Nonlinear Dynamic Modeling and Control of 2-DOF Tunable Prism Driven by Dielectric Elastomer

Dielectric elastomer-driven tunable prisms are novel liquid optical devices that enable two degree-of-freedom beam deflection. However, their periodic dynamic response exhibits hysteresis, creep, and rate-dependent viscoelastic behavior, which makes modeling the nonlinear dynamics and precise control challenging. This paper analyzes the dynamics and kinematics of a biconical tunable prism. Based on the principle of non-equilibrium thermodynamics, a nonlinear dynamic model of the tunable prism is established, taking into account the geometric configuration of the prism, the viscoelasticity of the DE, and the liquid resistance. We developed feedforward controller based on the model and combined with a PI feedback controller to form the hybrid controller. Experimental results show that the theoretical model can accurately predict the complex dynamic response of the system, with root mean square error of prediction lower than 5.59%. Single and dual axis deflection angle tracking root mean square error does not exceed 1.25%. These results demonstrate the effectiveness of the proposed dynamic modeling and tracking control method.