Zero Dynamics of Physical Systems From Bond Graph Models—Part I: SISO Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 10-17 ◽  
Author(s):  
S. Y. Huang ◽  
K. Youcef-Toumi
Keyword(s):  
System Analysis ◽  
Mimo Systems ◽  
Geometric Approach ◽  
Bond Graph ◽  
Graph Representation ◽  
Zero Dynamics ◽  
Feedback Systems ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems. Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics. However, the calculation of the zero dynamics is usually complicated, especially if a form which is closely related to the physical system and suitable for design is required. In this paper, a method is proposed to derive the zero dynamics of physical systems from bond graph models. This method incorporates the definition of zero dynamics in the differential geometric approach and the causality manipulation in the bond graph representation. By doing so, the state equations of the zero dynamics can be easily obtained. The system elements which are responsible for the zero dynamics can be identified. In addition, if isolated subsystems which exhibit the zero dynamics exist, they can be found. Thus, the design of physical systems including the consideration of the zero dynamics become straightforward. This approach is generalized for MIMO systems in the Part II paper.

Zero Dynamics of Physical Systems From Bond Graph Models—Part II: MIMO Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 18-26 ◽  
Author(s):  
S. Y. Huang ◽  
K. Youcef-Toumi
Keyword(s):  
System Analysis ◽  
Controller Design ◽  
Mimo Systems ◽  
Bond Graph ◽  
Relative Degree ◽  
Zero Dynamics ◽  
Input Output ◽  
Feedback Systems ◽  
Graph Models ◽  
Physical Systems

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems. Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics. In the Part I paper, a method is proposed to derive the zero dynamics of SISO systems from bond graph models. Using this approach, the design of physical systems, including the consideration of zero dynamics, can be performed in a systematic way. In this paper, the extension of the proposed method for MIMO systems is presented. It is shown that for MIMO systems, the input-output configurations determine the existence of vector relative degrees. If a system has a vector relative degree, it’s zero dynamics can be identified by a straightforward extension of the proposed method. If a system does not have a vector relative degree, a dynamic extension procedure may be used to fix the structure. By doing so, the zero dynamics can still be identified in a similar manner. It is also shown that if the input-output configurations are ill-designed, not only the relative degrees do not exist, but also the zero dynamics can not be reasonably defined. In that case, independent tracking controls for all the outputs are impossible. Therefore, the results in this paper provide a guideline for the design of the input-output configurations as well as the zero dynamics of MIMO systems.

Lagrange’s Equations for Complex Bond Graph Systems

1977 ◽  
Vol 99 (4) ◽  
pp. 300-306 ◽  
Author(s):  
Dean Karnopp
Keyword(s):  
Bond Graph ◽  
Writing System ◽  
Complex Mechanism ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems ◽  
Lagrange’S Equations ◽  
Alternative Means ◽  
Lagrange's Equations ◽  
State Functions

The standard means of imposing causality to extract state equations for bond graph models of physical systems can be inconvenient when algebraic loops and derivative causality in combination with nonlinear constraints are present. This paper presents an alternative means of writing system differential equations using energy and coenergy state functions and Lagrange’s equations. For certain types of systems, particularly mechanical and electromechanical systems, this indirect means of finding state equations turns out to be very convenient. In this technique, causality is used in a new way to establish generalized coordinates and generalized efforts for nonconservative elements. Finally, it is shown that in some cases in which a Lagrangian can be written by inspection for a complex mechanism, a detailed bond graph for this component is unnecessary and yet the equations of the mechanism can be easily coupled to the bond graph equations for the remainder of the system.

scholarly journals Analysing and simulating energy-based models in biology using BondGraphTools

2021 ◽  
Author(s):  
Peter Cudmore ◽  
Michael Pan ◽  
Peter J. Gawthrop ◽  
Edmund J. Crampin
Keyword(s):  
Systems Biology ◽  
Mathematical Models ◽  
Bond Graph ◽  
Experimental Measurements ◽  
Bond Graphs ◽  
Graph Models ◽  
Conservation Of Energy ◽  
Conservation Of Mass ◽  
Physical Systems ◽  
Complex Interactions

