Applying the Simplex Method to Design the Optimal Parameters of a Sliding Mode Controller for a System With Input Saturation and Unknown Disturbance Bound

Abstract

Sliding mode controllers have wide practical applications due to their simple structure and robustness to disturbance. Although various sliding mode controllers have been proposed, most relevant studies have only investigated the conditions required to stabilize the system. For example, system stability can be guaranteed if the parameters in the control law satisfy specific inequalities or boundary conditions. However, the control power of a real system has a saturation limit, which increases the complexity of the system. Moreover, even if a stable controller is identified, the response performance of the system may not achieve the expected results. Therefore, the determination of the optimal parameters is a key step in designing a sliding mode controller. This paper proposes an error-integral-type sliding mode controller whose main characteristic is that irrespective of the system order, it only needs to determine three key parameters. We used the Nelder–Mead simplex method to assist designers in searching for optimal controller parameters more efficiently, even when the real system has the limitation of input saturation and the disturbance bound is unknown. Finally, we performed numerical simulations on a magnetic levitation system to demonstrate the feasibility and effectiveness of the proposed method.

Keywords

• Integral sliding mode controller
• magnetic levitation system
• optimal control
• optimization method
• saturation
• simplex method