Natural logarithm sliding mode control for vibration control application

This paper presents the control synthesis of a nonlinear sliding mode control, known as the "natural logarithm sliding mode control" (lnSMC), for a general n-th order system. The lnSMC offers a simple and straightforward design approach because it only requires tuning two design parameters. The first parameter has a physical meaning corresponding to the bounds of the state variables, which can be easily determined without a trial-and-error process. The second parameter is related to the controller's feedback gains, which ensure that the system dynamics converged to the sliding surface. Lyapunov stability theory is used to analyze the closed-loop system and finite-time convergence stability. As a case study, the natural logarithm sliding mode controller is designed to suppress the vibration in a simple spring-mass system and an active suspension system. The simulation study shows that the proposed controllers have significant vibration suppression performance. Furthermore, the simulation study indicates that the sliding mode controller designed by using the natural logarithm sliding manifold outperforms the standard linear sliding manifold counterpart. In addition, due to the nature of the nonlinear switching function that creates boundary states, lnSMC has a huge potential to be applied in a wider area of vibration control.