Hybrid feedback PID-FxLMS algorithm for active vibration control of cantilever beam with piezoelectric stack actuator

FxLMS (Filtered-x Least Mean Square) algorithm and PID (Proportional Integral Derivative) controller have been widely used for AVC (Active Vibration Control). Yet, the convergence rate and vibration suppression performance are restricted by each other for both the classical FxLMS algorithm and the traditional PID controller. A hybrid PID-FxLMS algorithm which combines the feedback FxLMS algorithm and PID controller is proposed, and applied to improve the vibration control efficiency of piezoelectric cantilever beam. In order to conveniently install the piezoelectric stack on the beam structures, a new piezoelectric stack actuator is designed and installed at the root of cantilever beam. Meanwhile, a coupled finite element model of the piezoelectric stack actuator and cantilever beam is established in ABAQUS, and the state-space model of the coupled system is obtained. Subsequently, based on the obtained state-space model, an AVC simulation and experimental system is built to verify the effectiveness of the proposed algorithm. Numerical and experimental results show that convergence rate and vibration suppression performance of the hybrid PID-FxLMS algorithm are much better than that of the classical FxLMS algorithm or traditional PID controller alone, while the hybrid controller also has strong adaptability and anti-noise ability.