迭代学习控制系统的误差跟踪设计方法

摘要

This paper presents an iterative learning control method with which the error trajectory can be pre-specified. The method dose not require that the initial condition remains to be a fixed value for each iteration, whereas this requirement is usually assumed in conventional methods. The proposed strategy is to make the tracking error trajectory converge to the pre-specified one over the entire interval. The constant parametrization, time-varying parametrization, and a combined situation are respectively examined. By the Lyapunov-like approach, accordingly, learning laws are given and the learning systems are analyzed in details. With the help of unsaturated/saturated learning law, the system error coincides with the pre-specified error trajectory over the entire interval, and all the signals in close-loop system are guaranteed to be bounded. Numerical results are presented to demonstrate the effectiveness of the proposed learning control method.%提出能够实现期望误差轨迹完全跟踪的迭代学习控制系统设计方法,旨在放宽常规迭代学习控制方法的初始定位条件,在每次迭代时允许初值定位在任意位置.这种方法对于预先给定的期望误差轨迹,经迭代学习,使得实际跟踪误差收敛于预定的误差轨迹,这样,预设的误差轨迹即最终形成的误差轨迹.针对常参数、时变参数以及复合参数三种情形,分别采用类Lyapunov方法设计迭代学习控制系统.所设计的未含/含限幅作用的参数学习律,能够使得跟踪误差轨迹在整个作业区间上与预定轨迹完全吻合,并保证系统中所有信号的有界性.给出的仿真结果表明所提方法的有效性.