This article presents a controller design for an infinite dimensional system. After a short introduction, where the practical importance of vibration control is outlined and the investigated structure is introduced, a related finite dimensional system is analyzed. This part of the contribution is intended to illustrate the idea of the proposed controller design in the context of port controlled Hamiltonian systems. The application of the method to the infinite dimensional system finally results in a controller with well defined physical meaning. Finally a simulation demonstrates the applicability of the developed controller. This contribution presents a controller design for a distributed mechanical system, where the appearing partial differential equations are not approximated. The asymptotic stabilization of the flexible structure, with respect to a desired reference motion (e.g. the rigid body motion) is the goal of the controller design. The control problem is solved by the consideration of the kinetic and potential energy of a rigid reference system and the kinetic and potential energy of the actual motion of the flexible structure. The analysis of the difference between the energy stored in the desired and actual motion and its time derivative results, that this function is positive definite with respect to the rigid body motion and that one is able to define a control law that guarantees the negative semi definiteness of its time derivative. From physical observations one is able to assume, that this energy evolution is equivalent to the stabilization of the motion of the flexible structure with respect to the rigid body motion.
Vibration control of a flexible structure consisting of a car and a beam with tip mass
Schwingungsregelung einer flexiblen Struktur aus einem Automobil und einem Balken mit Spitzenmasse
2004
4 Seiten, 4 Bilder, 2 Quellen
Conference paper
English
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