Continuous dynamic modelling of bimorph piezoelectric cantilevered actuators considering hysteresis effect and dynamic behaviour analysis

Bimorph Piezoelectric Cantilevered (BPC) actuators have been of increasing interest in micro-manipulation processes during recent years. Due to properties such as transverse vibration, the performance and manoeuvrability have considerably improved, compared with conventional longitudinal piezoelectric actuators. Therefore, dynamic modelling of such actuators has been the centre of attraction. For this purpose, a target point on the actuator, e.g. the cantilever end tip, is usually considered as the actuator output. One degree of freedom lumped and continuous type dynamic models have been considered in prior research works. These types of modelling lead to two significant issues. First, the effect of higher vibrational modes in the actuator output is disregarded. Second, a minimum phase dynamic system is achievable for all target points regardless of position. In this paper, these two issues will be analytically and experimentally investigated. To this end, a linear continuous dynamic model for a general BPC actuator is derived and discretized by attaining exact mode shapes. The Prandtl–Ishlinskii (PI) model is utilized to model and identify the non-linear hysteresis behaviour. In contrast to previous works, dynamic behaviour analysis elaborates on the effect of higher modes in the actuator output response. In addition, the possibility of non-minimum phase behaviour based on the location of the target point is investigated. Simulation studies and experimental results confirm the validity of the proposed dynamic model and its behaviour analysis.