Dynamic modeling of a piezoelectric micro-lens actuator with experimental validation

Micro-lens actuators with low power consumption, fast response time, large deflection, and low driving voltage are highly desirable for micro-optics applications such as smartphone cameras, miniaturized confocal microscopy, and pico-projectors. Micro-lens piezoelectric actuation with feedback control has shown promising characteristics in this regard. The accurate dynamic model of the piezoelectric actuator is required to facilitate novel feedback control design. However, there are no dynamic models, available in the literature for multi-layer thin film piezoelectric micro-actuators that consider the effect of the driving voltage and residual stress in the layer. Here, we present a dynamic analytical model of a piezoelectrically driven multi-layer micro-lens actuator taking into account the residual stress and the driving voltage. The modified Euler–Bernoulli beam equation is used to model the micro-lens actuator, and it is validated with both Finite Element Analysis (FEA) and experiments. The first resonance frequency calculated using the analytical model shows excellent agreement with the experimental and FEA results. The micro-lens displacement to driving voltage transfer function is derived from the dynamic model to obtain the time-domain characteristics of the micro-lens actuator. The settling times for the driving step input voltage obtained from the transfer function, FEA, and experiments agree well. The model not only accurately predicts the dynamic behavior of the piezoelectric micro-lens actuators but also can be applied to other multi-layered piezoelectric micro-structures. It also facilitates advanced control design that improves the dynamic response of piezoelectric actuators for micro-optic applications.