Influence of the PZT actuator asymmetry on the LQR control parameters in the active reduction vibrations of beams

The paper deals with the active reduction of beam vibrations using piezoelectric transducers (PZT). The LQR parameters of the control of an asymmetric actuator (a-PZT) depending on the length of its arms were analysed. The results were compared to those of the symmetrical PZT (s-PZT), so far used as standard. The actuator is modeled with two bending moments or two pairs of forces. The design of the LQR controller also took into account the location of the PZT on the beam. The reduction efficiency can also be increased by using asymmetrical PZT. To obtain the vibration asymmetry of the beam, simply supported at both ends, an asymmetrically point mass was added. The LQR control was applied to an asymmetric actuator on the beam. Two-parameter optimization was used to find the optimal proportions of the a-PZT arms. For such a problem, the LQR control parameters were found, which ensure the highest efficiency of vibration reduction.