Free Chattering Fuzzy Sliding Mode Controllers to Robotic Tracking Problem

Sliding mode control (SMC) is a powerful approach to solve the tracking problem for   dynamical systems with uncertainties. However, the traditional SMCs introduce actuator chattering phenomenon which performs a desirable behavior in many physical systems such as servo control and robotic systems, particularly, when the zero steady state error is required.  Many methods have been proposed to eliminate the chattering from SMCs which use a finite DC gain controller. Although these methods provide a free chattering control but they deals with only the steady state error and are not able to reject input disturbances. This paper presents a fuzzy combined control (FCC) using appropriate PID and SMCs which presents infinite DC gain. The proposed FCC is a free chattering control which guarantees a zero steady state error and rejects the disturbances. The stability of the closed loop system with the proposed FCC is also proved using Lyapunov stability theorem. The proposed FCC is applied to a two degree of freedom robot manipulator to illustrate effectiveness of the proposed scheme.