Discrete-Time Sliding Mode Control with Time Varying Switching Hyperplane which is Moving in the Specified Region

Abstract

Sliding Mode Control (SMC) is nonlinear robust control to attempt stabilizing by restraining the state to switching hyperplane. There is a feature of having excellent robustness for disturbance and the uncertainty which fulfill matching condition. In addition, it is known because high control performance is obtained for a nonlinear system and the parameter variation.However, in a principle of SMC, it becomes a factor that the oscillatory phenomenon called chattering is produces because the existence of dead time may influence a high-speed switch of the control input to restrain the state to the switching hyperplane. Moreover, chattering is generated in discrete time system because the sampling time is limited.When SMC is applied to the actual system, the state of the system causes the oscillations such as the high-frequency vibrations and spill-over near the switching hyperplane when chattering is caused, and may lead to the deterioration of the controller.In order to solve this problem, authors proposed a time varying swithcing line of two dimensions designed by the state as a method for newly decreasing chattering (Fig. 1).There is the following feature in this method.

Sliding Mode Control with a State Predictor for Time Delay Control System

“…However, according to the principle of SMC, the oscillatory phenomenon called chattering is produced because the existence of a time delay might influence the high-speed switch of the control input, which limits the state to the switching hyperplane [4].…”