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Stefano Stramigioli, Romeo Ortega, Alessandro Macchelli
"Modelling and control of dynamical systems. The port Hamiltonian approach"
 
Type Other
Author(s) Stefano Stramigioli, Romeo Ortega, Alessandro Macchelli
Title Modelling and control of dynamical systems. The port Hamiltonian approach
Editor Tutorial at the 43rd IEEE Conference on Decision and Control (CDC'04)
Keywords port Hamiltonian systems, modeling, nonlinear control
Abstract

A fundamental concept in engineering sciences is the notion of an open system, that is a system having a direct interface with its environment. The concept of an open system is directly linked to the notion of network, where open systems are coupled to each other through their interfaces. Complementary to the network modeling of complex systems is the design and control of systems with a required functionality obtained by coupling open system components. From this perspective, a physical system can be modeled as the result of the interconnection of a small set of atomic elements, each of them characterized by a particular energetic behavior (e.g. energy storing, dissipation or conversion). Moreover, each element can interact with environment through a port, that is a couple of input and output signals whose combination gives the power flow. The network structure allows a power exchange between these components and describes the power flows within the system and between the system and the environment.

Common examples of controlled systems interacting with environments can be easily found in several domains which may seem very different from each other, such as the mechanical (devices for advanced manipulation, telemanipulation and haptic systems, legged robots), the electromechanical (electric motors, power converters) and the chemical ones.

Elegant and general mathematical tools for modelling and controlling interacting physical systems belonging to different domains are framed in the Hamiltonian formalism and their use can be very helpful in solving complex problems, where other approaches may lead to more heuristic or confuse solutions. In order to describe and to manipulate these dynamical models in a systematic way, it is convenient to use a coordinate-free, geometric framework for their mathematical formulation, especially because of the intrinsic and strong nonlinearities in their system behavior. The framework of port Hamiltonian systems, where the physical components are formulated as generalized Hamiltonian systems coupled to each other through power ports, will be presented in this Tutorial by leading researchers. In this context, the resulting complex physical system can be geometrically described as a Hamiltonian system with respect to the geometric object of a Dirac structure representing the power conserving network structure. This framework allows the description of a wide class of finite dimensional nonlinear systems, such as mechanical, electro-mechanical, hydraulic and chemical ones. Moreover, the port Hamiltonian representation has been recently generalized in order to cope with the infinite dimensional case, thus generalizing the classical Hamiltonian formulation of a distributed parameter system. The key point is the notion of infinite dimensional interconnection structure, namely Stokes-Dirac structure.

The main goal of the Tutorial is to present methods, techniques and tools for modelling and control complex dynamical systems, using an integrated system approach allowing to deal with physical components stemming from different physical domains (electrical, mechanical, thermodynamic), both in the lumped-parameter and in the distributed parameter case. This Tutorial aims to represent an occasion to describe with precision and attention the topics that are developed within the European sponsored project GeoPlex, reference code IST-2001-34166.

Notes
A workshop web site has been prepared in order to provide the potential audience of all the necessary informations concerning the workshop itself (schedule, speakers, notes). The site is reachable at http://www-lar.deis.unibo.it/people/amacchelli/cdc04-tutorial/ . Once the workshop will be concluded, also copies of the slides will be available electronically together with journal and conference papers of interest for further studies.
Document 7fed.Document.pdf (77891 bytes)
Year 2004


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