Technical Report DC 2012.039 Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts

In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints and dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint is closed. Hence, when a reference trajectory experiences an impact, the constraint of a nearby plant trajectory is expected to close just before or after the impact of the reference, introducing a small time mismatch between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Considering mechanical systems with a unilateral constraint and dissipative impacts, we design continuous-time controllers that can handle this impact time mismatch, and achieve accurate tracking of reference trajectories containing impacts. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.