A survey of bond graphs : Theory, applications and programs

A Survey of Bond Graphs : Theory, Applications and Programs byJENNY

MONTBRUN-DI

FILIPPO,

MARISOL DELGADO

Departmento de Procesos y Sistemas, Caracas 1081 -A, Venezuela CLAUDE

BRIE

Lahoratoire d’Automatique, Rennes Cedex, France und

Universidad Simon Bolivar, Apdo. 89000,

HENRY

INSA,

20 Avenue des Buttes de Coesmes, 35043

M. PAYNTER

Mechanical Engineering Texas, U.S.A.

Department,

The University

of’ Texas at Austin, Austin,

ABSTRACT : This paper presents (I survey ojthe bond graph method from its conception and creation by Prof. Henry Puynter to the present. A thematic chss$cation of the bibliographical material is given depending on whether work deals with the dejmition sf theoretical details of bond graphs, applications of’ bond gruphs to particular ,jields, or y’ it deals with a computer program developed using the bond graph theory. A list ofjournals which publish bond graph related articles, as well as textbooks is also presented. The surrey, though exhaustive, does not pretend to be all inclusive. Some M,orks may have been unintentionally omitted due to obvious limitations on accessinq und listing all the relevant literature concerning the topic.

I. Introduction

The bond graph technique, used for modeling dynamical multiport systems of a multidisciplinary nature was created in 1959 by Professor Henry Paynter of the Mechanical Engineering Department of the Massachusetts Institute of Technology (U.S.A.). Since its invention, hundreds of papers, books and articles have been published by Paynter and others in the United States and other countries. Some of them refer to the mathematical theory and techniques of bond graph, others refer to the application of the method to different fields, and still others refer to the development of computer programs using the method. Paynter’s effort to develop a general theory for engineering systems began in 1950, with the belief that energy and power alone are the fundamental dynamical variables, and that such variables are the ones that allowed all physical interactions and transactions. One of the reasons for the creation of the bond graph technique, as Paynter acknowledges, was to generalize the electric circuit diagram concept, as well as to remove some of its limitations. While trying to generalize concepts and

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seek graphical representation of them, he was influenced by many people and many theories, and it was on April 24, 1959 that he completed the system of bond graphs. Since then. it has become a formal discipline.

II. Theoq The theory of bond graphs has been under continuous development. The early concepts of the technique were first published by Paynter in 1958 (1) and 1959 (2), showing the representation of power interactions with a single line but without the operating rules since they were not yet formulated. Another early publication (3) presented an almost complete bond graph system. but without the O- and Ijunctions. From then on, the development of the theory for the bond graph method started. There are some specific papers which deal with the theoretical basis and dennitions of the method (448), with its structural properties (9912), with fundamental definitions, and its properties versus traditional schemes (such as flow graphs and block diagrams) (13), with the properties of the power conserving elements, both in terms of equations and bond graph elements (9), with a new matrix representation of bond graphs (where the arrows on bonds have already been assigned) (14). with a brief review on the relationship between the structure of bond graph and the system models of linear, time-invariant systems (15) and with a procedure which formalizes the techniques and an unambiguous notation (16). Some other works on theoretical details of the method deal with the definition of state variables; equations and equation formulation through bond graphs (17 24) ; a procedure for the systematic generation of linear state equations in terms of energy variables (25); which was expanded to cover systems containing nonlinearities (26) ; the writing of equations using energy and co-energy state functions and Lagrange’s equations (27); a procedure where the original equations are reduced to a form suitable for modal decomposition (28. 29) ; an automatic generation technique of nonlinear system equations (30.31) : the derivation of the state space equations for parallel systems (32) ; the derivation ofdifferential equations for mechanical systems, approached in several ways (33); the study of implicit equations and fields (34440), the automated symbolic derivation of state equations (41), bond graph adapted dual space formulation (42) and bond graph sign conventions (43). Theoretical works on the study of junction structures are: four theorems that together establish the number and types of basis and variables for simple and weighted. standard and proper junction structures (44) ; simple computational rules for determining the solvability of the linear junction structure equations for multiport systems (45, 46) ; the theoretical basis for junction structures (47) ; sonic fundamental theorems concerning the relationship between the junction structure and the effort and flow equations (48) ; the solvability of certain classes ofjunction structures (49) ; the relationship between the port constitutive equations of bond graph junction structure and the constitutive equations of its individual junctions (50) ; the properties of bond graph junction structure matrices (51) ; linear junction

Surcey qf Bond Graphs

structures (52) ; and three upper bounds for the number of bases of an arbitrary weighted junction structure (53). Works on the study of causality are as follows : the rules for causality assignment (54-56); some useful bond graph identities which often eliminate paradoxical situations, in which sign conventions and causality interact strangely (57); the application of causality in order to understand the model (58) ; the use of causality for direct programming of continuous system simulation languages (59) ; how bond graphs and the sequential causality assignment algorithm (SCAP) can be used in building a qualitative model of a system (60); and a fast complete method for automatically assigning causality to bond graphs (61). Papers on theoretical aspects of lumped and distributed systems are the following : bond graphs and modal decomposition to simulate the interacting lumped and distributed systems with very short characteristic times (62, 63) ; bond graphs for large-scale lumped structures (64) ; for finite models of distributed systems (65, 66) ; for distributed system models (67, 68) ; for the modeling of 1-dimensional distributed systems using vector bond graphs or multibond graphs (69, 70) ; and for distributed parameter models (71). There are papers on the comparison of linear graphs and bond graphs (72-74), and the demonstration that hypernetworks (a generalization of the linear graph concept) give an equivalent description of multiport systems as bond graphs (75). There are some papers that present bond graphs as a unified modeling theory for physical systems (76-89) and the modeling of dynamical systems by Hamiltonian analysis (90). Some other theoretical work on bond graphs is related to the extensions of the method for the delay bond graph technique (91), Lagrangian bond graphs (92, 93), gyrobondgraphs (12,94-98), vector bond graphs or rather multibond graphs (69, 70, 99-103), thermodynamic bond graphs or rather generalized bond graphs (104-112) and pseudo bond graphs (113-119). Regarding new system elements : the development of the memristor (120, 121) ; the inductance and capacitance mutators (122); the RS-fields (123, 124) ; the multiport transformer (125-127) ; the gyristor (128, 129) ; the symplectic gyrator (104, 105); and the two-port transactor (130). Additional theoretical works are : an approach for extracting information about the eigenvalues of a linear, time invariant dynamic system (97, 131) ; controlability tests for linear systems (132) ; how a bond graph can be used to construct observers for systems (21); the relationships between the power and energy in a nonlinear physical system, and the analogous quantities associated with variables representing small deviations from steady-state values (133), and how the method was used to perform a fast graphical diagnosis on a desired input-output behavior of a non-linear controlled system (134). An algorithm which enables one to determine the nature of the equilibrium state of a system with constant inputs by direct inspection of its bond graph representation (135), model simplification using bond graph techniques (136), and a dynamic data graphic description of a bond graph (137) has been described. A constitutive and modulation structure that might be put on bond graphs (138), a type of model for rapidly switched devices which is easily adjusted to minimize Vol 328. No 516. PP 565-606. 1991 Prmtrd ,n Great Br~tam

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numerical stiffness problems (139), transformation from bond graph to system graph (140), and the theory of bond graphs to describe fluidic or electric systems (141) have been described. Articles describing a method that extends the use of bond graphs to nonholonomic systems (142-144), how the bond graph graphic symbols are used to visualize computer simulations of dynamic systems (145), and the connection between Gabriel Kron’s method of tearing (diakoptics) and bond graphs (146, 147) have been published. How to construct finite mode, long wavelength of multidimensional structures (148). order reduction of multiscale systems (149. 150), restrictions on the structure of mathematical models of physical systems which endow the equations with the same modularity of the physical system (151), repeated systems with non-identical, non-communicative interactions (152), uses of bond graphs for open systems or Eulerian frames (153) and non-energetic multiports (154) have been described. Throughout thirty years of development of the method, its utility in modeling systems and in generating mathematical equations has been demonstrated, but as mentioned in Ref. (155). “there is currently no theory of bond graphs as mathematical structures. on which the models are based”. References (1555160) present a theory of the mathematical foundations of bond graphs, showing them to have a combinatorial structure. They defined an abstract bond graph as a precise mathematical structure based on the concept of bond graph junction structure. The theory developed is entirely mathematical and combines linear algebra, graph theory and combinatorics. Reference (155) summarizes the basics of a theory for bond graphs which should supply the mathematical foundation for the method : the fundamental combinatorial procedures of selection of a base and co-based and the orientation of the cycles and co-cycles of the bond graph ; Refs (156, 157) give a rigorous mathematical definition and theoretical explanation of bond graphs, using elementary mathematical concepts from linear algebra to define vector spaces ; Ref. (158) defines the cycle and co-cycle matroids of a bond graph. and investigates the relationship between these structures ; Ref. (159) examines matrix representations of bond graph matroids, and the use of this concept provides rigorous proof of a mathematical equivalence of linear graphs and bond graphs; and Ref. (160) analyzes the technique of directing bonds by adding half-arrows, which is crucial to the application of bond graphs to physical systems modeling. III. Applications The first applications of the bond graph technique to physical systems were made on mechanical, thermodynamic and physiological systems. The applications were further extended to chemical, fluidic, biological, electrical, economic and magnetic systems, and, in recent years. such applications have even been extended to agricultural, solar and nuclear systems. In the following sections, an account is given of the most representative published work concerning applications of the bond graph technique, which has been catalogued according to the kind of systems. In some cases the work is reported in more than one type of system, because it can be a combination of different types of systems.

