Stabilizing Control for a Ball and Beam System Considering Restricted Beam Angle

Abstract

This paper develops for a ball and beam system a design method of control system transferring the ball to a target position considering restricted beam angle. First, we compensate the beam drive system as a second-order delay system to reduce the beam angle constraint to an input one. Using modal decomposition methods, we decompose the plant into the stable and unstable subsystems, and derive a nested saturating control law globally asymptotically stabilizing the unstable one. The control system using this control law has the property that when the ball is transferred, its speed is mostly limited less than a specified value. To reduce the steady-state error of the ball position as well as to alleviate the reset windup, a new type of IMC controller is introduced where a saturated output error between the actual plant stabilized by the saturating control law and the model is fed back. The effectiveness of the control law is demonstrated numerically and experimentally.