This paper deals with the stabilization via Casimir generation and energy shaping of linear, lossless, distributed port-Hamiltonian systems. Once inputs and outputs of the distributed port-Hamiltonian system have been chosen to obtain a well-defined boundary control systems, conditions for the existence of Casimir functions in closed-loop and of the associated semigroup are given, together with a criterion to be used to check asymptotic stability. Casimir functions suggest how to select the controller Hamiltonian to introduce a minimum at the desired equilibrium, while stability is ensured if proper "pervasive" boundary damping is present. The methodology is illustrated with the help of a Timoshenko beam with full-actuation on one side.

A. Macchelli (2012). Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems. Amsterdam : Elsevier [10.3182/20120829-3-IT-4022.00041].

Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems

MACCHELLI, ALESSANDRO
2012

Abstract

This paper deals with the stabilization via Casimir generation and energy shaping of linear, lossless, distributed port-Hamiltonian systems. Once inputs and outputs of the distributed port-Hamiltonian system have been chosen to obtain a well-defined boundary control systems, conditions for the existence of Casimir functions in closed-loop and of the associated semigroup are given, together with a criterion to be used to check asymptotic stability. Casimir functions suggest how to select the controller Hamiltonian to introduce a minimum at the desired equilibrium, while stability is ensured if proper "pervasive" boundary damping is present. The methodology is illustrated with the help of a Timoshenko beam with full-actuation on one side.
2012
4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, Proceedings of
120
125
A. Macchelli (2012). Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems. Amsterdam : Elsevier [10.3182/20120829-3-IT-4022.00041].
A. Macchelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/153054
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