Suwey

qf Bond Graphs

Mechunical systems The widest application of the bond graph technique is to mechanical systems, and, as mentioned before, mechanical systems represent the first field in the application of its theory, This is because the earliest workers in the field were mechanical engineers. In mechanical systems, the bond graph technique has been used for the study of multibody systems (161-166); vehicle dynamics (165, 167-178) and vehicle suspensions (179-185) ; for the study of torsional energy dynamics (186-189) ; for the use of MTF and MGF in rotational mechanical systems (161, 162, 190-193) ; for the analysis of mechanisms (128, 129, 194-201); for the modeling of 3-D mechanical systems (174, 175, 202-204), pendular systems (205-209), and mechanically distributed systems (62,210) ; for the modeling of mechanical transmission (199,211), robotics (119, 171,203,212-216), and vibration and sound phenomena (63,217-227). It is also possible to mention other applications : the study of structural dynamics (228), the dynamic behavior of a vacuum cleaner (229) and offshore structures (230): the analysis of manipulators (216, 231-236), of rigid-body dynamics (9, 194,237,238), and large mechanical systems (239) ; and the modeling of hysteresis in electromechanical components (240, 241). Thermul and thevmo&wumic systems The extension of the method to thermal and thermodynamic systems is well known as in the case of thermofluidic systems (242-245) ; in the analysis of heat exchanger dynamics (114, 116, 244-250) ; in the representation of thermodynamic systems (105. 106, 107, 110, 111, 251-256); in network thermodynamics (124, 257265, 300). It has been used also for thermal energy transport and entropy flow (113, 123,2666269) ; for compressible thermofluidic systems (270,271) ; for modeling an automotive gas turbine (272-274) ; and for the application of network theory to non-isothermal systems (275). There are also applications to irreversible thermodynamics (104, 2766278) ; in the solution of diffusive differential equations (279); in the model of a radio telescope (280) ; in thermodynamics of bionetworks (262, 281, 282) ; in the study of the dynamics and control of refrigerators (283) ; in the modeling of a U-tube steam generator (284) ; a marine boiler (117) ; and diesel engines (118). Bioloqicul and physiological .s~~stems The applications of bond graphs to biological and physiological systems involve different topics. One of the main advantages of the method is based on the fact that it can be used at different levels to represent difficult processes, like the transport and union of metabolic reactions in the endoplasmic reticulum of rabbits (285). There are applications of bond graphs in the development and analysis of biological systems (286-292), biochemical models (119, 263, 293-295), plant biosystems (296), and the thermodynamics of bionetworks (262, 281, 282). The bond graph can be used in the modeling and analysis of generalized physiological systems, as translational and rotational mechanical systems (125,216,297Vol. 328, No 5.,6, pp. 565-606, Prmkd ,n Great Britain

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299). or as thermodynamic systems (264) ; in the modeling of the aorta as a fluidic system (36) ; to model and simulate physiological systems (300-305) ; and skeletal muscle glucose metabolism (306) ; to model cardiovascular physiology (3077309), respiratory systems (310), muscular action (294, 311), pharmacokinetic systems (312), and for the representation of a photoreception model (313).

In the field of chemical systems the bond graph technique has been used to model and simulate biochemical systems (119, 263, 2933295), and entropy flux and chemical potential (269), and to study chemical reactions and diffusion (292, 294, 3133320).

In fluidic systems there are applications of bond graphs in fluidic control systems (321-329). in the general study of fluidic systems (330-340), in the modeling of fluid lines (271, 341-346) and pneumatic systems (318. 347. 348), in research into the dynamic characteristics of Auid power systems (3499351), in acoustics (310, 352 -359), in the analysis of servomechanisms (360-364), in the modeling of open surface channel nets (365), in the study of the dynamics and control of Eulerian turbomachines (366), and as a tool for hydraulic system design (332, 367). and hydrostatic bearings design (368). There are also applications in electropneumatic systems (215. 362), in electrohydraulic systems (215, 230, 360, 362, 3699380), in the study of valves (321, 327,329,360,364,381-385,407), and in the modeling of fluid networks (386) and pumps (339,387.388).

There have been widespread applications to electrohydraulic systems, as mentioned earlier (215,230. 360,362,369380). electromechanical systems (389 -392), electroacoustic systems (355,357.358) and in the introduction of generalized bond graphs to describe electromagnetic systems (112. 393, 394). There have also been applications in electrical networks (395. 396). in electronic systems (397, 398). in the modeling of electrical machines (390, 399- 403), in the modeling of an electric battery (404) and for electromagnetic and electrostatic field systems (122).

In the field of socio-economic systems, the bond graph technique has been applied to microeconomic systems (405), to study economic systems (406, 107). to model social systems (cause -effect relations) (408), age-dependent renewal (115) and technical communication (409).

In this field. the application of bond graphs has been in the study of electrotnagnetic systems (I 12,393,394). magnetic field engineering systems (122,410), in the modeling of magnetic systems, using relations in the energetic domain (411,

Surcey qf Bond Graphs 412), to model the hysteresis of magnetic bearings (193).

of magnetic

components

(240) and for the analysis

Acoustic systems The bond graph has been used for the analysis of acoustic (310, 352-354) and electroacoustic systems (355357,358) ; and for the study of acoustoelastic systems using modal bond graphs (356, 359). Agricultural systems In this field, the bond graph has been used for the design and analysis of agricultural engineering systems (413), in the study of a greenhouse climate (414-420) and in the modeling of plant biosystems (296). Solar .sjj.sterns There are some applications of bond graphs to solar heating systems (421,422), to the study of solar-regulated buildings (423-425) and for the simulation of the dynamics of a solar collector system (426). Nuclear systems There are few applications dynamics (427, 428).

in this field, like the modeling

of nuclear

reactor

IV. Pvopmls The use of digital computers and simulation languages as tools for computeraided design and simulation has spread widely through scientific and engineering fields, as a mean of predicting the behavior of a system as well as reducing the time taken for the design and analysis steps. This is a very helpful tool, since one can concentrate on the construction of the model from the physics of the system as well as subsequent examination of the simulation results. The development of modeling and simulation programs based on the bond graph technique began in 1963, when the idea of the creation of an n-port or ENPORT program to simuilate bond graph models of linear multiport systems was proposed by Paynter. A series of modeling and simulation programs based on the same fundamentals has been developed since then. In the following, a description of each program is provided based on : The author or authors who developed the program, showing all the theoretical references included in the paper’s bibliography. a The input data for the program, which can be either in line code or in graphic form. l The output of the program, which can be in the form of parametric or numeric state space equations, the simulation results, frequency response or code for other simulation programs. l

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The specific characteristics of the program, such as the type of systems it can handle (linear or nonlinear), whether it can treat derivative causality or algebraic loops, etc. The programming language used for the implementation of the program as well as the computer or microcomputer on which it is implemented. Some applications of the program.

The programs over time.

will be shown in chronological

order to show their developments

ENPORTproymtm (N-PORTS) ENPORT is the name given to a set of digital computer procedures designed to allow the direct simulation of the dynamic physical systems represented by bond graphs. Rosenberg is the author of all the existing versions of ENPORT programs, originally developed as a part of his Sc.D. thesis at M.I.T. (429). ENPORT-I, ENPORT-4. ENPORT-5. ENPORTand ENPORTare the currently available versions. In the following, a chronological list of ENPORT programs is given. ENPORT-I was developed at M.I.T. (U.S.A) (429) ; for more theoretical information about the program, see (430-433). Reference (25) shows the methodology for the generation of the state-space equations used. In it, the necessary input data are supplied in line code which includes: the bond graph model, the numerical value of the parameters. the source vector. and the initial conditions for simulation. The program generates as output the state space equations of the system, and, from these, the dynamic response may be obtained through the exponential matrix calculation technique. Only linear, constant coefficient systems can be treated by the program, but the simulation of the time response for certain types of nonlinear systems can be performed when a system can bc rcprcscnted conveniently by diffcrcnt linear systems in different regions of its state space. ENPORT-I cannot handle systems with more than eight state variables. The programming language of ENPORT-I is FORTRAN and it was implemented on an IBM 7094 with a 32K tncmory. ENPORTwas the first large-scale bond graph simulation program, and was developed at Michigan State University (U.S.A.) (434); more theoretical information can be found in (435,436). The input, output, system type and programming language are the same as in ENPORT-I. This program was implemented on a CDC 6500 system, in both batch and interactive modes. ENPORT-5. developed at Michigan State University (U.S.A.). extended the application possibilities of the two previous versions through the introduction of two powerful features : the MACRO and the MICRO statements (437). The first feature allows the user to introduce and link large subsystems which have been defined in standard bond graph terms. The second feature helps the user to deal with distributed parameter phenomena by making possible the automatic repetition and linking of numerous clusters of bond graph elements : however. it is still limited to linear cases. ENPORTwas developed by Rosencode Associates Inc. (U.S.A.) and its major advantage is that it provides a unified treatment for large or small, complex or

