Control of a Class of Underactuated Mechanical Systems by Using Fuzzy Sliding Mode Control with low computing volume and without Chattering

In this paper, a fuzzy sliding mode controller is presented for controlling a class of underactuated systems. In order to present the proposed method, at first, the sliding mode method for a single input-single output system is expressed. In the following, based on this design method, a sliding mode controller for a class of single input-multi output systems is presented. The mathematical proof shows that the closed loop system, in the presence of structured and un-structured uncertainties, has global asymptotic stability. In the proposed control due to the use of the sign function in the control input, the incidence of chattering is inevitable. For this reason, a fuzzy system is designed and added to the sliding mode controller. The proposed fuzzy sliding mode control eliminates existing problems and its design is done in such a way as to ensure the global asymptotic stability of the closed loop system. Finally, to demonstrate the proposed control performance, three-stage simulations are implemented on the inverse pendulum system. Simulation results show the performance of the proposed control.