Data-Driven Model Development and Feedback Control Design for PZT Bimorph Actuators

In the paper, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in dynamic operating regimes. The actuator dynamics are initially modeled using the homogenized energy model (HEM) framework. This provides a comprehensive high-fidelity model, which can be inverted and implemented in real time for certain control regimes. To improve efficiency, we additionally discuss the development of data-driven models and focus on the implementation of a surrogate model based on a dynamic mode decomposition (DMD). Finally, we detail the design and implementation of a PI controller on the surrogate and high-fidelity models.