Direct method for TDS stability analysis

Walton, K.; Marshall, J.

doi:10.1049/ip-d.1987.0018

Cited by 293 publications

(233 citation statements)

References 7 publications

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“…From one point of view, the rightmost poles coincide with the dominant ones. However, this is not the best conception for our case since there are infinitely many rightmost roots, see (3). Another idea is to measure the dominancy by the distance from the zero (i.e.…”

Section: Extrapolation Methodsmentioning

confidence: 99%

“…eigenvalues) [1,2]. Much effort has been made to analyse the infinite spectrum of TDS of retarded as well as neutral type (NTDS), mainly when the endeavour to decide about system stability and its dependence on particular delays' values [3][4][5][6][7][8]. Compared to retarded ones, NTDS are much more advanced, tricky and intricate regarding spectral properties [1,4,9].…”

Section: Introductionmentioning

confidence: 99%

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A comparison of possible exponential polynomial approximations to get commensurate delays

Pekař

Chalupa

2016

MATEC Web Conf.

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Abstract. The paper is aimed at a comparative simulation study on three prospective ideas how to approximate a general exponential polynomial by another one having all its exponents in the exp-function as integer multiples of some real number. This work is motivated by spectral properties of neutral time-delay systems (NTDS) and the contemporary state of the knowledge about the spectrum of NTDS with commensurate delays which are characterized by the latter family of exponential polynomials. The three ideas are, namely, those: Taylor series expansion, the interpolation in points given by dominant roots estimates and the special extrapolation technique presented by the authors recently. The goal is to match dominant parts of both the spectra as close as possible. However, some properties from the so called strong stability point of view can not be, in principle, preserved. The presented simulation example demonstrates the accuracy and efficiency of all the methods.

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Section: Extrapolation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A comparison of possible exponential polynomial approximations to get commensurate delays

Pekař

Chalupa

2016

MATEC Web Conf.

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“…For this reason, most of the existing approaches study stability of such systems by finding the crossings of poles through the imaginary axis [8]. There has been a large effort to deal with this problem, as can be seen by the large quantity of articles dealing with it for the standard case (integer order systems); see [5], and others.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, taking an automatic computerbased control system or a process control with networked transmission for example, it is necessary and more reasonable to simultaneously consider the possible transmission delay for the corresponding control law and the device delay due to computing or processing. Recently, much attention has been paid to the subjects of stability, stabilization and control of the time delay systems [1] - [5]. Fractional order models would be more accurate than integer order models.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, an analitical direct approach to determine all possible stability regions in the parametric space of delay is proposed. The original idea in this strategy is derived based on the method reported in [5] to achieve the stability criteria of integer order delay systems. The proposed method is an analytically elegant procedure that first converts the transcendental characteristic equation into an algebraic equation without the transcendentality by eliminating the highest degree of commensuracy terms successively.…”

Section: Introductionmentioning

confidence: 99%

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Direct Method for Stability Analysis of Fractional Delay Systems

Pakzad

Nekui

2013

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

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In this paper, a direct method is presented to analyze the stability of fractional order systems with single and multiple commensurate time delays. Using the approach presented in this study, first, without using any approximation, the transcendental characteristic equation is converted to an algebraic one with some specific crossing points. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. Finally, the concept of stability is expressed as a function of delay. An illustrative example is presented to confirm the proposed method results.

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Impact of load sharing schemes on the stability delay margins computed by Rekasius substitution method in load frequency control system with electric vehicles aggregator

Naveed

Sönmez

Ayasun

2021

Int Trans Electr Energ Syst

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The impact of load sharing between the electric vehicles (EVs) aggregator and the conventional generator on stability delay margins in a two-area load frequency control (LFC) system is investigated in this work. A frequency-domain Rekasius substitution method is used to compute stability delay margins for different values of proportional-integral (PI) controller gains. The proposed method computes complex roots on the imaginary axis of the quasi-characteristic equation. The substitution first converts the quasi-characteristic equation of the LFC with EVs aggregator (LFC-EVs) system including delay-dependent exponential terms into an ordinary polynomial. Then, the Routh-Hurwitz stability method is applied to find those imaginary roots and the corresponding stability delay margins. The qualitative impact of different sharing schemes between the conventional generator and EVs aggregator and the impact of EVs gains on stability delay margins are thoroughly analyzed, and the results are validated by time domain simulations and quasi-polynomial mapping-based root finder algorithm. It is observed that for any given PI controller gains, stability delay margins decrease when the participation of EVs into the frequency regulation increases.

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Direct method for TDS stability analysis

Cited by 293 publications

References 7 publications

A comparison of possible exponential polynomial approximations to get commensurate delays

A comparison of possible exponential polynomial approximations to get commensurate delays

Direct Method for Stability Analysis of Fractional Delay Systems

Impact of load sharing schemes on the stability delay margins computed by Rekasius substitution method in load frequency control system with electric vehicles aggregator

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