Surwy qf Bond Graphs simple, nonlinear or linear engineering systems (438). The programming language is FORTRAN 77; it exists also in a microversion of ENPORTfor the MS-DOS operating system, developed for IBM PC and compatibles. ENPORTwas developed by Rosencode Associates Inc. (439) and its input data can be introduced in graphical form. A microversion of ENPORTis also available. The applications of all ENPORT programs have been numerous throughout the years, and a great variety of systems have been studied using them (152, 168, 179, 226, 291. 291, 335, 352,400,430&445). DBOND

(Delay BOND)

The DBOND computer program is used to simulate the behavior of systems represented by delay bond graphs (91). It was developed by Auslander as a part of his Sc.D. thesis at M.I.T. (U.S.A.) (446). The algorithm for it is shown in (71), and more theoretical information is given in (307, 447). Data must be supplied in line code form for the lines and the nodal elements, a wave delay time and impedance characteristics for each line; and resistances, sources, etc. for the static nodal elements. The program generates a transition matrix based on the topological data and the system parameters ; and the simulation results can be obtained on graphical or tabular form. There are applications of the DBOND program to different systems (71,91.188, 307, 447). THTSIM

(Technische

Hogrschool

Tuvnte SIMulutor-)

THTSIM is a block diagram oriented simulation program for the treatment of continuous dynamical systems developed at Twente University of Technology (Netherlands) by Kraan and Meerman (448, 449). More theoretical information on the program can be found in (450-453). The physical model, as a block diagram or a bond graph, is introduced as input data in line code. The bond graph must be translated using some elementary rules into block diagram form, in order to be accepted by the program as input data. The simulation of the system is generated then and it is also possible to obtain frequency response. THTSIM can use logic and dynamic function blocks. including nonlinear functions, PID controller, time delay, sample-hold and noise generator. The program was implemented in a PDP-11 and in a LSIl 1 series of DEC computers. It was written in MACRO1 1 assembler language, and an ANSI FORTRAN IV version is also available in order to make it transportable to nonDEC computers. Applications of the THTSIM program are provided in (302, 448-454). GEM (Generator

qfEquations of Motion)

This program was developed at the Industrial Institute of Construction Machinery (Poland) by Stepniewski and Grabowiecki to generate the state space equations of a system in an automatic form (455), the algorithm of the program is shown in (31). Vol 32X. No. 5.‘6, ,IP 565406. Prmcd m Great Bntain

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The user inputs in line code form the bond graph topological description of the system as a partly augmented bond graph, and the augmentation of the remaining bonds is made automatically by the program. Since an augmented bond graph is available. the state space equations can be developed in a very orderly pattern. GEM can also handle nonlinear systems. GEM is written in standard FORTRAN IV and was implemented on two computers : IBM 3701145 and PDP 1 l/70. Applications of GEM are shown in (31, 456). POLSYAS This program was developed at the Industrial Institute of Construction Machinery (Poland) by Grabowiecky, Stepniewski and Zgorzelski. It can be used to model and simulate the dynamic behaviour of systems (381, 457). The program allows as input the description of models of subsystems, in terms of bond graph, block diagrams with transfer functions and finite elements; all in line code. The mathematical model is generated in the form of a set of firstorder nonlinear differential-algebraic equations and the simulation is carried out subsequently. POLSYAS can also handle nonlinear systems. Applications of the program can be found in (56, 325, 382). TVTSIM (Twente Uniurrsity of Technoloy?, SIMulutor) TUTSIM can be considered as a microcomputer version of THTSIM, developed at Twente University of Technology (Netherlands) by Meerman and van Dixhoorn for the simulation of continuous dynamic systems. The 1979 manual of THTSIM can be taken as the original manual for TUTSIM (452). More theoretical information on the program can be found in (214,327,458-465). In this program, models are entered in line code as block diagrams, bond graphs (fully augmented) or a mixture of both. The program gives as output the system state equations. The transfer functions can be derived in an algorithmic way. The operating characteristics and the simulation results of the model are displayed graphically, in a numerical listing, or in a file, and they can be retained in the computer as hard copy. TUTSIM can handle nonlinear systems and logical functions, and includes many complex functions blocks such as a PID compensator. Casual conflicts and algebraic loops can also be handled by the program. The first programming language was the MACRO II Assembler version for PDPI I DEC computers, after it was converted to 6502 Assembler source code for an APPLE II personal computer and, later, to an 8086/S Assembler version for the IBM PC. Many applications of TUTSIM program to obtain system model simulations are presented in the literature; Refs. (177. 214, 229, 327, 346, 361, 363, 364, 460, 462-466) among others. VNIS YS (Un$ied Simulation System) The UNYSIS program was developed in joint work by Rosenberg of Michigan State University (U.S.A.) and Zgorzelski of the Industrial institute of Construction 574

Suroey of Bond Graphs Machinery (Poland) in order to model complex systems which typically contain distributed and lumped parameter subsystems in various energy domains (467). The program uses a bond graph based approach that allows finite element, transfer function, and bond graph description as input in line code. The main idea is to convert finite elements and block diagrams to bond graphs internally, and then to generate the state space equations from a unified bond graph description. The state equations are generated explicitly (i.e. in FORTRAN code segment form) and may be printed and inspected before continuing the analysis. It also provides the standard, well developed methods of linear system analysis, for example the user may obtain frequency response, phase portraits, or Bode and Nyquist plots, and it can be used for liner and nonlinear systems as well. ” An application of UNYSIS is shown in Ref. (467).

CAMP (Computer-Aided Modeling Program) CAMP was developed at the Californian State University (U.S.A.) by Granda as a computer preprocessor which generates a system description suitable for computation by a digital simulation language (468-470). The bond graph needs to be entered directly in line code from a terminal or from a file, in which the bond graph description is stored. It must include the system elements and junction structure. CAMP converts the bond graph description of a physical system into executable Fortran expressions that describe the system’s dynamics and combines them with functional blocks and commands to produce an integrated input for a digital simulation language such as ASCL, DSL, CSMP, and CSSL-IV. There are programs being developed that draw bond graphs on a graphical terminal and generate the line code for CAMP automatically (471). Nonlinear and complex systems can be analyzed using CAMP and also those with derivative causality and algebraic loops. Control systems can be attached to physical system models generated by CAMP, using the capabilities of the digital simulation languages already mentioned. The programming language for CAMP is FORTRAN. It was implemented in the 3000 and 4000 series of IBM computers, and also exists in a version for PDP and VAX computers. CAMP has been used for many applications of system model simulations (185, 329, 346, 468-470, 472, 473). CAMAS (Computer-Aided Modelling, Analysis and Simulation) CAMAS is a software environment that supports modeling and simulation of the dynamic behavior of physical systems. It was developed at Twente University of Technology (Netherlands) by Broenink and Nijen Twilhaar (474) ; more information is presented in (475,476). CAMAS accepts models described with SIDOPS (Structured Inter-Disciplinary Description of Systems) which is a language based on the theory of bond graph, developed by Welleweerd (477) and Broenink (478). The input can be introduced in line code and it is also possible to enter the bond graph on the screen, by drawing it literally via a graphical editor. The simulation results are displayed on either a Vol 328, No. 5,‘6, pp. 565-606. Printed in Great Britam

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screen or plotter and can be processed to make frequency analysis. CAMAS can also handle nonlinear systems. Its programming language is PASCAL and there are several applications available (474, 475).

BAMMS is a software package that creates models for physical systems in an analytical form. It was developed at Delft University of Technology (Netherlands) by Verhuel and (479) ; more information can be found in (480). When the user has defined the model configuration as the input data in line code. the model is generated by connecting a group of predetined macros, it represents a certain subsystem. The program outputs are : the set of system equations. a bond graph structure table which can be used for simulation with the simulation language TUTSIM, the complete matrix system and their corresponding eigenfrequencies and eigenvalues. It is also possible to derive rrequency response functions for the model, and it can create simulation files for simulation in ASCL or in a simulation package designed specially for BAMMS models. The programming language is FORTRAN 77 and an application is found in (479.480). HYCAD

HYCAD is a special simulation program for fluid power systems which was developed by Zhang Haiping from the Shanghai Jiao Tong University (China) (481). There are six methods (one of which must be selected by the user) to input the parameters and components of the systems being simulated, which are circuit diagrams, bond graphs, characteristic curves, transfer functions or state equations (linear or nonlinear). From this, the simulation program is generated. The structure of the bond graph must be input interactively. It is possible to save the models constructed in a library model automatically, The output of the program could be the calculation of the static equilibrium 01 the system, the linear system at a given equilibrium, the transfer function between the given input and output. its Bode diagram and the time history of the system variables under the given duty cycles. This output could be shown on a terminal, a printer or a disk. The program language is a mix of PASCAL (50%). FORTRAN (40%). BASIC (7%) and 8086MASM (3%) and was implemented on an IBM PC/XT. CAh4S

(Cotttputw-Aidd

Modeling

System)

CAMS was developed at Simon Bdlivar University (sponsored by EPSON Latinoamerica) (Venezuela) by Delgado and Castillo (482). The input of the program is completely graphical and the user draws his bond graph directly on the screen of the microcomputer. in the same way as he draws on a piece of paper. The outputs of the program are the numerical state equations of the system in the form of matrices A, B. C. D and E and the vectors X, Y and c’.

