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Journal of Engineering
Volume 2014, Article ID 839128, 9 pages
Research Article

Adaptive Vibration Control of Piezoactuated Euler-Bernoulli Beams Using Infinite-Dimensional Lyapunov Method and High-Order Sliding-Mode Differentiation

1Department of Mechanical and Aerospace Engineering, King Mongkut’s University of Technology North Bangkok, 1518 Pracharat Sai 1, Bangkok 10800, Thailand
2Institute of General Mechanics, RWTH Aachen University, Templergraben 64, 52056 Aachen, Germany

Received 31 July 2014; Revised 26 November 2014; Accepted 8 December 2014; Published 22 December 2014

Academic Editor: Jyoti Sinha

Copyright © 2014 Teerawat Sangpet 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.


This paper presents an adaptive control scheme to suppress vibration of flexible beams using a collocated piezoelectric actuator-sensor configuration. A governing equation of the beams is modelled by a partial differential equation based on Euler-Bernoulli theory. Thus, the beams are infinite-dimensional systems. Whereas conventional control design techniques for infinite-dimensional systems make use of approximated finite-dimensional models, the present adaptive control law is derived based on the infinite-dimensional Lyapunov method, without using any approximated finite-dimension model. Thus, the stability of the control system is guaranteed for all vibration modes. The implementation of the control law requires a derivative of the sensor output for feedback. A high-order sliding mode differentiation technique is used to estimate the derivative. The technique features robust exact differentiation with finite-time convergence. Numerical simulation and experimental results illustrate the effectiveness of the controller.