Nonlinear observer-based robust controller design for ball and beam system: an LMI-based approach

Abstract

In this paper, a nonlinear observer-based robust controller for ball and beam system (BBS) is proposed. The BBS consists of a long beam tilted by a servo or electric motor together in which ball rolls back and forth on the top of the beam. The concept of one-sided Lipschitz function is applied to the BBS for the observer design. The sufficient and necessary conditions that satisfy the existence of observer are explored in the form of linear matrix inequality (LMI). On the basis of estimated states obtained from the nonlinear observer, a sliding mode controller (SMC) is proposed for the BBS. In the proposed control scheme, firstly a nonlinear sliding surface is established, and then a robust control law is designed for robust performances and fast convergence of response. To ensure the sliding motion, the existence of the switching surface is proved using proposed observer-based control law. Stability analysis of the overall closed loop system is done by using Lyapunov stability criteria. Simulation studies have been carried out to validate the performance of the proposed scheme. Finally, robustness issue has also been addressed on the basis of comparative evaluation.