具有输入死区的非线性系统的鲁棒重复控制

摘要

This paper deals with the robust repetitive controller design for a class of nonlinear systems with input deadzone,without the assumption that the periodic uncertainties can be parameterized.The unknown parameters involved in the deadzone nonlinearity are estimated by using integral adaptive algorithms,while the bounded term is treated by a robust approach,and the saturation function is adopted to avoid the possible chattering phenomenon.The non-parametric uncertainty is expressed with a periodically time-varying function,to which the periodic learning approach can be applied for estimation purpose.It is shown by theoretical and numerical results that both partially-and fully-saturated learning algorithms are effective to ensure asymptotic convergence of the tracking error,as well as boundedness of all the signals in the closed-loop system.%针对一类输入含死区非线性特性的周期时变系统,在周期时变参数不可参数化的情形下设计鲁棒重复控制器.采用微分自适应律估计未知死区参数,剩余的有界项通过鲁棒方法予以消除,为避免出现颤振现象,采用饱和函数替代符号函数.在系统输出跟踪周期轨迹的情形下,将非参数化不确定项转化为含周期时变参数的形式,以达到利用周期学习律进行估计的目的.理论分析与仿真结果表明,采用部分饱和或全饱和学习算法均能实现输出误差有界收敛,并保证闭环系统所有信号有界.