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.

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.

Dynamic Model of Dual Clutch Lever-Based Electromechanical Actuator

2011 ◽  
Author(s):  
Vladimir Ivanovic´ ◽  
Josˇko Deur ◽  
Milan Milutinovic´ ◽  
H. Eric Tseng
Keyword(s):  
Experimental Data ◽  
Dynamic Model ◽  
Model Validation ◽  
Bond Graph ◽  
Test Rig ◽  
Electromechanical Actuator ◽  
Actuator Dynamics ◽  
Operating Modes ◽  
Graph Modeling ◽  
Bond Graph Modeling

The paper presents a dynamic model of a dual clutch lever-based electromechanical actuator. Bond graph modeling technique is used to describe the clutch actuator dynamics. The model is parameterized and thoroughly validated based on the experimental data collected by using a test rig. The model validation results are used for the purpose of analysis of the actuator behavior under typical operating modes.

scholarly journals Quasi-Steady-State Models of Three Timescale Systems: A Bond Graph Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-20
Author(s):  
Gilberto A. González ◽  
Noe G. Barrera ◽  
Gerardo Ayala ◽  
J. Aaron Padilla ◽  
David Z. Alvarado
Keyword(s):  
Mathematical Model ◽  
Complete System ◽  
Bond Graph ◽  
Singularly Perturbed ◽  
Quasi Steady State ◽  
Singularly Perturbed System ◽  
Reduced Models ◽  
Perturbed System ◽  
State Models ◽  
The Mathematical Model

Modelling in bond graph to obtain reduced models of systems with singular perturbations is applied. This singularly perturbed system is characterized by having three timescales, i.e., slow, medium, and fast dynamics. From a bond graph whose storage elements have an integral causality assignment (BGI), the mathematical model of the complete system can be determined. By assigning a derivative causality assignment to the storage elements for the fast dynamics and maintaining an integral causality assignment for the slow and medium dynamics on the bond graph, reduced models for the slow and medium dynamics are obtained. When a derivative causality to the storage elements for the fast and medium dynamics is assigned and an integral causality assignment to the slow dynamics is applied, the most reduced model is determined. Finally, the proposed methodology to the Ward Leonard system is applied.

A Synoptic–Dynamic Model of Subseasonal Atmospheric Variability

2007 ◽  
Vol 135 (2) ◽  
pp. 449-474 ◽  
Author(s):  
Klaus Weickmann ◽  
Edward Berry
Keyword(s):  
Dynamic Model ◽  
Time Scales ◽  
Life Cycles ◽  
Extreme Weather Events ◽  
Recurrence Time ◽  
Frictional Torque ◽  
Multiple Time ◽  
Fast Time ◽  
Tropical Forcing ◽  
Time Space

Abstract A global synoptic–dynamic model (GSDM) of subseasonal variability is proposed to provide a framework for real-time weather–climate monitoring and to assist with the preparation of medium-range (e.g., week 1–3) predictions. The GSDM is used with a regional focus over North America during northern winter. A case study introduces the time scales of the GSDM and illustrates two circulation transitions related to eastward-moving wave energy signals and their connection to remote tropical forcing. Global and zonal atmospheric angular momentum (AAM) is used to help define the synoptic evolution of the GSDM components and to link regional synoptic variations with physical processes like the global mountain and frictional torque. The core of the GSDM consists of four stages based on the Madden–Julian oscillation (MJO) recurrence time. Additionally, extratropical behaviors including teleconnection patterns, baroclinic life cycles, and ∼monthly oscillations provide intermediate and fast time scales that are combined with the quasi-oscillatory (30–70 day) MJO to define multiple time-/space-scale linear relationships. A unique feature of the GSDM is its focus on global and regional circulation transitions and the related extreme weather events during periods of large global AAM tendency.

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.

scholarly journals On the Linear Quadratic Optimal Control for Systems Described by Singularly Perturbed Itô Differential Equations with Two Fast Time Scales

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 30
Author(s):  
Vasile Dragan
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Time Scales ◽  
Performance Criterion ◽  
Singularly Perturbed ◽  
Algebraic Riccati Equation ◽  
Fast Time ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Stabilizing Solution

In this paper a stochastic optimal control problem described by a quadratic performance criterion and a linear controlled system modeled by a system of singularly perturbed Itô differential equations with two fast time scales is considered. The asymptotic structure of the stabilizing solution (satisfying a prescribed sign condition) to the corresponding stochastic algebraic Riccati equation is derived. Furthermore, a near optimal control whose gain matrices do not depend upon small parameters is discussed.

scholarly journals Slow and Fast Time Scales in Cardiomyocyte Beating

2019 ◽  
Vol 116 (3) ◽  
pp. 162a
Author(s):  
Ohad Cohen ◽  
Samuel Safran
Keyword(s):  
Time Scales ◽  
Fast Time

Delay-Bond Graph Models for Geared Torsional Systems

1974 ◽  
Vol 41 (2) ◽  
pp. 366-370 ◽  
Author(s):  
N. T. Tsai ◽  
S. M. Wang
Keyword(s):  
Transmission Line ◽  
Gear Tooth ◽  
Nonlinear Damping ◽  
Bond Graph ◽  
Dynamic Responses ◽  
State Variables ◽  
Graph Models ◽  
Wave Variables ◽  
Tooth Stiffness ◽  
Line Elements

The dynamic responses of geared torsional systems are analyzed with the delay-bond graph technique. By transforming the power variables into torsional wave variables, the torsional elements are modeled as transmission line elements. The nonlinear elements, e.g., varying tooth stiffness, gear-tooth backlash, and nonlinear damping, are incorporated into the ideal transmission line element. A computational algorithm is established where the state variables of the system are expressed in terms of wave scattering variables and the dynamic responses are then obtained in both time and space domains. The simulation results of several simple examples of linear and nonlinear geared torsional systems are presented to demonstrate the feasibility of this algorithm.

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