Optimal Control of a Ball and Beam System through LQR and LQG

This paper presents the design of an optimal control strategy for a 2 degree of freedom standard laboratory system - Ball and Beam. The system is an open loop and non-linear system, which is inherently unstable. A linear quadratic regulator (LQR) is designed and implemented with an objective to control the position of ball on the beam by varying the angular position of beam. As all states of system are not measurable, therefore, an observer based state feedback is applied. The modelling and simulation of the LQR strategy for controlling the system is carried out on MATLAB SIMULINK platform. The LQR strategy is very effective in stabilizing the system. A comparative analysis is also presented for LQR and Linear Quadratic Gaussian (LQG) control under the effect of sensor noises in simulation.