一类双线性系统的变结构控制

Variable Structure Control of A Class of Bilinear Systems

本文研究了对于一类具有参数不确定性和外部干扰的双线性系统的变结构控制问题,通过引入一个随状态收敛而收缩到原点的切换区,利用积分变换对切换函数进行修正,形成了一种新型的变结构控制器,其特点是在产生拟滑动模态的同时,消除了高频颤动,并且不会在原点附近形成极限环。本文证明了拟滑动模态的存在性,可达性和渐近稳定性。

This paper is concerned with the regulation problem of bilinear systems of parameter uncertainties and external disturbances by variable structure controller. By introducing a proper switching zone which shrinks to the origin as the state variable converges to zero and modifying the switching function by integral transformation, a novel variable structure controller is formed. Such control system features good properties that high-frequency chattering is suppressed and limit cycle near the origin of the state space is avoided while retaining the ideal properties of sliding mode. The conditions of the existence, reachability and asymptotic stability of sliding mode are also proved in this paper.