Adaptive hierarchical sliding mode control for ball-beam systems Online publication date: Sat, 30-Aug-2014
by Dianwei Qian; Xiangjie Liu; Linguang Li
International Journal of Advanced Mechatronic Systems (IJAMECHS), Vol. 4, No. 5/6, 2012
Abstract: Ball-beam system is one of the most enduringly popular and important laboratory models for teaching control systems engineering. It is very simple to understand as a system, but there exist strong non-linearities and dynamic couplings to illustrate control methods and control concepts. It belongs to a class of second-order under-actuated systems with gravity term and two degrees of freedom. The methodology of hierarchical sliding mode control (SMC) is developed for the class. But it excludes the ball-beam system due to its special dynamic model. In this paper, an adaptive hierarchical SMC law is addressed for the class. By modifying the expression of the hierarchical SMC, the presented method is able to cover the special case. The adaptive law and the control law are deduced from Lyapunov direct method. The asymptotic stability of all the sliding surfaces is proven by Barbalat's lemma and Lasalle's invariance principle. Simulation results show the feasibility of this method by stabilisation control of a ball-beam system.
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