Survey qf Bond Graph The program microcomputers.

was developed

using Language

C and it runs on IBM compatible

PLUS-M (PLUridisciplinary Systems Modeling) PLUS-M is a bond graph based modeling preprocessor, which, used jointly with a simulation program, allows the analysis and simulation of physical systems. It was developed by Cornet of University of Li&ge (Belgium) and Lorenz of the Herstal National Fabric (Belgium) (483, 484). The program accepts bond graphs as well as block diagrams and it can use two input interfaces : a direct graphical interface and an alphanumerical interface. As soon as a model has been completed, it can be stored for future use in a database model in a fully acausal form. In this way, the user has the opportunity to select a single model by choosing one of each description blocks. PLUS-M generates as output a code for CSSL-4 and NEPTUNIX programs in order to obtain the system analysis and simulation. It can also handle causality conflicts, integrative and derivative causality, algebraic loops and can also make dependent field detections. An application of PLUS-M can be seen in (483). DART (Design Analysis ,for Reliahilit~~ Tool) DART is a tool for dynamic physical system design and analysis. It was developd in the Research Division of the IBM Corporation (U.S.A.), by Hood and Palmer (485,486) and it is still under development. The modeler introduces the bond graph representation of the dynamic system through a full screen graphic editor, together with the constitutive laws and initial conditions. The program generates the model of the system in the form of firstorder ordinary differential equations, which can be solved using the Dynamic Simulation Language (DSL). DART can handle nonlinear systems but cannot handle bond graphs with derivative causality. The programming language is FORTRAN and has been used in various applications (485,486). MS- BOND (Modeling Systems M’itff BOND graph) This program was developed at Simon Bolivar University (Venezuela) by Delgado (487) to allow the modeling of dynamic systems. The user can enter the bond graph to the program in line code and a user friendly graphical option is available too, making the program more practical and useful. The program then generates the state equations of the system in the form of matrices and equations using the Rosenberg method (25) for ENPORT programs. _. Actually the program only carries linear systems. The programming 750 system.

language

is FORTRAN

77 and is implemented

on a VAX

MOSAIC MOSAIC is a modeling and simulation program which permits the possibility of easy simulation of block diagrams or causal bond graphs. It was developed at Vol. 128, No. 5/h, pp. 561-606. Printed in Chat Britam

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University of Twente (Netherlands) by Breedveld, Broenink, van Luenen, Baardman and Uitentuis (488). and presented by the authors as an intermediate program between TUTSIM and CAMAS. The program is menu-driven and the input data is the model in an acausal form. This acausal form consists of a main model, functions, submodels and simulation specification. A submodel is built from the blocks, which are present in the MOSAIC library and the functions are MIMO blocks of which the user determines the contents. The outputs are the results of the simulation which can be either graphical or alphanumerical. The program is written in Language C, runs on a microVAX and is currently ported to a PC-AT. The applications are currently few due to the short time the program has been available (488). ARCHER ARCHER can be used for the determination of mathematical models of physical systems, mixing the use of artificial intelligence techniques and the bond graph methodology. It was developed at the Institut Industriel du Nord (France) by Coutereel, Bouayad, Dauphin-Tanguy (489) and Seuer (490). The introduction of the model is made in user language, which is very close to the natural language of the physical structure of the system, by means of the description of the topological architecture of the interconnected components. Moreover, it allows the bond graph specialist to introduce directly his bond graph model. The database of ARCHER contains information at several levels : in the first level, the basic elements and the junction structure elements are defined, in the second level, the bond graph models appear, and in the third level, the specific bond graph models of complex system are pre-defined and pre-modeled. By using these facilities. the user can construct models readily in an interactive form. Where there are causality conflicts, the processor informs the user, but cannot propose solutions to solve the problem. The outputs are the information to construct (by hand) the complete bond graph model. the alphanumeric and numeric state equations of the system and the simulation results using ASCL or some similar software as well. The programming language is Turbo-Pascal and it was implemented on an IBM-PC AT computer. The papers which present the processor contain some applications (489, 490).

DESIS is being developed in joint work by Delgado of Simon Bolivar University (Venezuela) and Brie of the Institute of Applied Sciences INSA of Rennes (France) (491, 492). The program can be used for the modeling and simulation of linear systems. It has a graphical input with a completely user-friendly interface, where the user only has to draw the bond graph of the system on the screen of the computer and DESIS generates the state equations and simulates them showing the results in a graphical manner. The state equations are generated in a parametric and numeric form, and

Survey of Bond Graphs for this generation, DESIS used the “Road Method” (17) which is very similar to the manual method. The user communicates with the program by the use of menus or by means of questions and answers. At each instant the program analyses its response and sends an error or warning message if necessary. The user can observe the bond graph on the screen and can modify the power flow directions, the causalities, the number of bonds, the numerical values of the system elements, etc. DESIS can handle derivative causality and algebraic loops. The program is written in FORTRAN 77 and uses GKS (Graphical Kernel System) to generate the graphical interface. It runs in PC-AT compatibles and some applications are shown in (491,492). MS1 (Model&g System I) MS1 is a program which is being developed in Belgium by Lorenz (493). Its innovative characteristic lies in the fact that it is not bound to a single model description formalism. In this way, the generic input may use block diagrams, signal flow graphs, linear graphs, bond graphs and compartmental models, through a graphical interface. The output formalism is not yet chosen but probably will be from the CSSL family. The program is being developed on workstation hardware using the UNIX operating system. The programing languages used were C + + , X-WINDOW (for the window management) and PHIGS (for the graphics). There are other programs based on the bond graph philosophy which has been developed for particular applications. Among them, a qualitative simulator for physiological models (295) ; a program to obtain state-space equations with nonlinear characteristics of electric, hydraulic and mechanical components (494) ; a simulation program for pneumatic systems (348) ; SIMUL-R, a simulation language for model-switching and analysis (495) ; an automatic model builder in cardiovascular dynamics (309); the BGSP (Bond Graph Simulation Program) (385, 496) and the DSH (Digital Simulation of Hydraulic systems) (496) which is directed towards the analysis and design of hydraulic systems. V. Journals There are several journals in which bond graph articles have appeared regularly. These journals are the Journal of the Franklin Institute, Transactions of the ASME Journal of Dynamic Systems, Measurement and Control, the Proceedings of the American Control Conference (IEEE), the Proceedings of the Joint Automatic Control Conference (JACC), and the Proceedings of the International Federation of Automatic Control (IFAC). It is important to note that in September 1972 the Transactions of the ASME Journal of Dynamic Systems, Measurement and Control published a Special Issue called “Special Collection on Modeling Applications of the Bond Graph Language” which offered the state-of-the-art in bond graphs for 1972, with a content largely in the domain of mechanical engineering. In September 1979, the Journal of the Franklin Institute published another Special Issue called “Bond Graph Techniques for Dynamic Systems in Engineering and Biology” which Vol. 328, No. 5/6, pp. 565406, Printed in Great Britam

