Robust discrete-time variable structure control methods

The invariance and robustness properties of variable structure control are lost in digital implementation. This paper presents three discrete-time var iable structure control (DVSC) methods that can recover those properties fo r linear uncertain systems. The first method uses a disturbance compensator formulated in the variable structure framework and a decoupling law to sep arate the disturbance estimation dynamics from the closed loop dynamics. In the second approach, a recursive switching function is developed, which al lows recovering the lost invariance and robustness properties, without usin g the disturbance compensator. The first method can result in slow transien t dynamics, and the second can result in a large overshoot. In the third me thod, a new recursive switching function is developed and combined with the decoupled disturbance compensator method to recover the lost invariance an d 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 thi rd method provided the best result. [S0022-0434(00)02204-8].