Presenting of a novel high-order sliding mode control based on Lyapunov theory

In this paper, we present a novel control scheme based on high-order sliding mode control (HOSM) for nonlinear systems under uncertainty. The stability and robustness of the proposed controller have been proven using Lyapunov’s method. The controller not only withstands uncertainties and disturbances but also significantly reduces the amplitude and frequency of chattering compared to existing algorithms. Furthermore, the suggested high-order sliding mode controller provides the ability to adjust the chattering frequency through its parameters. Initially, the sliding surface is introduced for second-order dynamics, followed by the necessary stability assumptions to ensure system stability. Then, a new second-order sliding mode controller is proposed and its stability is verified through Lyapunov’s method. Detailed simulation results using a planar robot demonstrate the controller's performance, which is compared with existing algorithms. The results confirm that the new controller effectively manages uncertainties, ensuring stable system control. The proposed controller not only reduced the frequency of chattering but also decreased the steady-state error for a two-links robot. Simulation shows the decrease in root mean square error compared to twisting and super-twisting controllers.