Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs

Roger Fotsu Ngwompo, Rene Galindo

Research output: Contribution to journalArticle

Abstract

Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of such
systems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo junction structure is proposed as an alternative representation for Linear Time-Invariant (LTI) bond graph models with internal modulated sources. The pseudo junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realising the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems.
LanguageEnglish
Pages14-28
JournalProceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering
Volume231
Issue number1
DOIs
StatusPublished - 1 Jan 2017

Fingerprint

Control systems
Mechatronics
Constitutive equations
Energy conservation
Dynamical systems
Modulation

Keywords

  • Bond graph, passivity, junction structure, cascade interconnection, dissipassive systems, conservative systems

Cite this

@article{dee45a63ade6404e9243eedd94f44322,
title = "Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs",
abstract = "Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of suchsystems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo junction structure is proposed as an alternative representation for Linear Time-Invariant (LTI) bond graph models with internal modulated sources. The pseudo junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realising the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems.",
keywords = "Bond graph, passivity, junction structure, cascade interconnection, dissipassive systems, conservative systems",
author = "Ngwompo, {Roger Fotsu} and Rene Galindo",
year = "2017",
month = "1",
day = "1",
doi = "10.1177/0959651816682144",
language = "English",
volume = "231",
pages = "14--28",
journal = "Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering",
issn = "0959-6518",
publisher = "Sage Publications",
number = "1",

}

TY - JOUR

T1 - Passivity analysis of linear physical systems with internal energy sources modelled by bond graphs

AU - Ngwompo, Roger Fotsu

AU - Galindo, Rene

PY - 2017/1/1

Y1 - 2017/1/1

N2 - Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of suchsystems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo junction structure is proposed as an alternative representation for Linear Time-Invariant (LTI) bond graph models with internal modulated sources. The pseudo junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realising the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems.

AB - Integrated dynamic systems such as mechatronic or control systems generally contain passive elements and internal energy sources that are appropriately modulated to perform the desired dynamic actions. The overall passivity of suchsystems is a useful property that relates to the stability and the safety of the system, in the sense that the maximum net amount of energy that the system can impart to the environment is limited by its initial state. In this paper, conditions under which a physical system containing internal modulated sources is globally passive are investigated using bond graph modelling techniques. For the class of systems under consideration, bond graph models include power bonds and active (signals) bonds modulating embedded energy sources, so that the continuity of power (or energy conservation) in the junction structure is not satisfied. For the purpose of the analysis, a so-called bond graph pseudo junction structure is proposed as an alternative representation for Linear Time-Invariant (LTI) bond graph models with internal modulated sources. The pseudo junction structure highlights the existence of a multiport coupled resistive field involving the modulation gains of the internal sources and the parameters of dissipative elements, therefore implicitly realising the balance of internal energy generation and dissipation. Moreover, it can be regarded as consisting of an inner structure which satisfies the continuity of power, and an outer structure in which a power scaling is performed in relation with the dissipative field. The associated multiport coupled resistive field constitutive equations can then be used to determine the passivity property of the overall system. The paper focuses on systems interconnected in cascade (with no loading effect) or in closed-loop configurations which are common in control systems.

KW - Bond graph, passivity, junction structure, cascade interconnection, dissipassive systems, conservative systems

UR - https://doi.org/10.1177/0959651816682144

U2 - 10.1177/0959651816682144

DO - 10.1177/0959651816682144

M3 - Article

VL - 231

SP - 14

EP - 28

JO - Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering

T2 - Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering

JF - Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering

SN - 0959-6518

IS - 1

ER -