AbstractLike all physical systems, biological systems are constrained by the laws of physics. However, mathematical models of biochemistry frequently neglect the conservation of energy, leading to unrealistic behaviour. Energy-based models that are consistent with conservation of mass, charge and energy have the potential to aid the understanding of complex interactions between biological components, and are becoming easier to develop with recent advances in experimental measurements and databases. In this paper, we motivate the use of bond graphs (a modelling tool from engineering) for energy-based modelling and introduce, BondGraphTools, a Python library for constructing and analysing bond graph models. We use examples from biochemistry to illustrate how BondGraphTools can be used to automate model construction in systems biology while maintaining consistency with the laws of physics.

State-Space Formulation for Bond Graph Models of Multiport Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 35-40 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
State Space ◽  
Bond Graph ◽  
Graph Representation ◽  
Initial System ◽  
Field Equations ◽  
Graph Models ◽  
Reduction Procedure ◽  
Space Formulation ◽  
Systematic Reduction

A novel procedure for systematically generating state-space equations for multiport systems is presented. The method is based upon a bond graph representation of the system and causal manipulation of the field equations. Principal advantages of the method are the ability to anticipate formulation properties before writing equations, the availability of a simple check for correctness of the initial system relations, and the specification of a systematic reduction procedure for obtaining state-space equations in terms of energy variables.

scholarly journals BOND GRAPH METHODOLOGY IN THE RLC CIRCUIT ANALYSIS

2019 ◽  
pp. 261-270
Author(s):  
Darina Hroncová
Keyword(s):  
General Class ◽  
Bond Graph ◽  
Operating Conditions ◽  
Coupled Systems ◽  
System Model ◽  
Electrical System ◽  
Bond Graphs ◽  
State Equations ◽  
Mechatronic Systems ◽  
Physical Systems

Urgency of the research. The bond graphs theory aim for to formulate general class physical systems over power interactions. The factors of power are effort and flow. They have different interpretations in different physical domains. Yet, power can always be used as a generalized resource to model coupled systems residing in several energy domains. Target setting. Formalism of power graphs enables to describe different physical systems and their interactions in a uniform, algorithmizable way and transform them into state space description. This is useful when analyzing mechatronic systems transforming various forms of energy (electrical, fluid, mechanical) by means of information signals to the resulting mechanical energy. Actual scientific researches and issues analysis. Over the past two decades the theory of Bond Graphs has been paying attention to universities around the world, and bond graphs have been part of study programs at an ever-increasing number of universities. In the last decade, their industrial use is becoming increasingly important. The Bond Graphs method was introduced by Henry M. Paynter (1923-2002), a professor at MIT & UT Austin, who started publishing his works since 1959 and gradually worked out the terminology and formalism known today as Bond Graphs translated as binding graphs or performance graphs. Uninvestigated parts of general matters defining. The electrical system model is solved with the help of the above mentioned bond graphs formalism. Gradually, the theory of power graphs in the above example is explained up to the construction of state equations of the electrical system. The state equations are then solved in Matlab / Simulink. The statement of basic materials. Using bond graphs theory to simulate electrical system and verify its suitability for simulating electrical models. In various versions of the parameters of model we can monitor its behavior under different operating conditions. The language of bond graphs aspires to express general class physical systems through power interactions. The factors of power i.e., effort and flow, have different interpretations in different physical domains. Yet, power can always be used as a generalized coordinate to model coupled systems residing in several energy domains. Conclusions. We introduced a method of systematically constructing a bond graph of an electrical system model using Bond graphs. A practical example of an electrical model is given as an application of this methodology. Causal analysis also provides information about the correctness of the model. Differential equations describing the dynamics of the system in terms of system states were derived from a simple electrical system coupling graph. The results correspond to the equations obtained by the classical manual method, where first the equations for individual components are created and then a simulation scheme is derived based on them. The presented methodology uses the reverse procedure. However, manually deriving equations for more complex systems is not so simple. Bond charts prove to be a suitable means of analysis, among other systems and electrical systems.

