Nonlinear PD Regulation for Ball and Beam System

Abstract

The ball and beam system is one of the most popular laboratory experiments for control education. There are two problems for ball and beam control: (1) many laboratories use simple controllers such as PD control, but theory analysis is based on linear models, and (2) nonlinear controllers for the ball and beam system have good theory results, but they are seldom used in laboratories. Little effort has been made to analyse PD control with nonlinear models. In this paper we modify the normal PD control in two ways for the ball and beam system: parallel and serial PD regulations; then we analyse the stability of these types of PD regulations with the complete nonlinear model. Real experiments are applied to test our theory results. This paper gives a good example of how to apply nonlinear theory in the laboratory for control education.