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has a set of papers ranging from the mathematical theory of bond graphs to the new applications in engineering and biological modeling. In I985 the Journal of the Franklin Institute published a second Special Issue, “Physical Structure in Modeling”, which shows a large variety of contributions in many disciplines, modeled in a unified fashion. In 1978, the Journal Computer Programs in Bionzrdicine included six articles that represented dynamic biological systems in terms of bond graphs and network thermodynamics. They showed the potential of bond graph formulations, and the studies in the issue provided examples of the type of biological systems that can be simulated using ENPORT. These papers were also presented at the 1977 Biomedical Engineering Symposium held at the University of California, Davis. In the 10th IMACS World Congress on System Simulation and Scientific Computation held in Canada in 1982, many works on bond graphs were presented, as well as in the 1984 American Control Conference (IEEE) held in San Diego. the AI Applied to Simulation European Conference held in Ghent. Belgium 1986, the 1987 American Control Conference held in Minneapolis, the 2nd European Simulation Congress held in Belgium in 1986, and the IMACS 12th World Congress on Scientific Computation. Paris 1988. In 1983, van Dixhoorn and Karnopp organized at Twente University of Technology (The Netherlands), a 3-day Bond Graph Workshop called “Physical Structure in Modelling” which brought together about 40 European workers in this field and whose contributions appeared mainly in the 1985 Special Issue of the Journul of’the Frunklin Institute. There are some publications also in journals from other countries such as the Internutiorzal Journal of Control, Trutwuctiom on Instnm~n~tution Meusuretwr~t und Control, Internutionul Journal qf’circuit Theor?. und Applicutions and Journul of’ Soundunu’ Vihrution from Great Britain ; Encrgie, Fluid et Lubricants H_wlruuliyuc Pneumutiyue Asscrrissernents and RA IRO Autonwtique S~st&es A~lul~~.sc.ret Contrcile from France ; Transactions qf the S0ciet.v ?f Instrumentation and Control Engineeritq and S?‘.stem.s Control from Japan ; R~~~elzrr~~ystec~hnikand Messen Stcurcn Rqyeln from Germany ; S~stetm D~nutnics. P~iE1ektrotcc.h. Electrorz. and Computer. Pmyrunw in Biomedicine from The Netherlands ; Duliun Got~,y.\-uy~~run Xqpo from China ; Rozpru,r~J’ Ei~~c.trotcc.hrzic.=Me and S~,.stcm Scicncc~ from Poland ; Technische Runclschu~r and Nc>ue Technik from Switzerland ; Prosthet. Orthot. Int. from Denmark and Elettrotecnicu from Italy. VI. Books There are several books dealing with bond graph, starting in 1961 with Paynter’s book, “Analysis and Design of Engineering Systems” (497). This book is not only devoted to bond graphs, but contains the “seeds” of the method. The first book devoted exclusively to the study of physical system dynamics using bond graph was Karnopp and Rosenberg’s “Analysis and Simulation of Multiport SystemsThe Bond Graph Approach to Physical System Dynamics” (430), published in 1968. This book, together with two others by Karnopp and Rosenberg, “System Dynamics : A Unified Approach” (443) published in 1975 and “Introduction to

Survey

of Bond Graphs

Physical System Dynamics” (498) in 1983, give bond graph methodology in considerable detail and are an excellent guide to the basic theory of the method and its many applications to simple systems. There are also three books from Thoma, “Grundlagen und anwendungen der bonddiagramme” (499) published in 1974, “Introduction to Bond Graphs and their Applications” (444) published in 1975, and “Simulation by Bond Graphs. Introduction to a Graphical Method” (500) in 1989. In the first there is a succinct introduction to bond graphs, in German. A (501), published in 1970, book by Takahashi, Rabins and Martens, “Control” devotes Chapter 6 to bond graphs. Another book published in 1974 by Van Dixhoorn and Evans, “Physical Structure in Systems Theory”, included many articles, among them Van Dixhoorn (202), Polder (211), Rietman (267) and Thoma (268). The book by Welstead, “Introduction to Physical System Modelling” (502), published in England in 1979, also explains the bond graph method in Chapter 8. VII. Conclusions It can be concluded that the bond graph technique is a very useful tool for systems modeling. The variety of systems where it has been employed easily shows its usefulness and versatility. All this is due to the fact that the simple definition of the basic variables of a system (effort and flow) makes possible the use of bond graph theory for modeling any type of system. The great development of modeling and simulation programs based on the bond graph technique shows its applicability to the analysis and design of systems. It is possible to find programs like GEM, CAMS arid MS-BOND that only provide system equations. There are also others that can provide the possibility of obtaining the simulation and analysis of the system, such as the ENPORT versions, THTSIM, TUTSIM, CAMAS, MOSAIC, POLSYAS, DESIS and frequency response like UNYSIS and HYCAD. Lastly, a group of programs like CAMP, DART, PLUSM, BAMMS and ARCHER which process bond graph representation of systems into suitable source input is used by digital simulation languages such as ACSL, DSL, CSSL-IV and CSMP. These programs have a general application, but there are programs applied to a particular system like DSH, BGSP and others. VIII. Bibliography (I) H. M. Paynter, “Generalizing

(2) (3)

(4) (5)

the concepts of power transport and energy ports for system engineering”, ASME paper 58-A-296, presented at the 1958 Annual Meeting, New York, NY, 1958. H. M. Paynter, “Hydraulics by analog-an electronic model of a pumping plant”, J. Boston Sac. Civil Engnq, pp. 197-219, July 1959. H. M. Paynter, “Computer representations of polyphase alternating current systems for dynamic analyses and control”, Automatic and Remote Control, Proceedings of the First International Congress of the International Federation of Automatic Control, Moscow, 1960. R. C. Rosenberg and D. C. Karnopp, “A definition of the bond graph language”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 94, No. 3, pp. 179-182, 1972. J. U. Thoma and D. C. Karnopp, “Simulation stetiger systeme durch diagramme”,

Vol 328. No. 5/6, pp. S-606. Printed in Great Bntam

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(6)

(7)

(8) (9)

(10)

(11)

(12) (13) (14)

(15)

(16) (17)

(18) (19) (20) (21) (22) (23)

(24)

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in “Simulation technischer Systeme I” (Edited by A. Schoene), pp. 59-102, Carl Hanser, 1973 (in German). D. C. Karnopp, “Synthetic dynamics : bond graphs in design”, in “Basic Questions of Design Theory” (Edited by W. R. Spillers), pp. 225-240, North Holland, New York, 1974. D. C. Karnopp, “Multiple energy domain systems”, in “Shock and Vibration Computer Programs” (Edited by Piekle), Shock and Vibration Monograph No. 10, pp. 3-7. The Shock and Vibration Information Center, Naval Research Laboratory, Washington DC, 1975. P. C. Breedveld, “Fundamentals of bond graphs”, IMACS 1988‘Proceedings of the 12th World Congress on Scientific Computation, Vol. 1. pp. 7-12, 1988. D. C. Karnopp, “Power-conservating transformations : physical interpretations and applications using bond graphs”, J. Frunklin Inst., Vol. 288, No. 3, pp. 1755201, 1969. N. Suda, “Bond graphs: structural properties and augmentation algorithm”, Proceedings of Conference on System Control Theory and Application to Dynamic Economic Models, Japan, 1976. N. Suda and T. Hatanaka, “Structural properties of systems represented by bond graphs”, in ‘Complex and Distributed Systems : Analysis, Simulation and Control” (Edited by S. G. Tzafestas and P. Borne), Elsevier, Amsterdam, 1986. A. Zeid, ‘Some bond graph structural properties : eigen spectra and stability”, Truns. ASME J. Dyn. Sy‘st. Meas. Control, Vol. Ill, pp. 3822388, 1989. L. Campello and C. Cob&, “Bond graphs for the modelling of dynamics systems”, Elettrotechnica, Vol. 64, No. I, pp. 53-68, Jan. 1977. N. Suda and A. Enoki, “A new matrix representation of bond graphs and equivalence condition”, Truns. Sot. Instrum. Control Engng, Vol. 13, No. 4, pp. 324-329, 1977 (in Japanese). N. Suda, “Effect of parasitic storage elements in systems represented by bond graph”, IMACS 1988 Proceedings of the 12th World Congress on Scientific Computation, Vol. I, pp. 17719, 1988. P. C. Breedveld, “A systematic method to derive bond graph models”, Proceedings of the 2nd European Simulation Congress, pp. 3844, 1986. M. Delgado and C. Brie, “A computational method for the generation of state and output equations”. 13th IMACS World Congress on Computation and Applied Mathematics, Dublin, Ireland, 22-26 July 1991. N. Suda, “A graph theoretic approach to bond graph”, Syst. Control, Vol. 17, NO. 11, pp. 706-713, Nov. 1973 (in Japanese). D. C. Karnopp, “Letter re sensible state variables”, Trans. ASME J. Dyn. Syst. Meus. Control, Vol. 98, No. 3, pp. 85598, 1977. D. C. Karnopp, “Lagrange’s equations for complex bond graph systems”, Trans. ASME J. Dyn. Syst. Meus. Control, Vol. 99, No. 4, pp. 300-306, 1977. D. C. Karnopp, “Bond graphs in control : physical state variables and observers”, J. Franklin Inst., Vol. 308, No. 3, pp. 219-234, Sept. 1979. A. N. Andry Jr and R. C. Rosenberg, “On the dimension of state space for physical systems”, Proc. of the JACC, San Francisco, CA, 1980. D. C. Karnopp, “Alternative bond graph causal patterns and equation formulation for dynamic systems”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 105, NO. 2, pp. 58-63, 1983. D. Karnopp, “Structure in dynamic system models-why bond graph is more IMACS 1988 Proceedings of the 12th World informative than its equations”, Congress on Scientific Computation, Vol. 1, pp. l-4, 1988.

