Dynamic Modeling and Focus Control of a Piezo-Actuated Liquid Tunable Lens

The piezo-actuated liquid tunable lens exhibits complex characteristics, including electromechanical coupling, fluid dynamics, membrane and plate vibration, and hysteresis nonlinearities, which pose significant challenges to achieving precise focus control. To address these issues, this article proposes a dynamic model that integrates these factors into a unified framework for the piezo-actuated liquid tunable lens. The model employs a spring-damper-mass particle chain system to equivalently represent the coupled dynamics of the membrane-fluid-plate system in the liquid tunable lens. An equivalent circuit is used to capture the electromechanical coupling effect of the piezoelectric actuator (PEA). Furthermore, a discrete-form Duhem equation is introduced to model the hysteresis nonlinearities in the PEA. Using this dynamic model, a model-based parameter-tuned PID controller is implemented to achieve precise focus control of the lens. Experimental results demonstrate that the proposed theoretical model aligns well with experimental data, and the controller successfully achieves precise focus control of the piezo-actuated liquid tunable lens.