Robust Discrete-Time Variable Structure Control Methods

Abstract

The invariance and robustness properties of variable structure control are lost in digital implementation. This paper presents three discrete-time variable structure control (DVSC) methods that can recover those properties for linear uncertain systems. The first method uses a disturbance compensator formulated in the variable structure framework and a decoupling law to separate the disturbance estimation dynamics from the closed loop dynamics. In the second approach, a recursive switching function is developed, which allows recovering the lost invariance and robustness properties, without using the disturbance compensator. The first method can result in slow transient dynamics, and the second can result in a large overshoot. In the third method, a new recursive switching function is developed and combined with the decoupled disturbance compensator method to recover the lost invariance and robustness properties. The three DVSC methods are applied to control the motion of an xy-stage of a CNC milling machine. In this experiment, the third method provided the best result. [S0022-0434(00)02204-8]