Survey of Bond Graphs (25) R. C. Rosenberg, “State-space formulation for bond graph models of multiport systems”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 93, NO. 1, pp. 35-40, 1971. (26) H. R. Martens, “Simulation of nonlinear multiport systems using bond graphs”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 95, pp. 49-53, 1973. (27) H. M. Paynter, “Discussion state-space formulation for bond graph models of multiport systems”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 93, pp. 123-124, 1971. of models of large scale lumped (28) D. L. Margolis and G. E. Young, “Reduction structures using normal modes and bond graphs”, 1977 Joint Automatic Control Conference, pp. 650-655, 1977. of models of large scale structures (29) D. L. Margolis and G. E. Young, “Reduction using normal modes and bond graphs”, J. Franklin Inst., Vol. 304, No. 1, pp. 6579, July 1977. (30) B. J. Joseph and H. R. Martens, “The method of relaxed causality in the bond graph analysis of nonlinear systems”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 96, pp. 95-99, 1974. (31) K. A. Grabowiecki, A. Rybicki and W. Stpeniewski, “Bond graph based automatic generation technique of nonlinear systems state equations”, IFAC Symposium on CAD of Control Systems, pp. 273-278, Zurich, Switzerland, 1979. (32) B. Samanta and A. Mukherjee, “Dynamics of a class of repeated system with nonidentical elastic and visco-elastic interconnections, a bond graph approach”, J. Franklin Inst., Vol. 319, No. 5, pp. 473-497, 1985. (33) A. M. Bos, “Solvability of DAEs derived from bond graphs of mechanical systems”, IMACS 1988 Proceedings of the 12th World Congress on Scientific Computation, Vol. 1, pp. 60-63, 1988. (34) J. Barreto and J. Lefevre, “Bond graph fields and implicit equations”, Proceedings of the First IASTED Symposium on Applied Informatics, pp. 133-136, Lille, France, March 1983. (35) J. Barreto and J. Lefevre, “Bond graph fields and implicit equations”, J. Modelling Simulation, Vol. 4, No. 3, pp. 102-105, 1984. (36) J. Barreto and J. Lefevre, “R-field in the solution of implicit equations”, J. Franklin Inst., Vol. 319, No. l/2, pp. 227-236, 1985. (37) J. Barreto and M. Noirhomme-Fraiture, “Minimal modelling: a bond graph approach”, IMACS Conference on Modelling and Simulation for Control of Lumped and Distributed Parameter Systems, France, June 1986. (38) J. J. Beaman and R. C. Rosenberg, “Additional structure in bond graph modelling”, Proceedings of the 1987 American Control Conference, Vol. 2, pp. 1444-1450, 1987. (39) S. J. Hood, R. C. Rosenberg, D. H. Withers and T. Zhou, “An algorithm for automatic identification of R-fields in bond graphs”, IBM J. Res. Diu., Vol. 31, No. 3, pp. 382-390, 1987. (40) R. C. Rosenberg and J. Beaman, “Clarifying energy storage field structure in dynamic systems”, Proceedings of the 1987 American Control Conference, pp. 1451-1456, 1987. (41) J. MacFarlane and M. Donath, “The automated symbolic derivation of state equations for dynamic systems”, Proceedings of the Fourth Conference on Artificial Intelligence Applications (Cat. No. 88CH2552-8), pp. 215-22, 1988. (42) B. Samanta and A. Mukherjee, “ Role of zero frequency modes in bond graph adapted dual space formulation”, J. Franklin Inst., Vol. 322, No. 516, pp. 305-324, 1986. Vol. 328, No. 5/6, pp. 565-606, Printed in Great Britain

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Trans. ASME J. D)n. Syst. Mms. (43) A. Pcrelson, “Bond graph sign conventions”, Control, Vol. 97, No. 2, pp. 184-l 88. 1975. (44) R. C. Rosenberg and B. Moultrie. “Basis order for bond graph junction structures”, IEEE Trans. Circuits Syst.. Vol. CAS-27, No. IO. pp. 909-920, Oct. 1980. (4% R. C. Rosenberg and A. N. Andry. “Solvability of bond graph junction structures with loops”, Proceedings of the Lawrence Symposium on Systems and Decision Science, pp. 49953, 1977. (46) R. C. Rosenberg and A. Andry. ‘Solvability of bond graph junction structures with loops”, IEEE Trans. Circuits Slsst., Vol. CAS-26. No. 2. pp. 130.-137, 1979. multiport systems, junction structures (47) N. Suda and A. Enoki, “Power conservating of the Eighth Triennial World Congress of the and bond graph”, Proceedings lntcrnational Federation of Automatic Control, Vol. 3, pp. 1761-1766, 1982. (48) J. R. Ort and H. R. Martens, “The properties of bond graph junction structure matrices”, Truns. ASME J. DJ,H. Sl.st. Mctrs. Control, Vol. 95, pp. 3622367, 1973. (49) R. C. Rosenberg and A. N. Andry. “Solvability of certain classes of bond graph junction structures”, Proceedings of the 2nd International Symposium on Large Engineering Systems. pp. S37- 541, 197X. Trms. ASME .J. D~,tz. S)‘.rt. Mctrs. “Bond graph junction structures”, WV A. Per&on. Control, Vol. 97. No. 2, pp. 189 --195. 1975. (51) A. S. Perelson and H. Paynter, “The properties of bond graph junctions structure matrices”, Discussion. Trar~s. ASME J. DJ,~. SFst. Mcas. Control, pp. 209 21 11 June 1976. Bull. Sci. (52) H. Nakano and T. Kawasc, “A brief note on linear junction structures”, Engrzg Rcs. Luh., Waseda University. Tokyo, No. 84, pp. I -20, 1979. (53) B. Moultric. “Upper bounds for port bond casual orientations of weighted junction structures”. J. Frmklin Inst.. Vol. 308, pp. 353 360, 1979. of the I I th (541 F. Lorenz, “Bond graphs revisited: a systematic view”, Proceedings IMACS World Congress on System Simulation and Scientific Computation. Vol. 4. pp. 313 -316. 1985. (55) F. Lorenz and J. Wolper, “Assigning causality in the case of algebraic loops”, J. Frmklin Imt., Vol. 319. No. 112, pp. 2377241, 1985. (56) A. Cornet and F. Lorena. “Equation ordering using bond graph causality analysis”. IMACS 1988 Proceedings of the 12th World Congress on Scientific Computation, Vol. 1, pp. 43346. 1988. Trmc. (57) D. C. Karnopp. ‘Some bond graph identities involving junction structures“, ASME J. D_Jw.Slxt. Mcus. Control, Vol. 97. No. 4, pp. 4399440, 1975. “Exploiting bond graph causality in physical system mod&“. (58) R. C. Rosenberg, Trans. ASME J. Din. SJst. Mcas. Control. Vol. 109. No. 4, pp. 37X383. DCC. 1987. of continuous system simulation languages using (59) D. Karnopp. -‘Direct programming bond graphs causality”. Truns. SW. Computrr Sindution. Vol. I, No. 1. pp. 49 60, 1984. (60) J. M. Barrcto. “The role of bond graphs in qualitative modelling”. Proceedings oi the 12th IMACS World Congress on Scientific Computation, Vol. I. pp. 84~~87, 1988. (61) S. J. Hood, E. R. Palmer and P. M. Dantzig, “A fast, complctc method for automatically assigning causality to bond graphs”. J. Franklin Inst., Vol. 326. No. I. pp. 83392. 19X9. of models of interacting lumped and (62) D. L. Margolis and M. Tabrizi. “Reduction distributed systems using bond graphs and repeated modal decomposition”. J. Frmklin Inst., Vol. 317, NO. 5. pp. 3099322, May. 1984.

