基于幂次函数的离散滑模控制算法

Algorithm of discrete-time sliding mode control based on power-function

利用幂次函数构造一种新的趋近律离散滑模控制算法,并给出了无抖振的理论证明.对于标称系统,该算法可使切换函数无抖振、无正负交替地快速趋近于零;对于满足匹配条件的不确定性系统,可使切换函数无抖振、单调地收敛于与外干扰相关的某一数值.利用倒立摆模型进行了数值仿真,结果表明,控制器的输出、切换函数、被控系统的输出均不存在抖振现象,而且被控系统表现出了良好的动态品质.

A new algorithm of reaching law discrete-time sliding mode control is designed by using power-function.Theory analysis about non-chattering is also given.As to nominal system,this algorithm can make the value of switch function reach zero speedily without chattering.As to uncertain system accorded with matching condition,this algorithm can make the value of switch function monotonously reach a certain value which is related with external disturbance.Numerical value simulation is given by using inverted pendulum model.Simulation results show that there is no chattering hundred-percent in the output of controller,the value of switch function,and the output of the controlled system.This algorithm also makes the controlled system achieve excellent dynamic performance.