Supervisory hybrid control of piezoelectric actuators utilized in tracking piecewise continuous trajectories

This article presents a supervisory hybrid control design for piezoelectric actuators utilized in tracking trajectories with intermittent jump discontinuities. We use a previously developed robust adaptive controller and a standard PID controller to construct this hybrid control strategy. We show that when the sub-controllers are used for step tracking, while primarily tuned for continuous trajectory tracking, large undesirable oscillations occur. Conversely, when the controllers are retuned for step tracking, their performance degrades in tracking high-frequency continuous trajectories. Thus, a supervisory hybrid controller is developed to track desired trajectories with occasional discontinuities, using both the robust adaptive and the PID controllers. The robust adaptive controller performs as the primary controller for tracking the continuous segments of the desired trajectory, while the PID controller is activated when the steps occur. Results indicate that the proposed supervisory hybrid controller outperforms both sub-controllers in tracking high-frequency trajectories with intermittent discontinuities.