跳变参数下柔性机械臂的切换H_∞滑模控制

Switched H_∞ Sliding Mode Control of Flexible Manipulators with Jumping Parameters

探讨一类柔性机械手臂在负载跳变时的跟踪控制问题。用切换模型中的切换信号表示由负载切换带来的参数跳变,建立柔性机械臂模型。依据奇异摄动法将柔性机械臂分解为快变、慢变系统,再分别对这2个系统进行设计。为实现慢变系统对目标轨迹的跟踪,采用多李雅普诺夫函数及平均驻留时间方法为慢变系统设计切换滑模控制器。针对快变系统中的振动问题,则采用共同李雅普诺夫函数方法及参变系统设计方法设计振动抑制控制器。该方法通过柔性双连杆机械臂进行仿真,结果表明,柔性机械臂可在负载跳变下,实现目标轨迹的渐近跟踪,而且能有效地抑制弹性振动。

The tracking control problem of a flexible manipulator with switching load is discussed. A switched model for the flexible manipulator is established, and the switching signal is used to describe the parameter jump caused by the load switching. According to the singular perturbation method, the flexible manipulator is decomposed into a fast and a slow varying system, and the two systems are designed respectively. In order to achieve the tracking target, the multi-Lyapunov functions and the average dwell time method are used to design the switched sliding mode controller for the slow varying system. As for the vibration problem of the rapidly changing system, a vibration suppression controller is designed using the common Lyapunov function method and the parameter varying system design method. The simulation of flexible two link manipulators shows that the flexible manipulator can track the target trajectory asymptotically, and can effectively suppress the elastic vibration.