Publication Date

Fall 2009

Degree Type


Degree Name

Master of Science (MS)


Mechanical and Aerospace Engineering


Ji Wang.

Subject Areas

Engineering, Aerospace.; Engineering, Mechanical.


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.