Numerical Analysis on Chattering Suppression Ability of Smoothening Function in SMC

Tong, Weng Sun (2019) Numerical Analysis on Chattering Suppression Ability of Smoothening Function in SMC. Final Year Project (Bachelor), Tunku Abdul Rahman University College.

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Abstract

Sliding mode controller is a widely known robust controller, providing outstanding control performances especially in disturbance forces rejection. However, the control performance and applicability of sliding mode controller is often constrained by the chattering phenomenon that induced undesired vibration. This undesirable phenomenon is caused by the high frequency of oscillation, originating from the signum function in mathematical formulation of the controller. This dissertation proposes a smoothening method in designing the sliding mode controller to reduce the chattering effect induced by the signum function. This proposed method modifies the mathematical algorithm of the control laws in original sliding mode controller, where the original signum function in control laws is replaced by proposed smoothening functions, namely; Hyperbolic tangent function, Langevin function, Gauss error function and Sigmoid-like function. In addition, the response optimization method is use to iteratively search for the controller gain parameter of sliding mode controller, i= {K, λ} and i= {d} for the extra parameter of sigmoid-like function respectively to objective function. The initial set up parameters of response optimization is based on step response envelope and signal bound in this design. The control performances of sliding mode controller with proposed smoothening functions are analyzed and compared with the original sliding mode controller with signum function in simulation. Which the control performances of sliding mode controller with proposed smoothening functions are analyzed based on the root mean square of tracking error, maximum tracking error, and changes in amplitude of chattering.