Incremental bond graph approach to the derivation of state equations for robustness study

2004 ◽  
Vol 12 (1) ◽  
pp. 41-60 ◽  
Author(s):  
W. Borutzky ◽  
G. Dauphin-Tanguy
Keyword(s):  
Bond Graph ◽  
State Equations

Modeling and Designing an Intelligent Controller using Bond Graph for a Satellite Controlled by Magnetic Actuators

2012 ◽  
Vol 2 (1) ◽  
pp. 72-90 ◽  
Author(s):  
Majid Habibi ◽  
Alireza B. Novinzadeh
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Electrical Current ◽  
Bond Graph ◽  
Control Logic ◽  
State Equations ◽  
Magnetic Actuators ◽  
Advantages And Disadvantages ◽  
Aerospace Technology ◽  
Short Time

Satellite state control has always been an important topic in aerospace technology. Because it is required that when the satellite is stationary in orbit, it would be directed to a special object and this task should be performed in a situation where there isn’t access to the satellite. This task is performed using various technologies and one of these is the use of magnetic actuators. Magnetic actuators use mechanical torque that is resulted by interaction of electrical current of coils in the satellite and the earth’s magnetic field. The satellite is subjected to such disturbance torques, thus corrupting the direction of the satellite. This method has its advantages and disadvantages. Its drawback is that the magnetic torque is produced only perpendicular to the direction of the magnetic field and the axis of the coil. This paper models a satellite having magnetic actuators using bond graph, and finds out its state equations, and then constructs the control logic that is needed for its control. A model of three dimensional attitude maneuvers and magnetic systems using bond graph is described. The actuators are tuned using the method of particle swarm optimization (PSO). It is observed that using this method a small satellite reaches to the desired angle in a short time and becomes stationary.

Bond Graph Model of a Squirrel Cage Induction Motor With Direct Physical Correspondence

2000 ◽  
Vol 122 (3) ◽  
pp. 461-469 ◽  
Author(s):  
Jongbaeg Kim ◽  
Michael D. Bryant
Keyword(s):  
Induction Motor ◽  
Mechanical Energy ◽  
Graph Model ◽  
Bond Graph ◽  
Graph State ◽  
State Equations ◽  
Squirrel Cage ◽  
Squirrel Cage Induction Motor ◽  
Cage Induction Motor ◽  
Cage Rotor

An existing bond graph of a squirrel cage induction motor was modified to make the bond graph physically more representative. The intent was to form a one-to-one correspondence between motor components and bond graph elements. Components explicitly represented include the stator coils, the squirrel cage rotor bars, and the magnetic flux routing section. The final bond graph spans electrical, magnetic, and mechanical energy domains, and contains common motor faults. From this bond graph. state equations were extracted and simulations performed. Simulated were the response of healthy motors, and motors with shorted stator coils and broken rotor bars. [S0022-0434(00)01203-X]

scholarly journals Causality in Models of Thermal Processes in Ship Engine Rooms with the Use of Bond Graph (BG) Method

2017 ◽  
Vol 24 (s1) ◽  
pp. 32-37 ◽  
Author(s):  
Marian Cichy ◽  
Zbigniew Kneba ◽  
Jacek Kropiwnicki
Keyword(s):  
Energy Systems ◽  
Physical Nature ◽  
Bond Graph ◽  
Thermal Processes ◽  
Electrical System ◽  
Thermodynamic Process ◽  
State Equations ◽  
Simulation Experiments ◽  
Systems Models ◽  
Single Approach

AbstractWith a single approach to modeling elements of different physical nature, the method of Bond Graph (BG) is particularly well suited for modeling energy systems consisting of mechanical, thermal, electrical and hydraulic elements that operate in the power system engine room. The paper refers to the earlier presented [2] new concept of thermal process modeling using the BG method. The authors own suggestions for determining causality in models of thermal processes created by the said concept were given. The analysis of causality makes it possible to demonstrate the model conflicts that prevent the placement of state equations which allows for the direct conduct of simulation experiments. Attention has been drawn to the link between the energy systems models of thermal processes with models of elements of different physical nature. Two examples of determining causality in models of complex energy systems of thermal elements have been presented. The firs relates to the electrical system associated with the process of heat exchange. The second is a model of the mechanical system associated with the thermodynamic process.

Modeling and Simulation for Dual-Drive Transmission System of TBM Based on Bond Graph

2010 ◽  
Vol 44-47 ◽  
pp. 1703-1707
Author(s):  
Chao Lin ◽  
Xin Hong Su ◽  
Da Tong Qin ◽  
Song Song Yu
Keyword(s):  
High Power ◽  
Dynamic Performance ◽  
Graph Model ◽  
Tunnel Boring Machine ◽  
Bond Graph ◽  
Transmission System ◽  
State Equations ◽  
Response Curves ◽  
Tunnel Boring ◽  
Planetary Transmission

The dual-drive system to be used in the tunnel boring machine (TBM) is a new kind of high-power planetary transmission system. On the basis of the system’s transmission theory and the bond graph principle, the bond graph model of the dual drive transmission system is established and then the state equations are deduced. Based on this model, dynamic performance of the system is simulated by means of MATLAB/Simulink and the dynamic response curves of the speed and torques are acquired. The simulation response illustrates that the bond graph model of dual drive transmission systems is accurate. In addition this system is suitable for three types of TBM and can satisfy the requirements of dramatic changes of load in the running of TBM.

Fault indicators and unique mode-dependent state equations from a fixed-causality diagnostic bond graph of linear models with ideal switches

2018 ◽  
Vol 232 (6) ◽  
pp. 695-708 ◽  
Author(s):  
Wolfgang Borutzky
Keyword(s):  
Linear Time ◽  
Bond Graph ◽  
Differential Algebraic Equations ◽  
Fault Detection And Isolation ◽  
Mode Switching ◽  
State Transitions ◽  
Algebraic Equations ◽  
State Equations ◽  
Analytical Redundancy ◽  
Junction Structure

Analytical redundancy relations are fundamental in model-based fault detection and isolation. Their numerical evaluation yields a residual that may serve as a fault indicator. Considering switching linear time-invariant system models that use ideal switches, it is shown that analytical redundancy relations can be systematically deduced from a diagnostic bond graph with fixed causalities that hold for all modes of operation. Moreover, as to a faultless system, the presented bond graph–based approach enables to deduce a unique implicit state equation with coefficients that are functions of the discrete switch states. Devices or phenomena with fast state transitions, for example, electronic diodes and transistors, clutches, or hard mechanical stops are often represented by ideal switches which give rise to variable causalities. However, in the presented approach, fixed causalities are assigned only once to a diagnostic bond graph. That is, causal strokes at switch ports in the diagnostic bond graph reflect only the switch-state configuration in a specific system mode. The actual discrete switch states are implicitly taken into account by the discrete values of the switch moduli. The presented approach starts from a diagnostic bond graph with fixed causalities and from a partitioning of the bond graph junction structure and systematically deduces a set of equations that determines the wanted residuals. Elimination steps result in analytical redundancy relations in which the states of the storage elements and the outputs of the ideal switches are unknowns. For the later two unknowns, the approach produces an implicit differential algebraic equations system. For illustration of the general matrix-based approach, an electromechanical system and two small electronic circuits are considered. Their equations are directly derived from a diagnostic bond graph by following causal paths and are reformulated so that they conform with the matrix equations obtained by the formal approach based on a partitioning of the bond graph junction structure. For one of the three mode-switching examples, a fault scenario has been simulated.

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.

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 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.

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.

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