Tracking control of time-varying discontinuous trajectories with application to probe-based imaging and nanopositioning

In this effort, a supervisory switching control strategy is proposed for effective control of piezoelectric actuators in tracking harmonic trajectories with sudden discontinuities. A piezoelectrically-driven nanopositioning stage with high resolution capacitive position sensor is utilized in a set of experiments to study the performance of controllers tuned for tracking of continuous trajectories in tracking of stepped trajectories, and vice versa. Using a mixed Lyapunov-based robust adaptive and PID controller, it is observed that the controllers tuned for continuous trajectory tracking demonstrate large oscillations with light damping rate in tracking of stepped inputs. Conversely, when they are tuned for smoother step tracking, poor performance is achieved in tracking of continuous trajectories within a desired frequency range. Hence, a switching strategy is proposed to track desired trajectories using two controllers separately tuned for continuous and stepped trajectories. Switching conditions and transformation laws are then derived and experimentally implemented. Results indicate that the proposed framework presents higher performance compared to the individual controllers in tracking of discontinuous trajectories.