Trajectory Tracking Control Employing Nonlinear Compensator and State Observer for Photothermal-Driven Liquid Crystal Elastomer Actuator

The trajectory tracking control for the photothermal-driven liquid crystal elastomer (LCE) actuator presents a significant challenge due to its hysteresis nonlinear characteristic and its inherent complex deformation mechanism. To address this challenge, this article proposes a trajectory tracking control method for the LCE actuator utilizing a nonlinear compensator and a state observer. The proposed control is a multistep control, which includes temperature control from the input voltage to the LCE temperature and displacement control from the LCE temperature to the LCE displacement. In the proposed method, we design a non-Lipschitz continuous state-feedback controller to realize finite-time convergence control of the temperature. As for the displacement control, we design a state observer to estimate the change rate of the LCE displacement. Meanwhile, a nonlinear inverse compensator is designed to compensate for the hysteresis nonlinearity of the LCE dynamics, which simplifies the complex nonlinear control problem into a linear control problem. Hence, the pole placement method can be utilized to design a trajectory tracking controller to achieve the control objective. The proposed control method is validated by tracking control experiments with different target trajectories.