Stability analysis of PD regulation for ball and beam system

Many nonlinear controllers for ball and beam system can achieve in some cases asymptotic stability. Only a few of them apply their nonlinear control theory results in real experiment. On the other hand, many laboratories use PD control for the ball and beam system, but theory analysis is based on a linear approximate model. Little effort has been made to analyze the PD control via the complete nonlinear model. In this paper we propose an asymptotically stabilizing PD controller that ensures that, for a well defined set of initial conditions, the ball remains on any point of the bar. Complete nonlinear model of ball and beam system and stability analysis of PD control are proposed in this paper. Real experiments are applied to test our theory results