Fast Generation of Stability Charts for Time-Delay Systems Using Continuation of Characteristic Roots

Samukham, Surya and Uchida, Thomas K. and Vyasarayani, C. P. (2020) Fast Generation of Stability Charts for Time-Delay Systems Using Continuation of Characteristic Roots. Journal of Computational and Nonlinear Dynamics, 15 (11). ISSN 1555-1415

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Many dynamic processes involve time delays, thus their dynamics are governed by delay differential equations (DDEs). Studying the stability of dynamic systems is critical, but analyzing the stability of time-delay systems is challenging because DDEs are infinite-dimensional. We propose a new approach to quickly generate stability charts for DDEs using continuation of characteristic roots (CCR). In our CCR method, the roots of the characteristic equation of a DDE are written as implicit functions of the parameters of interest, and the continuation equations are derived in the form of ordinary differential equations (ODEs). Numerical continuation is then employed to determine the characteristic roots at all points in a parametric space; the stability of the original DDE can then be easily determined. A key advantage of the proposed method is that a system of linearly independent ODEs is solved rather than the typical strategy of solving a large eigenvalue problem at each grid point in the domain. Thus, the CCR method can significantly reduce the computational effort required to determine the stability of DDEs. As we demonstrate with several examples, the CCR method generates highly accurate stability charts, and does so up to 10 times faster than the Galerkin approximation method.

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IITH Creators:
IITH CreatorsORCiD
Vyasarayani, Chandrika Prakash
Item Type: Article
Uncontrolled Keywords: Characteristic equation; Characteristic roots; Computational effort; Delay differential equations; Galerkin approximations; Linearly independents; Numerical continuation; Stability of time-delay systems
Subjects: Physics > Mechanical and aerospace
Divisions: Department of Mechanical & Aerospace Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 28 Jun 2021 07:09
Last Modified: 04 Mar 2022 05:07
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