Active vibration control of a flexible beam

ACTIVE VIBRATION CONTROL OF A FLEXIBLE BEAM by Shawn Le There has been tremendous growth in the study of vibration suppression of smart material structures with lead zironate titanate (PZT) material by the control engineering community. This thesis considers a cantilever beam with bonded piezoceramic actuators and a sensor for the study of vibration control. The flexible beam dynamic model is first derived analytically according to the Euler Bernoulli Beam Theory. The first three mode shapes and natural frequencies of the beam are constructed analytically and verified with finite element analysis. The validity of the smart structure was experimentally verified. The natural frequencies and damping parameters for each mode were experimentally verified and adjusted. In this study, a transfer function consisting of the first three modes is constructed to implement both classical derivative (D) and proportional and derivative (PD) control. Then a state space model consisting of the first two modes of the beam is constructed to design and implement the modern linear quadratic regulator (LQR) state feedback control algorithm. A smart-structure beam station was built according to the instruction of Steven Griffin [6]. The Griffin's analog circuit was modified to integrate with the Matlab-Quanser real-time control unit. In the analytical and experimental study, the D, PD, and LQR state-feedback controller provided significant vibration suppression. ACKNOWLEDGEMENTS First and foremost I would like to thank my committee chair and advisor, Professor Ji Wang, for his guidance and support for making this work possible. I would like to thank Professor Winncy Du and Professor Neyram Hemati for taking the time and interest in serving as my committee members. I would like to thank my two close electrical engineering friends from San Diego, Khang Nguyen and Lam Tran. They have been great in helping me understand the electrical circuit of this work. I would especially like to thank my friend and classmate Howlit Ch'ng for keeping me company while working on this thesis in the San Jose State University Control Lab. In addition, I would like to thank him for helping me set up and use the Matlab-Quanser real-time control system.