Bond-graph Input-State-Output Port-Hamiltonian formulation of memristive networks for emulation of Josephson junction circuits

A bond graph Input-State-Output Port-Hamiltonian formulation of memristive networks for Josephson junction circuits in state space is presented. The methodology has applications to the modeling of SQUIDs and other non-linear transducers and enables the formulation of input-output models of complex components embedded in non-linear networks

Modeling of inertial and compliance parametric uncertainties in Port-Hamiltonian systems using LFR

This paper presents a Linear Fractional Representation of a Port Hamiltonian System for which uncertainties are concentrated on the Hamitonian parameters. A basic block-diagram is provided and an illustration is shown on a hand-held cutting tool viewed as an effort multiplier

From canonical Hamiltonian to Port-Hamiltonian modeling application to magnetic shape memory alloys actuators.

International audienceThis paper presents the modelling of an actuator based on Magnetic Shape Memory Alloys (MSMA). The actuation principle relies on the ability of the material to change its shape under the application of a magnetic field. Previous models proposed by authors were based on canonical (symplectic) Hamiltonian modeling and thermodynamics of irreversible processes. These models, though physically cogent, are non-minimal differential algebraic dynamical models and hence less adapted for control purposes.This paper therefore proposes a modified and systemoriented modeling procedure which lends itself naturally to a port-Hamiltonian model. The latter is found to be a minimal realization of the above whereby interconnection between subsystems is clearly visible. Using Lagrange multipliers, constraints which arise due to causality and interconnection are expressed. In the last section, Differential Algebraic Equations (DAE) resulting from previous models are reduced to Ordinary Differential Equations (ODE) and by using coordinate transformations, constraints are decoupled from the system input/output. The resulting model is well-suited for control

Automated Generation of Explicit Port-Hamiltonian Models from Multi-Bond Graphs

Port-Hamiltonian system theory is a well-known framework for the control of complex physical systems. The majority of port-Hamiltonian control design methods base on an \emph{explicit} input-state-output port-Hamiltonian model for the system under consideration. However in the literature, little effort has been made towards a systematic, automatable derivation of such explicit models. In this paper, we present a constructive, formally rigorous method for an explicit port-Hamiltonian formulation of multi-bond graphs. Two conditions, one necessary and one sufficient, for the existence of an explicit port-Hamiltonian formulation of a multi-bond graph are given. We summarise our approach in a fully automated algorithm of which we provide an exemplary implementation along with this publication. The theoretical and practical results are illustrated through an academic example

Derivation of Input-State-Output Port-Hamiltonian Systems from bond graphs

This paper presents methods to obtain models in the form of Input-State-Output Port-Hamiltonian Systems from causal nonlinear bond graph models. This is done first establishing equivalences among key variables in both domains through the comparison of the expressions of the stored system energy in both formalisms. Later, with the help of the general field-representation of bond graphs and its associated standard implicit form, the functions characterizing this class of Port-Hamiltonian Systems, i.e., interconnection, dissipation and input/output matrices, as well as their properties, are immediately expressed in terms of bond graphs parameters. Under suitable assumptions, the method supports the direct derivation of Input-State-Output Port-Hamiltonian Systems – which is an explicit type of PHS – even from bond graphs having causally coupled dissipators and storages in derivative causality, which are known to imply algebraic and implicit differential equations. The methods are illustrated with some application examples covering different causal situations. Besides its intrinsic interest as a technique for model conversion, the contribution is seen as a useful step towards implementing Port-Hamiltonian based control system design methods with the support of BG techniques

Automated Model Generation and Observer Design for Interconnected Systems : a Port-Hamiltonian Approach

Vernetzte Systeme stellen einen unverzichtbaren Teil moderner Gesellschaften dar. Mit dem Ausrollen neuer Kommunikationstechnologien und in Folge der fortgeschrittenen Nutzung von Synergiepotenzialen entstanden in den letzten Jahren vernetzte Systeme ungeahnten Ausmaßes. Aufgrund der Komplexität dieser Systeme, gelangen bestehende Modellierungs- und Beobachterentwurfsmethoden an ihre Grenzen. Modelle und Beobachter können deshalb häufig nur unter erheblichen Vereinfachungen entwickelt werden. Die vorliegende Dissertation schafft Abhilfe. Leitgedanke ist es, die Vorgänge der Modellerzeugung und des Beobachterentwurfs zu automatisieren. Hierzu werden in dieser Arbeit automatisierbare Modellierungs- und Beobachtermethoden auf Basis der Port-Hamiltonschen Systemtheorie entwickelt. Diese Methoden sind in einem Software-Prototyp namens AMOTO implementiert. In zwei Fallstudien wird AMOTO jeweils zur automatisierten Modellherleitung und zum automatisierten Beobachterentwurf eingesetzt. Computersimulationen weisen in beiden Fallstudien die Funktionstüchtigkeit der erzeugten Modelle und Beobachter nach und zeigen, dass diese genauere Ergebnisse liefern, als Modelle und Beobachter, die mit Methoden des bisherigen Stands der Technik entwickelt wurden. Dies unterstreicht die praktische Nutzbarkeit des vorgestellten Ansatzes. Es zeigt sich ferner, dass der Ansatz auf eine große Klasse vernetzter Systeme anwendbar ist. Somit leisten die Methoden, Algorithmen und Werkzeuge aus dieser Arbeit einen wichtigen Beitrag zur Bewältigung zukünftiger Herausforderungen in vernetzen Systemen