A Family of Sliding Mode Controllers: Analysis, Design and Comparison

Phuc Truong Loc Nguyen, Thanh T. Tran

Abstract: Sliding Mode Control (SMC) is a well-known and powerful approach for dealing with uncertainties in nonlinear dynamic systems. This paper presents an analysis, design, and comparison of different SMC controllers in the task of controlling a second-order single-input and single-output (SISO) nonlinear dynamic system. The nonlinear controller synthesis was formulated by utilizing the Backstepping Sliding Mode Control (BSMC) method, which applied a recursive design approach. In this technique, a switching function was directly selected and added to the controller during the design process. A family of hyperbolic and special functions was introduced and applied to the proposed controller with the aim of eliminating the chattering phenomenon and improving system stability as well as performance. A comparative study of these functions was done in two separate scenarios, where disturbances were applied and not. Numerical simulation results were compared between the traditional and novel approaches to validate the effectiveness and robustness of the BSMC controllers. Furthermore, the optimal shaping coefficient (SC) of each continuous switching function was identified and examined. As expected, the proposed continuous functions with their optimal SCs have delivered outstanding simulation results for the system when tracking some specific reference signals.