Robust time-optimal command shaping for velocity tracking of piezoelectric actuators

This paper introduces a robust time-optimal command shaping technique for the application of piezoelectric actuators on scanning tunneling microscopy (STM). Though feedback control has been widely used to improve the linearity, the maximum scan rate is substantially limited by the turnaround transients in the scan path. Therefore, feedforward approach is considered to improve the scan speed. In the authors' earlier work a robust input design method based on the command shaping technique of constrained least-square optimization was proposed for a general class of systems without rigid-body mode. When this method is applied to velocity tracking, however, unique problems arise. This paper proposes a solution to these problems by modifying the sufficient condition in the frequency domain for robust inputs of velocity tracking, and the search procedure for the time-optimal solution is illustrated.