Sampled data systems passivity and discrete port-Hamiltonian systems

In this paper, we present a novel way to approach the interconnection of a continuous and a discrete time physical system first presented in . This is done in a way which preserves passivity of the coupled system independently of the sampling time T. This strategy can be used both in the field of telemanipulation, for the implementation of a passive master/slave system on a digital transmission line with varying time delays and possible loss of packets (e.g., the Internet), and in the field of haptics, where the virtual environment should 'feel' like a physical equivalent system.

I. Introduction

The USE of network theoretical concepts and passivity is of great importance not only in electrical circuits, but also in robotics [4]– [6]. Recently, a very general and mathematically elegant way to handle general nonlinear networks in a geometrical way has been introduced which is based on Dirac structures [7]– [11]. Systems described in this form are called port-Hamiltonian. The port-Hamiltonian formalism is able to describe any physical system using the mathematical object of a Dirac structure together with some elements which do represent storage, dissipation and interaction of the system with the rest of the world. The interconnection of these parts is based on the concept of a power port which is rich enough to describe spatial mechanism interconnections [11] or even flexible structures [12]. The main idea stems from bond graphs introduced by Paynter [13] which has been incredibly enriched by a proper mathematical description and analysis. The importance of port-Hamiltonian theory has also been recognized by the European Union which recently sponsored a project called Geoplex (http://www.geoplex.cc ) whose goal is to study these kind of systems.