Performance Analysis of Ball and Beam System using Modern Control Techniques

The ball-and-beam system is an attractive laboratory experimental tool due to its inherent nonlinearity and open-loop instability. However, designing an effective ball-and-beam system controller is a challenge for researchers and engineers. In this paper, a mathematical model of the ball-and-beam system has been derived and the state space system model has been obtained. This system is an open loop unstable system because the system output (ball position) increases without a limit for a fixed input. To ensure that the ball will not fall down and only move or roll on the beam, a controller should be designed to control the system and make it stable. In this paper, modern control techniques such as full-state feedback controller and full-state feedback with integral action have been employed to study the system's response and achieve desired outcomes. In addition, a modern optimization control strategy known as linear quadratic regulator (LQR) has been employed too. MATLAB software has been used to design the controllers, analyze the system's behavior, and evaluate the effectiveness of the controllers in achieving stability. The step response of the system states using the suggested controller has been investigated and compared, in order to determine which control scheme provided the best performance. Finally, the results show that the integral full-state feedback controller is the most effective compared to other control methods, as it gives the best performance.