Optimization of piezoelectric actuator systems for vibration control of flexible structures

Actuator placement is a major concern in control system designs. Utilizing piezoelectric actuators increases the complexity of actuator designs, because both actuator location and dimensions need to be considered. A comprehensive study was conducted in this dissertation on the optimization of piezoelectric actuator designs for vibration suppression of flexible structures.

The investigation on the optimal piezoelectric actuator designs were grouped into two parts. Part one covered actuator designs when the same number of actuators as the controlled modes are used. Approaches were formed to optimally design piezoelectric actuators which requires least control efforts.

In part two of this dissertation, a method named the Weighted Pseudoinverse Method was introduced to deal with the cases in which fewer actuators than the controlled modes are utilized. The weighted pseudoinverse method yields a optimal transformation from modal control forces into the actuator-moments in physical space. Based on the Weighted pseudoinverse method, the piezoelectric actuator designs were optimized to ensure least-control-effort actuator designs. A simply-supported beam was used as an example to demonstrate the effectiveness of the design methods proposed in this dissertation. However, the design methods are applicable to general cases.