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. |