Nonlinear Dynamic Surface Control Design for Ball and Beam System with Parameter Uncertainties

This paper considers the design of nonlinear dynamic surface control (DSC) scheme for the ball and beam system with parameter uncertainties. It invokes adaptive nonlinear-in-parameter (NIP) approximator to model the uncertainty terms of the system. Then, the proposed scheme is designed by combining the DSC approach and the adaptive NIP approximator to control the position of the ball in the presence of parameter uncertainties. No prior knowledge about the uncertainties is required and all parameters of the approximator are adjusted during real time operation. Stability analysis of the closed-loop system is guaranteed by the Lyapunov theorem. Also, it is shown that all the signals of the closed-loop system are uniformly ultimately bounded. Finally, some simulation results are presented to verify the robustness and effectiveness of the propose scheme.