Adaptive Control of a Ball and Beam System

Ball and beam balancing systems are commonly found in control systems laboratories because they are mechanically simple while presenting the challenge of controlling a nonlinear system. The main ideas of this paper are to model the ball and beam system and to control it using adaptive control. The model was formed by separating the system into two parts, and this was then controlled using a cascading control scheme. For the inner loop control, the motor was controlled using simple adaptive control (SAC) and compared to proportional derivative (PD) control. In the outer loop with the ball and beam system, ball position was controlled using PD control and was compared to linear quadratic regulator (LQR) control. Experimental results show that though PD control performed better when only controlling the motor, SAC performed better in the cascading control scheme when paired with either PD or LQR as outer loop control. When comparing PD and LQR, the results show that PD performs better.