Abstract
Variable Structure Systems (VSS) change the structure on both sides of a switching surface, which is instituted in the state space, and its change gives rise to sliding motion. The Sliding Mode Control (SMC) utilizes this sliding motion and carries out the feedback control by variable structure feedback elements. While in sliding motion, the SMC system remains insensitive to parameter variations and disturbances.
In this paper, we deduce the condition of a control gain for the SMC system in a mean sense of the white noise and state-dependent noise respectively. The Sliding region is an overall switching surface on the regulation problem of the SMC system, however, on the follow-up control problem, in this paper, sliding motion doesn't occur in a limited region, given by a function of the reference input. Furthermore, we derive an equation of an optimal switching surface, which is based on a quadratic evaluation of the state, from the equivalent control method. Lastly, through digital simulations of several examples we confirm the above results.
