A bond graph procedure for direct passivation of nonlinear systems

2007 ◽  
Author(s):  
A. Achir ◽  
C. Sueur
Keyword(s):  
Nonlinear Systems ◽  
Bond Graph

scholarly journals Approximation of Linearized Systems to a Class of Nonlinear Systems Based on Dynamic Linearization

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Raquel S. Rodríguez ◽  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Dynamic ◽  
Bond Graph ◽  
Physical Domain ◽  
Graph Models ◽  
Simple Task ◽  
Analysis And Synthesis ◽  
Simulation Results

An alternative method to analyze a class of nonlinear systems in a bond graph approach is proposed. It is well known that the analysis and synthesis of nonlinear systems is not a simple task. Hence, a first step can be to linearize this nonlinear system on an operation point. A methodology to obtain linearization for consecutive points along a trajectory in the physical domain is proposed. This type of linearization determines a group of linearized systems, which is an approximation close enough to original nonlinear dynamic and in this paper is called dynamic linearization. Dynamic linearization through a lemma and a procedure is established. Therefore, linearized bond graph models can be considered symmetric with respect to nonlinear system models. The proposed methodology is applied to a DC motor as a case study. In order to show the effectiveness of the dynamic linearization, simulation results are shown.

Steady State for a Class of NonLinear Systems: A Bond Graph Approach

2009 ◽  
Vol 42 (13) ◽  
pp. 483-488
Author(s):  
Gilberto Gonzalez-A ◽  
Aaron Padilla-G
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Bond Graph

scholarly journals A Quasi-Steady State Model of a Singularly Perturbed Wind Turbine with an Induction Generator and Nonlinear Frictions: A Bond Graph Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Aaron Padilla-Garcia ◽  
Gilberto Gonzalez-Avalos ◽  
Noe Barrera-Gallegos ◽  
Gerardo Ayala-Jaimes
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Wind Turbine ◽  
Bond Graph ◽  
Singularly Perturbed ◽  
State Model ◽  
Induction Generator ◽  
Quasi Steady State ◽  
State Variables ◽  
Steady State Model

The modelling in bond graph of a class of nonlinear systems with singular perturbations is presented. The class of nonlinear systems modelled by bond graphs is defined by the product of state variables and nonlinear dissipation elements. In order to obtain the mathematical model of the singularly perturbed nonlinear systems, a lemma based on the junction structure of the bond graph with a preferred integral causality assignment is proposed. The quasi-steady state model of the system is obtained by assigning a derivative causality to the storage elements for the fast dynamics and an integral causality to the storage elements for the slow dynamics. The proposed methodology to a wind turbine connected to an induction generator is applied. Simulation results of the exact and reduced models of this case study are shown.

The Method of Relaxed Causality in the Bond Graph Analysis of Nonlinear Systems

1974 ◽  
Vol 96 (1) ◽  
pp. 95-99 ◽  
Author(s):  
B. J. Joseph ◽  
H. R. Martens
Keyword(s):  
Nonlinear Systems ◽  
Mathematical Models ◽  
Bond Graph ◽  
Graph Analysis ◽  
Algebraic Equations ◽  
Underlying Principle ◽  
Systematic Derivation

A method is presented for the formulation of mathematical models of nonlinear systems. The method employs as the underlying principle the relaxation of the requirement of explicit causality at 0- and 1-junctions. Instead, causal assignments are made which are consistent with the computing causality of the nonlinear elements, thus leading to causal violations in the conventional sense. A classification of causal violations is identified which provides information useful in the systematic derivation of algebraic equations. A most attractive aspect of the method is the fact that causal relaxation is required only when needed, and only to the extent needed.

scholarly journals Direct Determination of Reduced Models of a Class of Singularly Perturbed Nonlinear Systems on Three Time Scales in a Bond Graph Approach

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 104
Author(s):  
Gerardo Ayala-Jaimes ◽  
Gilberto Gonzalez-Avalos ◽  
Noe Barrera Gallegos ◽  
Aaron Padilla Garcia ◽  
Juancarlos Mendez-B
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Model ◽  
Time Scales ◽  
Bond Graph ◽  
Singularly Perturbed ◽  
Fast Time ◽  
State Variables ◽  
Slow Dynamics ◽  
Reduced Models ◽  
Bond Graph Modeling

One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with singular perturbations is presented. The class of nonlinear systems is the product of state variables on three time scales (fast, medium, and slow). Through this paper, the symmetry of mathematical modeling and graphical modeling can be established. A main characteristic of the bond graph is the application of causality to its elements. When an integral causality is assigned to the storage elements that determine the state variables, the dynamic model is obtained. If the storage elements of the fast dynamics have a derivative causality and the storage elements of the medium and slow dynamics an integral causality is assigned, a reduced model is obtained, which consists of a dynamic model for the medium and slow time scales and a stationary model of the fast time scale. By applying derivative causality to the storage elements of the fast and medium dynamics and an integral causality to the storage elements of the slow dynamics, the quasi-steady-state model for the slow dynamics is obtained and stationary models for the fast and medium dynamics are defined. The exact and reduced models of singularly perturbed systems can be interpreted as another symmetry in the development of this paper. Finally, the proposed methodology was applied to a system with three time scales in a bond graph approach, and simulation results are shown in order to indicate the effectiveness of the proposed methodology.

Bond Graph Modeling of Planar Mechanisms With Realistic Joint Effects

1989 ◽  
Vol 111 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Ashraf Zeid
Keyword(s):  
Nonlinear Systems ◽  
Bond Graph ◽  
Dynamic Equations ◽  
Planar Mechanisms ◽  
Joint Effects ◽  
Graph Modeling ◽  
Multipliers Method ◽  
Bond Graph Modeling ◽  
Joint Clearances

This work demonstrates that the Karnopp-Margolis method for treating derivative causality in the bond graph produces a formulation that is equivalent to the classical Lagrange λ multipliers method for the modeling of planar mechanisms. It is then demonstrated that this formulation can be used to eliminate derivative causality in general. Furthermore, the method can be used as the basis for an algorithm which automates the derivation of the dynamic equations for nonlinear systems. It is also shown that the method can be used to treat the modeling of joint nonlinearities such as joint clearances and joint compliances.

Complementarity framework formulation from bond graphs to model a class of nonlinear systems and hybrid systems with fixed causality

SIMULATION ◽  
2018 ◽  
Vol 94 (9) ◽  
pp. 783-795 ◽  
Author(s):  
Noé Villa-Villaseñor ◽  
J Jesús Rico-Melgoza
Keyword(s):  
Nonlinear Systems ◽  
Modeling And Simulation ◽  
Hybrid Systems ◽  
Graph Model ◽  
Bond Graph ◽  
Switching Systems ◽  
Switching Converters ◽  
Bond Graphs ◽  
Systematic Method ◽  
Power Switching

A systematic method for constructing models in the complementarity framework from a bond graph is proposed. Bond graphs with and without storage elements in derivative causality are considered. The proposed method allows the study of switching systems represented by a bond graph model of fixed causality. The proposed methodology allows the complementarity framework to be exploited in different engineering areas by using bond graphs. The idea of representing a unidirectional switch with a model that is essentially the same as a diode is presented. By employing a similar representation for diodes and switches, the modeling and simulation of power switching converters are simplified and become more intuitive. Two application examples are shown. A non-inverting buck-boost converter and a zeta converter with an element in derivative causality are simulated.

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