Abstract
In recent year, Variable Structure Conrol System (VSCS) has become to be applied to control of a wide range. The notable feature of VSCS is that the sliding motion occurres on a switching surface. While in sliding mode, the system remains insensitive to parameter change and disturbances. However, when the Sliding Mode Control System receives random input, we haven't the condition of the sliding motion and a design method for an optimal switching surface for the present.
This paper deals with the sliding mode of VSCS which is subjected to white noise and state-dependent noise respectively, and the design of an optimal switching surface. First, we deduce the condition of a control gain for sliding mode in a mean sense. Secondly, we derive an equation of an optimal switching surface, which is based on a quadratic evaluation of a state, from the equivalent control method. Lastly, through digital simulation we confirm the above results and robustness of VSCS disturbed random input.
