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Mathematical Problems in Engineering
Volume 2014, Article ID 606817, 9 pages
http://dx.doi.org/10.1155/2014/606817
Research Article

Adaptive Robust Sliding Mode Vibration Control of a Flexible Beam Using Piezoceramic Sensor and Actuator: An Experimental Study

1School of Civil Engineering, Wuhan University, Wuhan, Hubei 430072, China
2Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA
3School of Civil Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China

Received 28 September 2013; Revised 23 December 2013; Accepted 8 January 2014; Published 26 May 2014

Academic Editor: ShengJun Wen

Copyright © 2014 Ruo Lin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents an experimental study of an adaptive robust sliding mode control scheme based on the Lyapunov’s direct method for active vibration control of a flexible beam using PZT (lead zirconate titanate) sensor and actuator. PZT, a type of piezoceramic material, has the advantages of high reliability, high bandwidth, and solid state actuation and is adopted here in forms of surface-bond patches for vibration control. Two adaptive robust sliding mode controllers for vibration suppression are designed: one uses a discontinuous bang-bang robust compensator and the other uses a smooth compensator with a hyperbolic tangent function. Both controllers guarantee asymptotic stability, as proved by the Lyapunov’s direct method. Experimental results verified the effectiveness and the robustness of both adaptive sliding mode controllers. However, from the experimental results, the bang-bang robust compensator causes small-magnitude chattering because of the discontinuous switching actions. With the smooth compensator, vibration is quickly suppressed and no chattering is induced. Furthermore, the robustness of the controllers is successfully demonstrated with ensured effectiveness in vibration control when masses are added to the flexible beam.