An Inversion-Based Model Predictive Control With an Integral-of-Error State Variable for Piezoelectric Actuators

Piezoelectric actuators have been widely employed in various nanopositioning systems. Hysteresis exhibited by piezoelectric actuators can degrade their behavior, and thus the tracking performance of positioning systems. To improve the performance of the systems, control of hysteresis has been drawing considerable attention. One of the issues that remain to be addressed in the controller design is how to deal with the constraints (e.g., the input voltage) that might be applied to the piezoelectric actuators. To avoid overloading the piezoelectric actuators, the mechanism of saturation is typically employed in control schemes, which, however, can degrade the control performance. This paper presents the development of an inversion-based model predictive control with an integral-of-error state variable to compensate for the piezoelectric-actuator hysteresis. The proposed method allows for the consideration of constraints in the controller design. Theoretical proof of the zero steady-state error and disturbance rejection properties of the proposed method is also provided. To verify the effectiveness of the control method, experiments were conducted with the results showing that the proposed method can improve the performance of piezoelectric actuators.