅普诺夫理论进行了稳定性证明。仿真结果表明:非奇异快速终端滑模控制器能够实现对时变正弦信号的有效跟踪,其平均误差为0.07μm,均方根误差为0.021μm;当采用RBF非奇异快速终端滑模控制器时,因神经网络的逼近作用,在相同时间内其平均误差为0.06μm,均方根误差为0.017μm。

In order to realize the precise position tracking for the nonlinear piezoelectric positioning platform,an adaptive control method based on radial basis function(RBF)neural network and non-singular fast terminal sliding surface was proposed.The adaptive modeling was carried out for the piezoelectric positioning platform,and the non-singular fast terminal sliding mode controller was designed.The controller performance was augmented by the RBF neural network,and the RBF non-singular fast terminal sliding mode controller and its parameter updating rule were proposed.The stability was proved based on the Lyapunov theory.The simulation results show that the non-singular fast terminal sliding mode controller can realize effective tracking for time-varying sinusoidal signals.The average error is 0.07μm,and the root mean square error is 0.021μm.By using RBF non-singular fast terminal sliding mode controller,the average error is 0.06μm and the root mean square error is 0.017μm within the same time due to the approximation effect of the neural network.