System Identification and Control Design of a Piezoelectric-Actuated Cantilever Beam

Abstract

Cantilever beams are widely found in many different applications such as aircraft wings and microelectromechanical devices. One of the problems associated with cantilever structures is that uncontrolled tip vibrations can cause serious structural damage. Piezoelectric materials can be used to control the vibration of cantilever beams. In this paper, a piezoelectric-actuated cantilever beam is utilized to help students understand basic concepts in system dynamics and learn state-space control design methods. The piezoelectric cantilever beam is modeled as a second-order system with one degree-of-freedom. The system parameters, including the natural frequency, the damping ratio and zeroes, are identified from the measurement of free and sinusoidal responses. An observer-based controller is then designed using the identified dynamics model. Both computer simulations and realtime experiments are conducted to demonstrate the accuracy of the model and the performance of the controller. Such a smart structure can be easily set up to improve the education in the area of controls at both the undergraduate and introductory graduate levels.