Discrete port-Hamiltonian systems: mixed interconnections

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling at the discrete level itself. The goal of this paper is to apply a previously developed discrete modeling technique to study the interconnection of continuous systems with discrete ones in such a way that passivity is preserved. Such a theory has potential applications, in the field of haptics, telemanipulation etc. It is shown that our discrete modeling theory can be used to formalize previously developed techniques for obtaining passive interconnections of continuous and discrete systems

Port-Hamiltonian systems: an introductory survey

The theory of port-Hamiltonian systems provides a framework for the geometric description of network models of physical systems. It turns out that port-based network models of physical systems immediately lend themselves to a Hamiltonian description. While the usual geometric approach to Hamiltonian systems is based on the canonical symplectic structure of the phase space or on a Poisson structure that is obtained by (symmetry) reduction of the phase space, in the case of a port-Hamiltonian system the geometric structure derives from the interconnection of its sub-systems. This motivates to consider Dirac structures instead of Poisson structures, since this notion enables one to define Hamiltonian systems with algebraic constraints. As a result, any power-conserving interconnection of port-Hamiltonian systems again defines a port-Hamiltonian system. The port-Hamiltonian description offers a systematic framework for analysis, control and simulation of complex physical systems, for lumped-parameter as well as for distributed-parameter models

The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction

Geometric Scattering in Robotic Telemanipulation

In this paper, we study the interconnection of two robots, which are modeled as port-controlled Hamiltonian systems through a transmission line with time delay. There will be no analysis of the time delay, but its presence justifies the use of scattering variables to preserve passivity. The contributions of the paper are twofold: first, a geometrical, multidimensional, power-consistent exposition of telemanipulation of intrinsically passive controlled physical systems, with a clarification on impedance matching, and second, a system theoretic condition for the adaptation of a general port-controlled Hamiltonian system with dissipation (port-Hamiltonian system) to a transmission line

Weak Form of Stokes-Dirac Structures and Geometric Discretization of Port-Hamiltonian Systems

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The geometric approximation of the Stokes-Dirac structure by a finite-dimensional Dirac structure is realized using a mixed Galerkin approach and power-preserving linear maps, which define minimal discrete power variables. (iii) With a consistent approximation of the Hamiltonian, we obtain finite-dimensional port-Hamiltonian state space models. By the degrees of freedom in the power-preserving maps, the resulting family of structure-preserving schemes allows for trade-offs between centered approximations and upwinding. We illustrate the method on the example of Whitney finite elements on a 2D simplicial triangulation and compare the eigenvalue approximation in 1D with a related approach.Comment: Copyright 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

Explicit Simplicial Discretization of Distributed-Parameter Port-Hamiltonian Systems

Simplicial Dirac structures as finite analogues of the canonical Stokes-Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input-output finite-dimensional port-Hamiltonian systems that emulate the behavior of distributed-parameter port-Hamiltonian systems. This paper elaborates on the matrix representations of simplicial Dirac structures and the resulting port-Hamiltonian systems on simplicial manifolds. Employing these representations, we consider the existence of structural invariants and demonstrate how they pertain to the energy shaping of port-Hamiltonian systems on simplicial manifolds

Port-Hamiltonian modeling for soft-finger manipulation

In this paper, we present a port-Hamiltonian model of a multi-fingered robotic hand, with soft-pads, while grasping and manipulating an object. The algebraic constraints of the interconnected systems are represented by a geometric object, called Dirac structure. This provides a powerful way to describe the non-contact to contact transition and contact viscoelasticity, by using the concepts of energy flows and power preserving interconnections. Using the port based model, an Intrinsically Passive Controller (IPC) is used to control the internal forces. Simulation results validate the model and demonstrate the effectiveness of the port-based approach

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

The wave equation as a port-Hamiltonian system and a finite-dimensional approximation

The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of di?erent geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a ?nite-dimensional port-Hamiltonian system, which also preserves the conservation laws

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 [1][2] [3]. 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