Tracking and disturbance rejection for fully actuated mechanical systems

In this paper, we solve the tracking and disturbance rejection problem for fully actuated passive mechanical systems. We assume that the reference signal rr and its first two derivatives ṙ,r̈ are available to the controller and the disturbance signal dd can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an arbitrary L2L2 signal. We combine the internal model principle with the ideas behind the Slotine–Li adaptive controller. The internal model-based adaptive controller that we propose causes the closed-loop state trajectories to be bounded, and the tracking error and its derivative to converge to zero, without any prior knowledge of the plant parameters. An important part of our results is that we prove the existence and uniqueness of the state trajectories of the closed-loop system.