Active Vibration Suppression of Smart Cantilever Beam with Sliding Mode Observer Using Two Piezoelectric Patches

  • Shibly A. AL-Samarraie Department of Control and Systems Engineering / University of Technology
  • Mohsin N. Hamzah Department of Mechanical Engineering / University of Technology
  • Imad A. Abdulsahib Department of Mechanical Engineering / University of Technology
Keywords: Smart materials, Active vibration, Piezoelectric, Sliding mode observer, Model ‎reduction, LQR controller

Abstract

This paper presents a vibration suppression control design of cantilever beam using two piezoelectric ‎patches. One patch was used as ‎an actuator element, while the other was used as a sensor. The controller design was designed via the balance realization reduction method to elect the reduced order model that is most controllable and observable. ‎the sliding mode observer was designed to estimate six states from the reduced order model but three states are only used in the control law. Estimating a number of states larger than that used is in order to increase the estimation accuracy. Moreover, the state ‎estimation error is proved bounded. An ‎optimal LQR controller is designed then using the ‎estimated states with the sliding mode observer, to ‎suppress the vibration of a smart cantilever ‎beam via the piezoelectric elements. The control spillover problem was avoided, by deriving an avoidance ‎condition, to ensure the ‎asymptotic stability for the proposed vibration ‎control design. ‎The numerical simulations were achieved to ‎test the vibration attenuation ability of the ‎proposed optimal control. For 15 mm initial tip ‎displacement, the piezoelectric actuator found ‎able to reduce the tip displacement to about 0.1 ‎mm after 4s, while it was 1.5 mm in the ‎open loop case.  The current experimental results showed a good performance of the proposed LQR control law and the sliding mode observer, as well a good agreement with theoretical results.

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Published
2017-03-31
How to Cite
AL-Samarraie, S., Hamzah, M., & Abdulsahib, I. (2017). Active Vibration Suppression of Smart Cantilever Beam with Sliding Mode Observer Using Two Piezoelectric Patches. Al-Khwarizmi Engineering Journal, 13(1), 50- 65. https://doi.org/10.22153/kej.2017.08.005
Section
Articles