Koopman Operator Learning Control of the Piezoelectric Actuator

The piezoelectric actuator is one kind of device that can drive nanoscale motion. However, the nonlinear hysteresis effect induced by its natural material greatly degrades its positioning accuracy. To handle this challenging issue, this work develops a Koopman model predict control (Koopman- MPC) framework for the piezoelectric actuator. Specifically, the Koopman operator theory is adapted for modeling the piezoelectric actuator dynamics. A simple yet powerful linear model spanned in a high-dimensional space is thus constructed to characterize the hysteresis dynamics. Subsequently, upon the established Koopman model, an MPC scheme is put forward for tracking control of piezoelectric actuators. Therein, by sustained optimizing a cost function containing future outputs and control increments, the control input is obtained. Moreover, extensive tracking simulations are carried out on a simulated piezoelectric actuator for verifying the feasibility and effectiveness of the Koopman- Mpc scheme.