重复学习控制及其在一类非线性系统中的应用

Repetitive Learning Control and the Study on Its Application to a Class of Nonlinear Systems

为跟踪或抑制仅周期已知的未知周期参考或扰动信号,提出一种新的重复学习控制方法.利用系统的稳态误差并通过迭代学习构造前馈补偿,实现了误差的渐近收敛.将所提出方法应用于一类常见的扰动信号和系统输出具有未知非线性关系的非线性系统,假设其满足连续里普希斯条件.利用重复学习控制器,系统的稳态误差可以减小到极低的程度.该方法控制精度高,实现简单,与传统的基于时延内模的重复控制方法相比,具有对非重复性干扰不敏感的优点.仿真结果验证了该方法的有效性.

A novel repetitive learning control method is proposed for the tracking or rejection of unknown periodic reference or disturbance with a known period. A feed-forward compensation is constructed by iterative learning with only the steady-state error to produce asymptotic error convergence. The proposed method is applied to a class of nonlinear systems frequently met in practice, where the disturbances have unknown nonlinear dependency on the output with only continuous Lipschitz condition imposed. With the repetitive learning controller, the steady state error of the system can be reduced to a very low degree. Compared with the conventional repetitive control method,the proposed method has the merits of high accuracy, easy implementation and being insensitive to non-repetitive disturbances. Simulation results confirm its effectiveness.