A novel reaching law for smooth sliding mode control using inverse hyperbolic function

This paper pertains to an important improvement in sliding mode control. The Sliding mode control is robust nonlinear control design technique well known for its robustness against certain class of disturbances and model uncertainties. The mentioned nonlinear design technique suffers from a phenomenon called chattering which consists of high frequency discontinuities introduced by the sliding mode controller. Various techniques have been suggested to remove the chattering however these techniques either result in decrease in the rigor or increase in the complexity of the resulting system. The purpose of this work is to formulate a new controller that intends to reduce the chattering effect and the Reaching Phase of the sliding mode control. The proposed Reaching law has been formulated by using inverse hyperbolic function in its gain term. The gain at the start of reaching phase is high which results in faster convergence towards the surface. Once the Sliding Mode starts the gain is reduced which reduces the chattering. Simulation results show significant reduction of chattering in the control input as well as in the output of the system.