Abstract: In order to solve the chattering phenomenon in sliding mode control of nonlinear the ball and plate system and the multi-disturbance problem in trajectory tracking, we studied a sliding mode control scheme based on a three-step method. Firstly, establish the ball and plate system state-space model, and design the sliding mode control law to overcome the uncertain disturbance of the system. Secondly, combining the three-step control law with the sliding mode control algorithm, design a three-step sliding mode controller to avoid the chattering phenomenon in the sliding mode control. Finally, prove the closed-loop control system stability by Lyapunov function. Compared with the simulation results, this method's trajectory tracking control effectiveness is further verified. 

Key words: ball and plate system, three-step method, sliding mode control, trajectory tracking