Mija S.J. and Susy Thomas


Variable structure control, discrete sliding mode control, optimalsliding surface, linear quadratic regulator, inverted pendulum


This paper presents an optimal sliding mode control (SMC) scheme for discrete time systems. Existing methods for sliding surface design are based on the pole placement of the equivalent system in sliding mode. The designed SMC in such methods, though capable of maintaining sliding mode motion, is not optimal, as the methodology does not involve any performance measure. In the proposed method, features of both SMC and optimal control are made use of to evolve a sliding surface, which ensures that the SMC is optimal from the control viewpoint. Also the performance measure is formulated in such a way as to ensure minimum transient error in the response. The proposed method is applied to an inverted pendulum stabilization problem to illustrate the effectiveness. Comparison with the conventional discrete SMC and linear quadratic regulator methods has been made to emphasize the advantages of the proposed method. The robustness of the proposed controller is also tested by incorporating 10% parameter variation.

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