State Dependent Riccati Equation based Nonlinear Controller Design for Ball and Beam System

Abstract

The design of robust controller for nonlinear uncertain system has three important challenges, namely, nonlinearity, parameter uncertainty and external disturbance. Hence implementing a control algorithm for nonlinear unstable system is always a challenging task. In this paper, we propose a nonlinear controller using State Dependent Riccati Equation (SDRE) technique for a ball and beam system, which is inherently nonlinear and unstable system. Using the first principles,the equation of motion of the ball and beam system is obtained, and the nonlinear dynamics of the system is transformed into State Dependent Coefficient (SDC) matrices using Extended Linearization Technique. One of the key advantages of expressing the dynamics of system in SDC is that it fully captures the nonlinear characteristics of the system. Moreover, in SDRE control, since the weighing matrices are also expressed as a function of state variables, it provides better tracking response than that of its linear counterpart, LQR. Simulations are carried out to assess the trajectory tracking response, disturbance rejection property of controller and robustness of the system against parameter uncertainty. Simulation results prove that the SDRE based control cannot only provide improved transient response but also make the system more robust against disturbance and parameter uncertainty.