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

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.

Keywords

• Smart materials
• Active vibration
• Piezoelectric
• Sliding mode observer
• Model ‎reduction
• LQR controller