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A. Macchelli, C. Melchiorri
"Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach"
 
Type Article
Author(s) A. Macchelli, C. Melchiorri
Title Modeling and Control of the Timoshenko Beam. The Distributed Port Hamiltonian Approach
Editor SIAM Journal On Control and Optimization (SICON), vol. 43, n.2, pag. 743-767
Keywords Modeling and control of flexible structures, Stokes--Dirac structures, Infinite dimensional port Hamiltonian systems, Control by damping injection, Casimir functions, Control by interconnection
Abstract
The purpose of this paper is to show how the Timoshenko beam can be fruitfully approached within the framework of distributed port Hamiltonian systems (dpH systems) so that rather simple and elegant considerations can be drawn regarding both the modeling and control of this mechanical system. After the distributed port Hamiltonian (dpH) model of the beam is introduced, the control problem is discussed. In particular, it is shown how control approaches already presented in literature can be unified, and a new control methodology is presented and discussed. This control methodology relies on the generalization to infinite dimensions of the concept of structural invariant (Casimir function) and on the extension to distributed systems of the so-called control by interconnection methodology. In this way, finite dimensional passive controllers can stabilize distributed parameter systems by shaping their total energy, i.e. by assigning a new minimum in the desired equilibrium configuration that can be reached if a dissipative effect is introduced.
Document caed.Document.pdf (242806 bytes)
Year 2004


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