Dissipative Physical Systems

Abstract

In this chapter we shall present a class of dissipative systems which correspond to models of physical systems and hence embed in their structure the conservation of energy (first principle of thermodynamics) and the interaction with their environment through pairs of conjugated variables with respect to the power. First, we shall recall three different definitions of systems obtained by an energy based modeling: controlled Lagrangian, input-output Hamiltonian systems and port controlled Hamiltonian systems. We shall illustrate and compare these definitions on some very simple examples. Second we shall treat a class of systems which gave rise to numerous stabilizing control using passivity theory and corresponds to models of robotic manipulators. In each worked case we show how the main functions associated to a dissipative system (the available storage, the required supply, storage functions) can be computed analytically and related to the energy of the physical system.