Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties

Abstract

It is shown that the network representation (as obtained through the generalized bond graph formalism) of non-resistive physical systems in interaction with their environment leads to a welldefined class of (nonlinear) control systems, called port-controlled Hamiltonian systems. A first basic feature of these systems is that their internal dynamics is Hamiltonian with respect to a Poisson structure determined by the topology of the network and to a Hamiltonian given by the stored energy. Secondly the network representation provides automatically (intrinsically to the notation) to every port-control variable (input) a port-conjugated variable as output. This definition of port-conjugated input and output variables, based on energy considerations, is shown to have important consequences for the observability and controllability properties, as well as the external characterization of portcontrolled Hamiltonian systems.

Port-Based Modeling and Simulation of Mechanical Systems With Rigid and Flexible Links

“…4(a). Similar results can also be obtained for (18). This nonlinear system can be written in port-Hamiltonian form and is characterized by a couple of power ports, i.e., a pair of twist/wrench, which represents finite-dimensional counterpart of the boundary conditions (13).…”

“…The flexible link is modeled as an infinitedimensional system in the form (12) or (18), with boundary conditions given by (13) that define a pair of power ports at the extremities of the link. A finite-dimensional approximation is necessary to carry out simulations with, possibly, varying boundary conditions originated, for example, by statefeedback controllers.…”

“…The mathematical description of the whole mechanical system, which is based on the port-Hamiltonian formalism [18]- [20], results from the interconnection of simpler components (e.g., rigid bodies, flexible links, and kinematic pairs). It is shown that, in this manner, it is not necessary, in the definition of the dynamic model, to simplify the elastic and nonlinear effects present in the flexible parts, and therefore, mechanisms with large deflections can also be handled easily.…”

“…As far as finite-dimensional systems are concerned, the dynamical model results from a power-conserving interconnection of a set of atomic elements characterized by a particular energetic behavior (e.g., storage, dissipation, and conversion) [18]- [20]. Each component can interact with the environment through a port, i.e., a pair of signals whose dual product gives the power flow.…”

Stability of Hybrid Dissipative Hamiltonian Systems

“…In recent years, Port-Controlled Hamiltonian (PCH) systems proposed by [7], have been well investigated in a series of works [9][10][11][12]. The Hamiltonian function in a PCH system, which is considered as the total energy, i.e., the sum of potential and kinetic energies in mechanical systems, is a good candidate of Lyapunov functions for many physical systems, and has been successfully applied to the control of power systems in some recent works, see [10] and references therein.…”