Synchronization of ball and beam systems with neural compensation

Abstract

Ball and beam system is one of the most popular and important laboratory models for teaching control system. It is a big challenge to synchronize ball and beam systems. There are two problems for ball and beam synchronized control: 1) many laboratories use simple controllers such as PD control, and theory 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. In this paper we first use PD control with nonlinear exact compensation for the cross-coupling synchronization. Then a RBF neural network is applied to approximate the nonlinear compensator. The synchronization control can be in parallel and serial forms. The stability of the synchronization is discussed. Real experiments are applied to test our theory results.

Adaptive backstepping control design for ball and beam system

“…SMC, both in its static and dynamic configurations, was applied in [13] considering simplifications in the ball and beam nonlinear dynamic model. In [14], a SMC method was proposed that utilizes the Jacobian for the linearization of the system. In [15], an integral SMC approach was employed for the control design of ball and beam system.…”

Gravitational search algorithm-based fuzzy control for a nonlinear ball and beam system

“…The ball and beam system is considered as a benchmark in control engineering whose underlying concept can be used for solving the stabilisation problem of diverse systems such as the balance problem of deals with goods to be carried by moving robots and also the spaceship position control systems in aerospace engineering (Glower & Munighan, 1997;Hauser, Sastry, & Kokotovic, 1992). Furthermore, many classical and modern control methods have been used to stabilise the ball and beam system (Li & Yu, 2010;Yu, 2009). On the other hand, the development of fuzzy controllers for various engineering problems has been a major research activity in recent years (Bui, Tran, & Vu, 2012;Chen, 2011;Harb & Smadi, 2004;Li, Liao, & Lei, 2012;Yeh, Chen, Lo, & Liu, 2012).…”

Fuzzy-modal control for the ball and beam system

“…However, the modal control law is linear, and the reaction time of the system does not depend on its initial state. For essentially nonlinear objects such an idealization is unsatisfactory, which stimulates the use of fuzzy [5,6] and neural network [7] methods for solving this problem.…”