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(63) D. Margohs, “Bond graph modelling for modal dynamics of interacting lumped and distributed systems”, J. Acoust. Sec. Am., Vol. 80, pp. S5-S6, 1986. (64) D. L. Margolis, “Computer representation of large-scale lumped structures using bond graphs”, Proc. Cun. Sot. Cir?il Engng, pp. 41 l-432, Oct. 1977. (65) D. L. Margolis, “Bond graph for distributed systems models admitting mixed causal inputs”, Trans. ASME J. Dpn. Syst. Meas. Control, Vol. 102, No. 2, pp. 944100, 1980. (66) D. L. Margolis, “An algorithm for incorporating subsystem models into several dynamic system models”, J. Franklin Inst., Vol. 310, No. 2, pp. 107-l 17, 1980. (67) L. S. Bonderson, “System properties of one-dimensional distributed systems”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 99, No. 2, pp. X5-90, 1977. (68) D. L. Margolis, “Bond graph for distributed systems models admitting mixed causal inputs”, ASME Paper No. 79-WA/DSC-24, 1979. (69) F. T. Brown, “A unified approach to the analysis of one-dimensional distributed systems”, ASME J. Basic En~9n,9,Vol. 89, No. 2, 1967. (70) L. S. Bonderson, “Vector bond graphs applied to one-dimensional distributed systems”, Trans. ASME J. Dp. Syst. Meas. Control, Vol. 91, No. I, pp. 75582, 1975. (71) D. M. Auslander, “Distributed-parameter models for continuous-time systems”, Proceedings of the 1970 Summer Computer Simulation Conference, pp. 242-25 1, June 1970. (72) A. Bell and H. Martens, “A comparison of linear graphs and bond graphs in the modeling process”. J. Am. Control Conjl Proc., pp. 7777794, 1974. (73) J. R. Ort and H. R. Martens, “A topological procedure for converting a bond graph to a linear graph”, Truns. ASME J. Dyn. SJN. Meas. Control, Vol. 96, No. 3, pp. 307-314. 1974. (74) A. Perelson and G. Oster, “Bond graphs and linear graphs”, J. Franklin Inst., Vol. 302, No. 2, pp. 1599185, 1976. (75) M. Gattinger and G. Wenzel, “Hypcrnetworks as tools for modelhng multiport systems”, J. Frunklin Inst., Vol. 317, No. 1, pp. I-6, 1984. (76) A. V. Balikshman and M. Thoma, “Lecture Notes in Control and Information Sciences”, Springer, New York, 198 1. (77) A. Blundcll, “Bond Graphs for Modelling Engineering Systems”, Ellis Horwood. Chichester, U.K., 1982. (78) J. J. van Dixhoorn, “Network graphs and bond graphs in engineering modelhng”, Ann. SJxt. Rrs., Vol. 2. pp. 22-38, 1972. (79) G. Y. McRac, “Modeling and simulation of dynamics engineering systems”, Computus Engng, Vol. 15, pp. 977101, May 1974. (SO) R. C. Rosenberg, “The bond graph as a unitied data base for engineering system design”, Truns. ASME J. Engng Ind., Vol. 97, No. 4, pp. 133331337, 1975. (81) B. W. Barnard, “System modelling by diagrams-the power bond graph technique”, SIMSIG-76 : Simulation Conference, Monash University, Melbourne, Australia. pp. 119-124, May 1976. (82) D. Singer, “Unified bond graph representation of dynamic systems, I”, Musxki Tudomuni, Vol. 55, pp. 233-248, 1978 (in Hungarian). (83) J. U. Thoma, “Bond graph methods from engineering to life sciences”, in “Systems Structures in Engineering” (Edited by Bjorn and Franksen), Tapir, Trondheim, 1978. (84) D. Singer, “Unified bond graph representation of dynamic system II”, Muszaki TudomunJ~, Vol. 56, pp. 19-38. 1979 (in Hungarian). Vol. 328, No. 36, PP. M-606, Prmted m Great Britain

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(106) P. C. Breedveld, “Thermodynamic bond graphs and the problem of thermal inertance”, J. Franklin Inst., Vol. 3 14, No. I, pp. 15-40, 1982. (107) P. C. Breedveld, “The thermodynamic bond graph concept applied to a flappernozzle valve”, Proceedings of the 10th IMACS Congress on System Simulation and Scientific Computation, Vol. 3, pp. 395-397, Canada, 1982. (108) J. J. van Dixhoorn, “Bond graphs and the challenge of a unified modelling theory of physical systems”, in “Progress in Modelling and Simulation” (Edited by Cellier), pp. 207-245, Academic Press, New York, 1982. (109) P. C. Breedveld, “Physical systems theory in terms of bond graphs”, Ph.D. Thesis, Department of Electrical Engineering, Twente University of Technology, 1984. (110) P. C. Breedveld, “System theoretical formulation of thermodynamics, part I : equilibrium thermodynamics”, in “Physical Systems Theory in Terms of Bond Graphs”, SISO 534 UDC53, Enschede, 1984. (111) P. C. Breedveld, “System theoretical formulation of thermodynamics, part II : nonequilibrium thermodynamics”, in “Physical Systems Theory in Terms of Bond Graphs” (Edited by P. C. Breedveld), SISO 534 LJDC53, Enschede, 1984. (112) G. D. Nijen Twilhaar, “Network representation of electromagnetic fields and forces using generalized bond graphs”, J. Franklin Inst., Vol. 319, No. l/2, pp. 183-200, 1985. (113) D. C. Karnopp, “Pseudo bond graph for thermal energy transport”, Trans. ASME J. Dyn. Syst. Meus. Control, Vol. 100, pp. 1655169, 1978. (114) S. Azarbaijani and D. C. Karnopp, “Bond graph structural models for heat exchangers”, ASME Paper 80-WA/Sol 17, 1980. (115) J. W. Brewer, “Bond graphs of age dependent renewal”, ASME Winter Annual Meeting, 80-WA/DSC-4, Chicago, 1980. (116) S. Azarbaijani and D. C. Karnopp, “Pseudo bond graph structural models for heat exchangers”, ht. J. Modrlling Simulation, Vol. 2, No. 3, pp. 138-141, 1982. (117) H. Engja and Jia Xinle, “A nonlinear mathematical model of a marine boiler using bond graph techniques”, I.S.M.E., Tokyo, 1983. (118) H. Engja and K. Strand, “Modelling for transient performance of diesel engines using bond graphs”, I.S.M.E., Tokyo, 1983. (119) J. Lefevre and J. Barreto, “A mixed block diagram bond graph approach to biochemical models with mass action and rate law kinetics”, J. Franklin Inst., Vol. 319, No. l/2, pp. 201-215, 1985. (120) G. Oster and D. Auslander, “The memristor: a new bond graph element”, Trans. ASME J. Dyn. Qst. Mpas. Control, Vol. 94, No. 3, pp. 249-252. 1972. (121) G. Oster, “A note on memristors”, IEEE Trans. Circuits Systems, pp. 152, Jan. 1974. (122) M. Ridzuan Salleh and M. Laughton, “Dynamic analysis of field energy systems using bond graphs”, ht. J. Control, Vol. 21, No. I, pp. 21-38, Jan. 1975. (123) J. U. Thoma, “Entropy and mass flow for energy conversion”, J. Franklin Inst., Vol. 299, No. 2, pp. 89-96, 1975. (124) J. U. Thoma and H. Atlan, “Network thermodynamics with entropy stripping”, J. Franklin Inst., Vol. 303, No. 4, pp. 3 19-328, 1977. (125) D. L. Margolis, “Bond graphs and the exploitation of power conserving transformations”, Computu Programs Biomed, Vol. 3 18, No. 8, pp. 165-l 70, 1978. (126) J. J. van Dixhoorn, “Physical modelling on a thermodynamic basis using the bond graph concept”, Proceedings of the 10th IMACS Congress on Systems Simulation and Scientific Computation, Vol. 3, pp. 3866391, Canada, 1982. (127) D. C. Karnopp, “Dynamic forces in multiport mechanics: direct and Lagrangian formulations”, J. Franklin Inst., Vol. 314, No. 5, pp. 265-270, 1982. Vol. 328, No. 5/h. pp. M-606, Printed in Great Britam

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Survey of Bond Graphs (149) G. Dauphin-Tanguy, “Sur la representation des systemes singulierement perturbes”, Ph.D. Thesis, University of Lille, France, 1983. (150) G. Dauphin-Tanguy, M. Lebrun and P. Borne, “Order reduction of multi-time scale systems using bond graphs, the reciprocal system and singular perturbation method”, J. Franklin Inst., Vol. 319, No. l/2, pp. 1577171, 1985. (151) N. Hogan, “Modularity and causality in physical system modelling”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 109, No. 4, pp. 3844391, Dec. 1987. non(152) A. Mukherjee and B. Samanta, “Analysis of repeated systems with non-identical, communicative interactions using bond graph adapted operator perturbation”, J. Franklin Inst., Vol. 323, No. 2, pp. 1699185, 1987. (153) J. J. Beaman and P. C. Breedveld, “Physical modelling with Eulerian frames and bond graphs”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 110, No. 2, pp. 182-188, 1988. (154) T. Kawase, “A supplementary note on non-energetic multiports”, Waseda University, Tokyo, Aug. 1979. (155) S. H. Birkett, P. H. Roe and J. U. Thoma, “A theory of bond graph junction structures : application from network analysis”, IMACS 1988 Proceedings of the 12th World Congress on Scientific Computation, Vol. 1, pp. 20-22, 1988. (156) S. H. Birkett and P. H. Roe, “The mathematical foundations of bond graph-I. Algebraic theory”, J. Franklin Inst., Vol. 326, No. 3, pp. 3299350, 1989. (157) S. H. Birkett and P. H. Roe, “The mathematical foundations of bond graph-II. Duality”, J. Frunklin Inst., Vol. 326, No. 5, pp. 691-708, 1989. foundations of bond graph-III. (158) S. H. Birkett and P. H. Roe, “The mathematical Matroids theory”, J. Franklin Inst., Vol. 327, No. 1, pp. 877108, 1990. (159) S. H. Birkett and P. H. Roe, “The mathematical foundations of bond graph--IV. Matrix representations and causality”, J. Franklin Inst., Vol. 327, No. 1, pp. 109128, 1990. (160) S. H. Birkett and P. H. Roe, “The mathematical foundations of bond graph-V. Directed bond graphs”, in preparation. (161) D. L. Margolis and D. C. Karnopp, “Bond graphs for flexible multibody systems”, Proceedings of IUTAM Symposium on Dynamics of Multibody Systems, Munich, Germany, 1977. (162) D. C. Karnopp, “The energetic structure of multibody dynamic systems”, J. Frunklin Inst., Vol. 306, No. 2, pp. 165-l 81, 1978. (163) D. L. Margolis and D. C. Karnopp, “Bond graph for flexible multibody systems”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 101, No. 1, pp. 50-57, March 1979. (164) T. Kawase, “Towards the modelling of multibody systems”, 1st report, Waseda University, Tokyo, 1983. (165) A. M. Bos, “Modelling multibody systems in terms of multibond graphs with application to a motorcycle”, Ph.D. Thesis, Twente University of Technology, 1986. (166) A. Zeid and D. Chang, “Multiport modeling of multibody systems : an approach to computer aided design of multibody controls”, Proceedings of the 1989 American Control Conference, Vol. 2, pp. 1816-I 821, 1989. (167) D. C. Karnopp, “Application of bond graph techniques to vehicle dynamics”, ASME paper 70-DE- 16, 1970. (168) D. C. Karnopp and R. C. Rosenberg, “Application of bond graph techniques to the study of vehicle drive line dynamics”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol 92, No. 2, pp. 355-362, 1970. (169) R. Allen and D. Karnopp, “Semi-active control on ground vehicle structural dynamics”, AIAA Paper 75-821, 1975. Vol. 328. No. S/6, pp 565406, Printed in Great Britain

