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A. Macchelli
"Port Hamiltonian systems. A unified approach for modeling and control finite and infinite dimensional physical systems"
Type PhD Thesis
Author(s) A. Macchelli
Title Port Hamiltonian systems. A unified approach for modeling and control finite and infinite dimensional physical systems
Editor University of Bologna - DEIS
Keywords port Hamiltonian system, modeling, control

from the Preface:

In Chapter 1, the port Hamiltonian class of dynamical system is introduced. The starting point is energy and the assumption that a system can be represented by a proper interconnection of a well-defined set of atomic elements, each of them characterized by a particular energetic behavior. From a mathematical point of view, this network can be described by means of a Dirac structure and system con¯guration can be easily given in terms of energy variables whose time evolution depends onthe variation of the internal energy. Furthermore, it is shown that the interaction between dynamical systems in port Hamiltonian form is simply a power exchange. Once the port Hamiltonian representation of a dynamical system is deduced, it is possible to approach the control problem. In Chapter 2, the classical theory on passive system and passive control is presented, together with some new results on the regulation of port Hamiltonian systems. Moreover, it is shown that it is possible to merge passivity-based control techniques with variable structure ones in order to achieve further robustness properties.

In Chapter 3, the port Hamiltonian formulation is generalized in order to cope with dis- tributed parameter systems. Classical in¯nite dimensional models are presented in this new formulation. Among them, the Maxwell's equations and the Timoshenko beam. Then, in Chapter 4, the control problem of distributed port Hamiltonian system is approached. By generalization of the energy-based control techniques developed for the finite dimensional case, the regulation problem of distributed parameter system in Hamiltonian form is discussed. New results for the stabilization of the Timoshenko beam and of a simple class of mixed finite and infinite dimensional port Hamiltonian systems are presented. Moreover, in Chapter 5, some aspects of the scattering theory within the framework of port Hamiltonian system are discussed. Starting from a novel formulation in finite dimensions, the scattering theory is generalized in order to deal with infinite dimensions. Well-established results valid for the finite dimensional case are generalized in order to study the power propagation and exchange phenomena for distributed parameter systems.

Finally, in Appendix B some results concerning the real-time control of robots with real- time Linux-based operating systems are presented.


This work has been done in the context of the European sponsored project GeoPlex, reference code IST-2001-34166. Further informations at

The research activity has been also supported by the Nonlinear and Adaptive Control (NACO2) network, funded by the European Commission's Training and Mobility of Researchers (TMR) Programme.

Document e499.Document.pdf (2295278 bytes)
Year 2003

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