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

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.

Download Full-text

Quasi-steady-state model of a class of nonlinear singularly perturbed system in a bond graph approach

Electrical Engineering ◽

10.1007/s00202-016-0507-x ◽

2016 ◽

Vol 100 (1) ◽

pp. 293-302 ◽

Cited By ~ 3

Author(s):

Gilberto Gonzalez-Avalos ◽

J. Aaron Padilla

Keyword(s):

Steady State ◽

Bond Graph ◽

Singularly Perturbed ◽

State Model ◽

Quasi Steady State ◽

Singularly Perturbed System ◽

Perturbed System ◽

Steady State Model

Download Full-text

New Conditions That Guarantee Uniform Asymptotically Stable and Absolute Stability of Singularly Perturbed Systems of Certain Class of Nonlinear Differential Equations

Journal of Advances in Mathematics and Computer Science ◽

10.9734/jamcs/2019/v32i230142 ◽

2019 ◽

pp. 1-12

Author(s):

Ebiendele Peter ◽

Asuelinmen Osoria

Keyword(s):

Differential Equations ◽

Absolute Stability ◽

Nonlinear Differential Equations ◽

Singularly Perturbed ◽

Asymptotically Stable ◽

Singularly Perturbed Systems ◽

Singularly Perturbed System ◽

Perturbed System ◽

Necessary And Sufficient ◽

The Mathematical Model

The objectives of this paper is to investigate singularly perturbed system of the fourth order differential equations of the type, to establish the necessary and sufficient new conditions that guarantee, uniform asymptotically stable, and absolute stability of the system. The Liapunov’s functions were the mathematical model used to establish the main results of this study. The study was motivated by some authors in the literature, Grujic LJ.T, and Hoppensteadt, F., and the results obtained in this study improves upon their results to the case where more than two arguments was established.

Download Full-text

Event-triggered stability of singularly perturbed system with time delay

2020 39th Chinese Control Conference (CCC) ◽

10.23919/ccc50068.2020.9188858 ◽

2020 ◽

Author(s):

Xiang Ren ◽

Fei Hao

Keyword(s):

Time Delay ◽

Singularly Perturbed ◽

Singularly Perturbed System ◽

Perturbed System ◽

System With Time Delay ◽

Event Triggered

Download Full-text

Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

Axioms ◽

10.3390/axioms8020071 ◽

2019 ◽

Vol 8 (2) ◽

pp. 71 ◽

Cited By ~ 1

Author(s):

Olga Tsekhan

Keyword(s):

Sufficient Conditions ◽

Singularly Perturbed ◽

Degenerate System ◽

Multiple Delays ◽

Complete Controllability ◽

Singularly Perturbed System ◽

System With Delay ◽

Perturbed System ◽

Time Invariant ◽

Controllability Conditions

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

Download Full-text

NUMERICAL COMPUTATION OF CANARDS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127400001742 ◽

2000 ◽

Vol 10 (12) ◽

pp. 2669-2687 ◽

Cited By ~ 57

Author(s):

JOHN GUCKENHEIMER ◽

KATHLEEN HOFFMAN ◽

WARREN WECKESSER

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Electrical Potential ◽

Slow Manifold ◽

Singularly Perturbed ◽

Singularly Perturbed Systems ◽

Singularly Perturbed System ◽

Chemical Systems ◽

Perturbed System ◽

Physical And Chemical

Singularly perturbed systems of ordinary differential equations arise in many biological, physical and chemical systems. We present an example of a singularly perturbed system of ordinary differential equations that arises as a model of the electrical potential across the cell membrane of a neuron. We describe two periodic solutions of this example that were numerically computed using continuation of solutions of boundary value problems. One of these periodic orbits contains canards, trajectory segments that follow unstable portions of a slow manifold. We identify several mechanisms that lead to the formation of these and other canards in this example.

Download Full-text