Non-iterative evaluation of multiphase thermal compliances in bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 13-19 ◽  
Author(s):  
F. T. Brown
Keyword(s):  
Bond Graph ◽  
The State ◽  
Refrigeration Cycle ◽  
State Variables ◽  
Unfinished Business ◽  
Bond Graphs ◽  
State Equations ◽  
Efficient Simulation ◽  
Multiple Phase ◽  
Iterative Evaluation

The practical use of bond graphs to organize the efficient simulation of multiple-phase thermodynamic systems is perhaps the most significant piece of unfinished business regarding the evolution of bond graphs. The most widely recognized form for these cases, called the pseudo bond graph, dictates particular causalities that require iteration, assuming the use of available state equations. This paper shows how the alternative convection bond graphs can direct non-iterative evaluation of state properties of multiphase thermal compliances. The state variables of a compliance become temperature, mass and volume. A refrigeration cycle is used as an example.

The Optimum Design of Spatial Frames Using the Method of Constrained Steepest Descent With State Equations

1971 ◽  
Vol 93 (4) ◽  
pp. 1261-1267 ◽  
Author(s):  
D. L. Bartel ◽  
E. J. Haug ◽  
Kwan Rim
Keyword(s):  
Nonlinear Programming ◽  
Mechanical Design ◽  
The State ◽  
Steepest Descent ◽  
Mathematical Programming Problem ◽  
State Variables ◽  
State Equations ◽  
Design Problems ◽  
Out Of Plane ◽  
Plane Frames

This paper considers the design of a class of spatial frames which occur frequently in mechanical systems: plane frames with out-of-plane loads. The design objective is to minimize the weight subject to constraints on stress and geometry. The method of constrained steepest descent with state equations is introduced to solve the resulting mathematical programming problem. This method differs from the usual methods of nonlinear programming in that the state variables and the state equations are used explicitly in the formulation. This results in a natural matching of the essential features of the design problem and the method used to obtain its solution. The method is effective and general in that it can be readily applied to a wide variety of design problems which occur in mechanical design.

TIME DOMAIN DIAKOPTIC ANALYSIS BASED ON REDUCED-ORDER STATE EQUATIONS

2007 ◽  
Vol 17 (10) ◽  
pp. 3625-3631 ◽  
Author(s):  
MIHAI IORDACHE ◽  
LUCIA DUMITRIU
Keyword(s):  
Analog Circuits ◽  
Large Scale ◽  
State Equation ◽  
The State ◽  
State Variables ◽  
State Equations ◽  
Integration Algorithm ◽  
Reduced Order ◽  
Decomposition Procedure ◽  
Minimum Number

In this paper we present some new tearing techniques to systematically formulate the state equations in symbolic normal-form for linear and/or nonlinear time-invariant large-scale analog circuits. The excess elements of the first and of the second kind are unitarily treated in order to allow a symbolic representation of the circuit with a minimum number of state variables. A procedure to reduce the state equation number of each subcircuit is also presented. The reduced-order is based on an implicit integration algorithm and on the successive elimination of the selected state variables. Examples are given to illustrate the decomposition procedure, the assignment of the connection sources and the reduced-order technique.

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.

A State-Space-Based Stress Analysis of a Multilayered Spherical Shell With Spherical Isotropy

2000 ◽  
Vol 68 (1) ◽  
pp. 109-114 ◽  
Author(s):  
W. Q. Chen ◽  
H. J. Ding
Keyword(s):  
Spherical Shell ◽  
Stress Analysis ◽  
Matrix Theory ◽  
Three Dimensional ◽  
The State ◽  
State Variables ◽  
State Equations ◽  
Independent State ◽  
Spherical Isotropy ◽  
Constant Coefficients

This paper presents an exact static stress analysis of a multilayered elastic spherical shell (hollow sphere) completely based on three-dimensional elasticity for spherical isotropy. Two independent state equations are derived after introducing three displacement functions and two stress functions. In particular, a variable substitution technique is used to derive the state equations with constant coefficients. Matrix theory is then employed to obtain the relationships between the state variables at the upper and lower surfaces of each lamina. By virtue of the continuity conditions between two adjacent layers, a second-order linear algebraic equation and a fourth-order one about the boundary variables at the inner and outer surfaces of a multilayered spherical shell are obtained. Numerical examples are presented to show the effectiveness of the present method.

