Abstract: In order to improve the problem of large trajectory tracking control error and low control accuracy of ball and plate system, a differential flatness-based backstepping sliding mode control method is proposed for enhancing the tracking accuracy in ball and plate system. Firstly, based on the Euler-Lagrange equation, the kinematic model of ball and plate system is established, the decoupled linear state-space model is obtained by reasonable simplification. Taking the X-direction controller design as an example, the target state quantity and feedforward control quantity of the system are obtained by using differential flatness technology, and an error system is constructed. Then, the backstep method is used to realize the sliding mode control of the error system, and the stability of the closed-loop system is proved by Lyapunov stability theory. The hyperbolic tangent function is used in the algorithm to suppress the jitter of the sliding mode, and the trajectory tracking control of ball and plate system is realized with high accuracy. Simulation results show that the proposed control strategy has high control accuracy and better control performance.

Key words: ball and plate system, trajectory tracking, differential flat, backstepping sliding mode control; hyperbolic tangent function