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D. C. Karnopp, “Bond graphs for vehicle dynamics”, Vehicle Syst. Dynamics, Vol. 5, No. 3, pp. 171-184, Oct. 1976. D. L. Margolis. “Finite mode bond graph representation of vehicle-guideway interaction problems”, J. Franklin Inst., Vol. 302, No. 1, pp. I-17, July 1976. D. L. Margolis, “Bond graphs, normal modes and vehicular structures”, Vehicle Syst. Dynamics, Vol. 7, No. 1, pp. 49963, 1978. D. C. Karnopp, “Application of bond graph techniques to vehicle dynamics”, ASME Paper 70-DE-I 6, 1979. H. B. Pacejka and G. G. M. Tol, “A bond graph to simulate the 3-D dynamic behavior of a heavy truck”. Proceedings of the 10th IMACS Congress on System Simulation and Scientific Computation, Montreal, Vol. 3, pp. 398-401, 1982. A. M. Bos, “Modelhng and simulation of 3-D mechanical systems using bond graph, applied to a motor bike”, MSc. Thesis, No. 1241.3272, Department of Electrical Engineering. Twente University of Technology, 7500 AE Enschede, 1983. P. Kleywegt, “Investigation into the influence of pay-load on the road holding of a truck using bond graph modelhng, simulation and experimental verification”, report VTW 004.83-A, Delft University of Technology, Vehicle Research Laboratory, June 1983 (in Dutch). H. B. Pacejka, “Modelling complex vehicle systems using bond graphs”, J. Franklin Inst., Vol. 319, No. l/2, pp. 67-81, 1985. A. Sugrue, P. J. Nolan and J. Brown, “Bond graph analysis of automatic guided vehicle dynamics”. Proceedings of the 2nd European Simulation Congress, pp. 790-796, 1986. “Bond graph simulation of high speed, roughR. R. Allen and D. C. Karnopp, terrain vehicle suspensions”, Proceedings of the 1971 Summer Computer Simulation Conference, pp. 540-549, 1971. “Simulation of nonlinear air cushion vehicle C. J. Radcliffe and D. C. Karnopp, Proceedings of the 1971 Summer Comdynamics using bond graph techniques”. puter Simulation Conference, Board of Simulation Conference, pp. 550-558. 1971. D. N. Wormlcy, D. Garg and H. Richardson, “A comparative study of the nonlinear and linear performance of vehicle air cushion suspension using bond graph models”, Tram. ASME J. 4,717. SJW. Mows. Control, Vol. 94, No. 3, pp. 189m 197. 1972. D. L. Margohs and J. L. Tylec, “Bond graph modeling techniques applied to nonlinear primary and secondary suspensions for high speed ground transportation vehicles”, Simulation Council Procwdings Srries, Vol. 4, No. 4, 1974. D. L. Margolis, J. L. Tylee and D. Hrovat, “Heavy mode dynamics of a tracked air cushion vehicle with semiactive airbag secondary suspension”, Trans. ASME .I. DJan, Slxt. Meas. C’ontrol, Vol. 97, No. 4. pp. 3999407, Dec. 1975. of the hydrostatic speed-control R. C. Rosenberg and S. C. Zhang, “Simulation system using bond graphs”, Proceedings of the International Computers in Engineering Conference and Exhibition, pp. 1477152, 1983. D. C. Karnopp, “Modelling and simulation of adaptativc vehicle air suspensions with pseudo bond graphs. CAMP and ACSL”, Proceedings of the I Ith IMACS V’orld Congress on Systems Simulation and Scientific Computation, Vol. 4, pp. 297 -300, 1985. N. Tsai and S. Wang, “Delay-bond graph models for geared torsional systems”, TWMS. ASME J. Appl. Mech.. Vol. 96, pp. 3666370, 1974. S. Wang and N. Tsai. “Torsional wave propagation in a nonlinear complex gear train system using bond graph modeling”, Design Technology Transfer ASME, pp. 375 383, 1974.

Survey of Bond Graphs (188) D. M. Auslander, N. Tsai and F. Farazian, “Bond graph models for torsional energy Trans. ASME J. D,vn. Svst. Meas. Control, Vol. 97, No. 1, pp. 53transmission”, 59, 1975. (189) D. M. Auslander, T. Tsai and F. Farazian, “Bond graph for torsional energy transmission”, Trans. ASME J. Dyn. Syst. Meas. Control, 1976. (190) D. Margolis and M. Hubbard, “An analysis of wave convention of rolling bodies”, Trans. ASME J. Engng Ind., Vol. 99, No. 4, pp. 835-840, 1977. (191) D. L. Margolis, “Bond graphs for some classic dynamic systems”, Simulation, Vol. 35, No. 3, pp. 81-87, 1980. (192) D. Hroyat and W. E. Tobler, “Bond graph modelling and computer simulation of J. Franklin Inst., Vol. 319, No. l/2, pp. 93-114, automotive torque converters”, 1985. (193) P. McDonald and M. Hubbard, “An actively controlled pendulous fly wheel with magnetic bearing”, Proceedings of the 20th Intersociety Energy Conversion Engineering Conference, Vol. 2, pp. 525-530, 1985. (194) R. C. Rosenberg, “Multiport models in mechanics”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 94, No. 3, pp. 206-212, 1972. (195) R. Allen and S. Dubowsky, “Mechanisms as components of dynamic systems: a bond graph approach”, Trans. ASME J. Engng Ind., Vol. 99, No. I, pp. 104-l 11, 1971. (196) R. R. Allen and D. M. Rozelle, “Describing function simulation of dynamic forces in single degree-of-freedom mechanisms”, Proceedings of the 5th World Congress on the Theory of Machines and Mechanisms, Montreal, Quebec. July 1979. (197) D. C. Karnopp and D. Margolis, “Analysis and simulation of planar mechanism systems using bond graph”, J. Me& Des., Vol. 101, No. 2, pp. 187-191, 1979. (198) R. R. Allen, “Dynamics of mechanisms and machine systems in accelerating reference frames”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 103, pp. 395-403, Dec. 1981. (199) J. S. Stecki, “Bond graph modelling of power transmission by torque converting mechanism”, J. Franklin Inst., Vol. 311, No. 2, pp. 93-l 10, 1981. (200) M. A. Mohamed, “Bond graph simulation of a mobile two-legged mechanism”, Proceedings of the Twelfth Annual Northeast Bioengineering Conference (Cat. No. 86CH2323-I), pp. 153-l 56, 1986. (201) A. Zeid, “Bond graph modeling of planar mechanisms with realistic joint effects”, Trans. ASME J. Dyn. Syst. Meas. Control, Vol. 111, No. 1, pp. 15-23, 1989. (202) J. J. van Dixhoorn, “The use of network graphs and bond graphs in 3-D mechanical in “Physical Structure in Systems Theory” model of motorcars and unbalance”, (Edited by J. J. van Dixhoorn and F. J. Evans), p. 83-109, Academic Press, New York, 1974. (203) M. J. L. Tiernego, “A new systematic bond graph modelling procedure for 3-D Proceedings of the 10th IMACS Congression mechanics applied to robotics”, System Simulation and Scientific Computation, Vol. 3, pp. 392-394, 1982. of 3-D mechanisms using h-dimensional (204) M. Beauwin and F. Lorenz., “Representation multibonds”, IMACS 1988 Proceedings of the 12th World Congress on Scientific Computation, Vol. 1, pp. 27-30, 1988. (205) M. Hubbard, “Whirl dynamics of pendulous flywheels using bond graphs”. J. Franklin Inst., Vol. 308, No. 4, pp. 405-421, Oct. 1979. (206) M. J. L. Tiernego, “Bond graph modeling and simulation techniques applied to a three-axis driven pendulum”, Simulation, 1980. Vol. 328, No. 5/6, pp. 565-606, Printed in Great Bntain

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