In order to improve the vibration suppression effect of the flexible beam system, active control based on soft piezoelectric macro-fiber composites (MFCs) consisting of polyimide (PI) sheet and lead zirconate titanate (PZT) is used to reduce the vibration. The vibration control system is composed of a flexible beam, a sensing piezoelectric MFC plate, and an actuated piezoelectric MFC plate. The dynamic coupling model of the flexible beam system is established according to the theory of structural mechanics and the piezoelectric stress equation. A linear quadratic optimal controller (LQR) is designed based on the optimal control theory. An optimization method, designed based on a differential evolution algorithm, is utilized for the selection of weighted matrix Q. Additionally, according to theoretical research, an experimental platform is built, and vibration active control experiments are carried out on piezoelectric flexible beams under conditions of instantaneous disturbance and continuous disturbance. The results show that the vibration of flexible beams is effectively suppressed under different disturbances. The amplitudes of the piezoelectric flexible beams are reduced by 94.4% and 65.4% under the conditions of instantaneous and continuous disturbances with LQR control.
Keywords: LQR; differential evolution algorithm; flexible beam; piezoelectric polymer; vibration control.