Stability of retarded delay differential systems

Arunsawatwong, Suchin

doi:10.1080/00207179608921701

Cited by 23 publications

(14 citation statements)

References 9 publications

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“…the right half plane zeros of a quasi-polynomial have to be determined. This was done by restricting the region within the right half plane where zeros can occur using an algorithm based on (Arunsawatwong, 1996). Then the poles were found by a direct search method.…”

Section: _11 [ Wd(s)s(s)mentioning

confidence: 99%

H ∞ Control of a Continuous Crystallizer

Vollmer

Raisch

2000

IFAC Proceedings Volumes

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Robustly stabilizing control of an open loop oscillatory crystallization process is considered. The crystallizer is described by a population balance model. From this distributed parameter model an irrational transfer function is obtained which has infinitely many poles and thus represents the infinite-dimensional nature of the system. An infinite-dimensional Hoc controller synthesis method is applied to solve the weighted mixed sensitivity problem for this transfer function. This procedure results in an irrational controller. For practical implementation, the controller needs to be approximated by a rational transfer function . The effectiveness of the controller is demonstrated in simulations.

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Section: _11 [ Wd(s)s(s)mentioning

confidence: 99%

H ∞ Control of a Continuous Crystallizer

Vollmer

Raisch

2000

IFAC Proceedings Volumes

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“…This is an extension of the design formulation which was first used in [5] in conjunction with rational systems and subsequently in [17,18] in conjunction with retarded delay differential systems.…”

Section: Discussionmentioning

confidence: 99%

“…In this connection, an economical algorithm for computing the abscissa of stability was given in [16], which avoids calculating all the characteristic roots. This useful approach was then extended to the case of retarded delay differential systems in [17,18] and to the case of RFDDSs in [19]. See also Section 3 for further details.…”

Section: Phase Imentioning

confidence: 98%

Design of retarded fractional delay differential systems using the method of inequalities

Arunsawatwong

Nguyen

2009

Int. J. Autom. Comput.

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Methods based on numerical optimization are useful and effective in the design of control systems. This paper describes the design of retarded fractional delay differential systems (RFDDSs) by the method of inequalities, in which the design problem is formulated so that it is suitable for solution by numerical methods. Zakian s original formulation, which was first proposed in connection with rational systems, is extended to the case of RFDDSs. In making the use of this formulation possible for RFDDSs, the associated stability problems are resolved by using the stability test and the numerical algorithm for computing the abscissa of stability recently developed by the authors. During the design process, the time responses are obtained by a known method for the numerical inversion of Laplace transforms. Two numerical examples are given, where fractional controllers are designed for a time-delay and a heat-conduction plants.

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“…So the numerical procedure is now converted into a simpler and more precise one, i.e., "real eigenvalue" determination of a constant matrix. [16,17,18,19,20,21]). This procedure follows a starting premise similar to that in the Schur-Cohn methodology in (a).…”

Section: Brief Review Of the Methodologiesmentioning

confidence: 99%

“…Therefore searching for the imaginary roots of (2.11) is a sufficient procedure for the mission. The practical usage of this analytically elegant procedure in the literature is very limited [16,18,20,21] because of the round-off errors it invites during the successive evaluation of CE p (s), albeit in alphanumeric form.…”

Section: (B) Elimination Of Transcendental Terms (As Introduced By [5mentioning

confidence: 99%

Stability Robustness of Retarded LTI Systems with Single Delay and Exhaustive Determination of Their Imaginary Spectra

Sipahi¹,

Olgaç²

2006

SIAM J. Control Optim.

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In this paper we consider the stability robustness of the general class of vector LTI (linear time invariant) equations with a single delay,ẋ(t) = Ax(t) + Bx(t − τ ), x ∈ R n . The robustness is against the uncertain, but constant delay, τ ∈ R + . We first present a set of novel propositions and state that the solution must start from the complete knowledge of imaginary spectra of the system, and the corresponding delays. The propositions claim that such spectra form a set of manageably small number of members, and this number is upper bounded by n 2 regardless of the composition of A and B matrices. They also claim that the infinite-dimensional system at hand has an outstanding discipline regarding these imaginary spectra. This discipline invites the recently developed concept called the cluster treatment of characteristic roots (CTCR). The CTCR procedure requires a complete and precise determination of the imaginary spectra of the system. There are many procedures in the literature to achieve this. They are, in fact, some variations of the five main methods of different levels of precision and complexity. There is, however, no study known to the authors for presenting a comparison among these methods. This paper addresses this need. We first offer an overview of each of the five methods and then compare their numerical performances over an example case study.

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Stability of retarded delay differential systems

Cited by 23 publications

References 9 publications

H ∞ Control of a Continuous Crystallizer

H ∞ Control of a Continuous Crystallizer

Design of retarded fractional delay differential systems using the method of inequalities

Stability Robustness of Retarded LTI Systems with Single Delay and Exhaustive Determination of Their Imaginary Spectra

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