Steady state determination using bond graphs for systems with singular state matrix

2011 ◽  
Vol 225 (7) ◽  
pp. 887-901 ◽  
Author(s):  
G González A ◽  
R Galindo
Keyword(s):  
Steady State ◽  
State Space ◽  
Linear Time ◽  
Bond Graph ◽  
State Variables ◽  
Bond Graphs ◽  
State Matrix ◽  
Independent State ◽  
Linear Time Invariant ◽  
Time Invariant

A bond graph procedure to get the steady state value for linear time-invariant systems is presented. The general case of a singular state matrix is considered. The procedure is based on a junction structure configuration with derivative causality assignment, and on relationships of the bond graphs with integral and derivative causality assignments. It is shown that the structurally null modes, i.e. the poles at the origin, are cancelled for steady state. The key to cancel the poles at the origin is that the adjugate matrix of sIn −  Ap multiplies Bp yielding the zeros at the origin with the same order that the structurally null modes, where ( Ap, Bp, Cp, Dp) is a state space realization of a linear time-invariant system, s is the Laplace operator and In, is an n ×  n identity matrix. Hence, this unstable part of the system is cancelled and the steady state can be obtained. Thus, the singularity of the state space matrix is avoided, and the steady state is obtained from the bond graph with derivative causality assignment. Since the singular state matrix is considered, it is shown that by using the bond graph with derivative causality assignment, an equivalent system with linearly independent state variables can be obtained. An example of an electrical system with an electrical transformer modelled by an I-field whose state matrix is singular is presented. Also, the proposed methodology for a load driven by two DC motors is applied.

Development of a Robust Nonlinear Observer for a Single-Link Flexible Manipulator

2004 ◽  
Author(s):  
Nabil G. Chalhoub ◽  
Giscard A. Kfoury
Keyword(s):  
Sliding Mode ◽  
Initial Conditions ◽  
The State ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Flexible Manipulator ◽  
State Variables ◽  
State Equations ◽  
On Line ◽  
Simulation Results

Accurate measurements of all the state variables of a given system are often not available due to the high cost of sensors, the lack of space to mount the transducers or the hostile environment in which the sensors must be located. The purpose of this study is to design a robust sliding mode observer that is capable of accurately estimating the state variables of the system in the presence of disturbances and model uncertainties. It should be emphasized that the proposed observer design can handle state equations expressed in the general form. The performance of the nonlinear observer is assessed herein by examining its capability of predicting the rigid and flexible motions of a compliant beam that is connected to a revolute joint. The simulation results demonstrate the ability of the observer in accurately estimating the state variables of the system in the presence of structured uncertainties and under different initial conditions between the observer and the plant. Moreover, they illustrate the deterioration in the performance of the observer when subjected to unstructured uncertainties of the system. Furthermore, the nonlinear observer was successfully implemented to provide on-line estimates of the state variables for two model-based controllers. The simulation results show minimal deterioration in the closed-loop response of the system stemming from the usage of estimated rather than exact state variables in the computation of the control signals.

Exploiting Bond Graph Causality in Physical System Models

1987 ◽  
Vol 109 (4) ◽  
pp. 378-383 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
Physical System ◽  
Dynamic Structure ◽  
Bond Graph ◽  
Additional Research ◽  
Bond Graphs ◽  
State Equations ◽  
Design Assessment ◽  
Direct Interpretation ◽  
Junction Structure ◽  
Structure Properties

Causality as a concept and a tool associated with bond graphs has seen use for more than twenty years. Our principal purpose in this paper is to bring together several different views and applications of causality in order to suggest how valuable it can be in understanding the dynamic structure of models. The topics considered include causality assignment, both traditional and nontraditional, and state equations; design assessment of models based on direct interpretation; and junction structure properties. The topics are illustrated by examples. Some opportunities for additional research into causality properties and applications are suggested.

Ideal physical element representation from reduced bond graphs

2002 ◽  
Vol 216 (1) ◽  
pp. 73-83 ◽  
Author(s):  
L. S. Louca ◽  
J. L. Stein
Keyword(s):  
Graph Model ◽  
Bond Graph ◽  
The Body ◽  
System Model ◽  
Bond Graphs ◽  
State Equations ◽  
Rigorous Approach ◽  
Reduction Techniques ◽  
Relative Value ◽  
Element Removal

Previous research has demonstrated that bond graphs are a natural and convenient representation to implement energy-based metrics that evaluate the relative ‘value’ of energy elements in a dynamic system model. Bond graphs also provide a framework for systematically reformulating a reduced bond graph model (and thus the state equations) of the system that results from eliminating the ‘unimportant’ elements. This paper shows that bond graphs also provide a natural and convenient representation for developing a rigorous approach for interpreting the removal of ideal energy elements from the system model. For example, when a generalized inductance in the mechanical domain is eliminated from a model, the bond graph shows whether the coordinate representing the motion of the body becomes free to move (zero inertia) or fixed to ground (infinite inertia). This systematic interpretation of element removal makes bond graphs an attractive modelling language for automated model reduction techniques. An illustrative example is provided to demonstrate how the developed approach can be applied to provide the physical interpretation of energy element removal from a mechanical system.

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

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