Stable synchronization control for two ball and bearn systerns

Ball and beam system is one of the most enduringly popular and important laboratory models for teaching control systems engineering. There are two main problems for ball and beam control: 1) many laboratories use simple controllers such as PD control, but theoretical analysis is based on linear models. 2) nonlinear controllers for ball and beam system have good theory results, but they are seldom used in real applications and almost nobody perform synchronization control for ball and beam systems. In this paper we modify the normal PD control in two ways for each ball and beam system: parallel and serial PD controllers for the regulation case are given then we analyze the stability of these types of controllers for the synchronization of two ball and beam systems. A simulation case is applied to test our theory results.