Automatic fourier synthesis based input-shaping for scanning piezo-electric actuators

This paper presents an automatic Fourier synthesis-based input-shaping algorithm for repetitive force-curve trajectories, applied to a piezo-electric actuator. A periodic scan-signal is generated by Fourier synthesis, consisting of the fundamental frequency and its even and odd harmonics. In order to compensate for the system dynamics of the used piezo-electric actuator, amplitude and phase response at these frequencies are identified. By adjusting amplitude and phase of each individual frequency component, the tracking error is reduced significantly. The presented method also demonstrates its capability of improving the non-linear behavior of piezoelectric actuators. The technique is experimentally evaluated on a piezo-electric stack-actuator, used as fast Z-actuator within an atomic force microscope (AFM). Comparing the presented method to an uncompensated triangular signal as well as input shaping methods, presented in literature, shows a significant reduction of tracking error of 84% and 65%, respectively.