Piezoelectric actuators (PEAs) are widely used in many nano-resolution manipulations. A PEA's hysteresis becomes the main factor limiting its motion accuracy. The distinctive feature of a PEA's hysteresis is the interdependence between the width of the hysteresis loop and the frequency or rate of the control voltage. Generally, the control voltage is first amplified using a voltage amplifier (VA) and then exerted on the PEA. In this VA-PEA module, the linear dynamics of the VA and the nonlinearities of the PEA are coupled. In this paper, it is found that the phase lag of the VA also contributes to the rate dependence of the VA-PEA module. If only the PEA's hysteresis is considered, it will be difficult to achieve high-frequency modeling and control. Consequently, great difficulties arise in high-frequency hysteresis compensation and trajectory tracking, e.g., in the fast scanning of atomic force microscopes. In this paper, the VA-PEA module is modeled to be the series connection of a linear subsystem and a nonlinear subsystem. Subsequently, a feedforward phase-dynamics compensator is proposed to compensate for both the PEA's hysteresis and the phase lag of the VA. Further, an unscented Kalman-filter-based proportional-integral-derivative controller is adopted as the feedback controller. Under this feedforward-feedback combined control scheme, high-bandwidth hysteresis compensation and trajectory tracking are achieved. The trajectory tracking results show that the closed-loop trajectory tracking bandwidth has been increased to the range of 0-1500 Hz, exhibiting excellent performance for fast scanning applications.
Keywords: direct inverse modeling; high frequency; hysteresis compensation; rate dependence; trajectory tracking.