Discrete-Time Sliding Mode Controlled Positional System with Two-Scale Reaching Law and Integral Action

This paper investigates the effects of signal quantization and velocity estimation on the quality of the discrete-time sliding mode (DSM) in a positional servo-system. Velocity estimation is based on a simple backward finite difference method using the measured quantizied discrete-time position samples. It is shown that such introduced and amplified measurement noise degrades sliding motion into the quasi-sliding mode and threatens to provoke chattering. Furthermore, a DSM control algorithm is proposed, which provides satisfactory performance under these conditions. To avoid chattering, system trajectories are slowed down near the sliding surface by dividing the state space into the fast and slow convergence zones. In the slow zone an additional integral action is employed to secure convergence under action of disturbances. The proposed DSM controller has been experimentally tested in an induction motor position control.