Discrete time reaching law based variable structure control for fast reaching with reduced chattering

In this paper, a variable structure control law is proposed for discrete time sliding mode control so as to reduce both reaching time and quasi sliding mode band reduction. This new law is composed of two different sliding variable dynamics; one to achieve fast reaching and the other to counter its effect on widening the quasi sliding mode band. This is accomplished by introducing a boundary layer around the sliding surface about which the transformation of the sliding variable dynamics takes place. This provides the flexibility to choose the initial dynamics in such a way as to speed up the reaching phase and then at the boundary transform this dynamics to one that reduces the quasi sliding mode band. Thus, the law effectively coalesces the advantageous traits of hitherto proposed reaching laws that succeed in either the reduction of reaching phase or the elimination of quasi sliding mode band. The effectiveness of the proposed reaching law is validated through simulations.