A Novel State Transformation Approach to Tracking of Piecewise Linear Trajectories

In this paper, we propose a novel approach for tracking of piecewise linear trajectories, such as triangular and staircase waveforms. We derive state and input transformations, which result in closed-loop error dynamics driven by a series of impulses. The proposed control structure takes the form of an output-feedback-feedforward system that is straightforward to implement. In contrast to the recently proposed tracking control methods for such trajectories, the closed-loop stability is not affected by the frequency of the desired triangular reference. The method is implemented on a nanopositioner serving as the scanning stage of an atomic force microscope.