Title :
Tracking control of mechanical systems with a unilateral position constraint inducing dissipative impacts
Author :
Biemond, J.J.B. ; van de Wouw, N. ; Heemels, W.P.M.H. ; Sanfelice, Ricardo G. ; Nijmeijer, H.
Author_Institution :
Dept. of Mech. Eng., Eindhoven Univ. of Technol., Eindhoven, Netherlands
Abstract :
In this paper, the tracking control problem is considered for mechanical systems with unilateral constraints with dissipative impacts. In these systems, impacts are triggered at the exact moment when the constraint becomes active. Typically, a small time mismatch is introduced between the impacts of the plant and the reference, even if this trajectory is arbitrarily close to the reference. Consequently, the Euclidean tracking error cannot behave stable in the sense of Lyapunov, such that standard tracking control approaches are unfeasible. However, desirable tracking behaviour does not imply that the Euclidean error vanishes asymptotically over time. We design continuous-time controllers that can handle the impact time mismatch and achieve accurate tracking of reference trajectories containing dissipative impacts for mechanical systems with a unilateral constraint. The behaviour of the resulting closed-loop dynamical system is illustrated with an exemplary bouncing ball system.
Keywords :
Lyapunov methods; closed loop systems; mechanical control equipment; position control; tracking; Euclidean error; Euclidean tracking error; Lyapunov; bouncing ball system; closed-loop dynamical system; continuous-time controller design; dissipative impacts; mechanical systems; tracking behaviour; tracking control; unilateral constraints; unilateral position constraint; Asymptotic stability; Convergence; Feedforward neural networks; Measurement uncertainty; Mechanical systems; Trajectory;
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2012.6426527