Optimal placement of piezoelectric torsional actuator based on genetic algorithm

Aiming at placement optimization of a piezoelectric torsional actutor bonded onto a thin-wall bar, a profound torsional vibration investigation was performed. Dynamic equations of the thin-wall bar-actuator system was theoretically derived using Lagrange equation and Assumed Mode Method, and the state-space expression of the dynamic system was developed. The thin-wall bar was divided into several position units, the controllability Grammian was chosen as the objective function, and optimal placement of piezoelectric torsional actuator was obtained using Genetic Algorithm. At last, feedback control was performed, and the first three closed-loop frequency response of the angular displacement of the free end was obtained. The results show that the procured optimal placement is feasible. The actuator is bonded onto this position for control where the system has the best controllability, and significant torsional vibration suppression is obtained.