Piezoelectric patch vibration control unit connected to a self-tuning RL-shunt set to maximise electric power absorption

This paper presents a modular vibration control unit formed by a piezoelectric patch connected to a self-tuning RL-shunt, which can be bonded on thin structures to reduce the resonant response of a specific target low-order flexural mode due to a stationary stochastic excitation. The resistive and inductive components of the shunt are tuned online with an extremum seeking gradient search algorithm in such a way as to maximise the time-averaged electric power absorbed by the shunt from the resonant response of the target flexural mode of the structure. The tuning is thus implemented locally in the unit without the need of additional sensors to monitor the vibration of the structure. The paper presents both simulation and experimental results for a thin rectangular panel model structure, which is excited by a broadband stationary stochastic force and is equipped with five piezoelectric patches connected to the proposed self-tuning RL-shunts. To start with, the study shows that the resistance and inductance necessary to minimise the time-averaged resonant response of the target flexural mode closely match the values that would maximise the time-averaged electric power absorption by the shunt from the resonant response of the target flexural mode. Also, it shows that these two cost functions describe mirrored bell-surfaces with constant-inductance and constant-resistance principal axes. Hence, it proposes an independent inductance and resistance tuning sequence, which is based on an extremum seeking gradient search algorithm along the two principal directions of the electric power cost function. Finally, the online convergence to the optimal RL values of the proposed tuning algorithm is verified experimentally using a digital shunt.