A method for open-loop control of dynamic motions of piezo-stack actuators

Precision control of three-dimensional dynamic motions of piezoelectric actuators is crucial for many applications of nanotechnology and precision engineering. In this paper, an open-loop technique to control the three-dimensional single-frequency motions of multi-axis piezo-stack actuators is presented. In this approach, the dynamic behavior of piezo-stack actuators is represented by the harmonic frequency response functions (hFRFs) that are obtained through an laser Doppler vibrometry (LDV)-based experimental characterization method. To obtain the desired motions at a given frequency, the actuator is excited at both the fundamental (motion) frequency and its harmonics, latter of which aiming to compensate for the unwanted higher-harmonic response components that arise due to non-linear dynamic behavior. The fundamental and the first-order compensatory excitation components are determined analytically using the inverse hFRFs. For the higher-order response terms, a compensation approach based on an iterative experimental technique is proposed. The effectiveness of the presented control method is demonstrated through a set of evaluation tests on two different three-axis piezo-stack actuators, where a set of motion-error metrics were defined and quantified. It was shown that the proposed method can be used to generate single-frequency motions with wide range of nanometric sizes with average errors less than 5% of the targeted motion amplitudes.