Variable structure control for affine systems based on sigmoid variable rate reaching law

The existing design approaches of variable structure control for a class of affine systems with uncertainties are discussed and three modified sigmoid variable rate reaching laws are proposed based on sigmoid function and normal distribution function. Variable structure control system designed by appling this types of reaching laws, better than the exponential rate reaching law and the variable rate reaching law can reach the region of the switching surface in finite pace and the stability of origin can be guaranteed. The approaches decrease system chattering effectively and fast speed is kept. The simulation result illustrates the feasibility and validity of the proposed approaches.