"Bond graph approach for input-output decoupling of linear MIMO systems with Derivative State Feedback"

2018 ◽  
Author(s):  
Christophe Sueur
Keyword(s):  
State Feedback ◽  
System Analysis ◽  
Mimo Systems ◽  
Bond Graph ◽  
State Feedback Control ◽  
Pole Placement ◽  
Control Law ◽  
Input Output ◽  
Placement Problem

"This paper presents a new solution for the well-known input-output decoupling problem of linear multivariable systems with a derivative state feedback control law. A simple solution to the pole placement problem is highlighted in the monovariable and multivariable cases with application to a mechanical system. Analysis up to control design are achieved structurally in the bond graph domain for the case study."

HYBRSIM—a modelling and simulation environment for hybrid bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 35-46 ◽  
Author(s):  
P. J. Mosterman
Keyword(s):  
Numerical Analysis ◽  
Event Detection ◽  
Bond Graph ◽  
Modelling And Simulation ◽  
Simulation Environment ◽  
Dynamic Coupling ◽  
Bond Graphs ◽  
Switching Element ◽  
Graph Models ◽  
Physical Systems

Bond graphs are a powerful formalism to model continuous dynamics of physical systems. Hybrid bond graphs introduce an ideal switching element, the controlled junction, to approximate continuous behaviour that is too complex for numerical analysis (e.g. because of non-linearities or steep gradients). HYBRSIM is a tool for hybrid bond graph modelling and simulation implemented in Java and is documented in this paper. It performs event detection and location based on a bisectional search, handles run-time causality changes, including derivative causality, performs physically consistent (re-)initialization and supports two types of event iteration because of dynamic coupling. It exports hybrid bond graph models in Java and C/C++ code that includes discontinuities as switched equations (i.e. pre-enumeration is not required).

The Bond Graph as a Unified Data Base for Engineering System Design

1975 ◽  
Vol 97 (4) ◽  
pp. 1333-1337 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
Data Base ◽  
Large Scale ◽  
Dynamic Models ◽  
Systems Design ◽  
Bond Graph ◽  
Graph Representation ◽  
Model Description ◽  
Engineering System ◽  
State Equations ◽  
Engineering System Design

In developing a unified data base for support of engineering systems design there are several important factors to consider, such as efficiency of model description, ease of modifying models, and characteristics of assembling device models into systems. The multipart model and its associated bond graph representation can serve very effectively as a unified data base, especially when devices and systems involve several energy domains simultaneously (e.g., electromechanical or hydromechanical transduction). In addition to providing a succinct, flexible data base for linear and nonlinear, static and dynamic models, bond graphs can be processed causally to reveal important information about alternative input-output choices and device-level coupling factors when submodels are assembled into systems. Particularly for large-scale nonlinear systems this is an important feature in aiding the formulation of state equations. Illustrations of the bond graph data base approach are given.

Bond Graph Models for Linear Motion Magnetostrictive Actuators

1996 ◽  
Vol 118 (1) ◽  
pp. 161-167 ◽  
Author(s):  
M. D. Bryant
Keyword(s):  
Transfer Functions ◽  
Mechanical Energy ◽  
Constitutive Relations ◽  
Graph Model ◽  
Bond Graph ◽  
Linear Motion ◽  
State Equations ◽  
Graph Models ◽  
Magnetostrictive Actuator ◽  
Audio Range

Bond graph models for the audio range response of a dynamically continuous, linear motion magnetostrictive actuator are formulated and presented. The actuator involves a continuous rod of magnetostrictive material that extends, contracts, and vibrates in modes when energized by magnetic flux produced by a coil. The left end is fixed, force is extracted from the right end. The bond graph model includes dynamics of the energizing coil, the flux routing circuit, magnetic to mechanical energy conversion, and mechanical elements. Constitutive relations for magnetostriction suggest use of a multipart capacitor with ports for magnetic and mechanical power flow; constraints imposed by modal dynamics require a separate mechanical port for each vibration mode. Values were assigned to bond graph parameters in a non-empirical manner: solely from theory and handbook data. State equations and transfer functions were extracted from the bond graph. For audio range operation, theory (the bond graph model) compared well with experiment (measurements taken on a magnetostrictive actuator designed and built by the author).

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