Combination of sign inverting and delay scheduling control concepts for multiple-delay dynamics

2015 American Control Conference (ACC)

2015

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This paper deploys a recent mathematical tool to predict and prevent thermoacoustic instability (TAI) in a simple combustor. Widely-accepted characteristic of TAI is its time-delayed dynamics which originates from the acoustic coupling terms. Independently from the combustion instability studies, systems specialists have been developing mathematical approaches on similar time-delay problems. This document offers a bridge between the two veins of research. It utilizes the recent mathematical tool called the Cluster Treatment of Characteristic Roots (CTCR) to predict the onset of instability (TAI) for this simple benchmark combustor, Rijke Tube. Beyond prediction, for the operating conditions which already induce an undesirable TAI, this paper proposes a feedback controller design strategy which can recover stability. The suggested control logic is implemented on a test bed and the theoretical results are verified experimentally. c A s Q J F H G Y X

Section: The Stability Assessment Methodologymentioning

confidence: 99%

“…Once the parameters corresponding to the experiment are substituted in(24) to check the strong stability, the bound on feedback gain is calculated as . The heater is located at a position, in which the.…”

mentioning

confidence: 99%

Feedback stabilization of a thermoacoustic device with experiments

Zalluhoglu

Kammer

2015 American Control Conference (ACC)

2015

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“…For the completeness of the discussion we present a brief overview of CTCR, borrowing from [12,13]. The stability assessment methodology based on this paradigm can essentially be decomposed into two main sub-tasks.…”

Section: Stability Assessment Methodology and A Brief Overview Ofmentioning

confidence: 99%

“…The authors resort to a recent development of their group, at this juncture, which is the paradigm called CTCR, as mentioned earlier in this paper. This paradigm, indeed; provides a unique, exhaustive and exact resolution of the stability question in the domain of ሺ߬ ଵ , ߬ ଶ ሻ ∈ ব ଶା [9][10][11][12][13]. The rest of this paper is devoted to the adaptation of CTCR to the system given in (5).…”

Section: Non-conservative Stability Assessment Of Lti Dynamics With Dmentioning

confidence: 99%

“…In this study we provide such a tool. It is the paradigm called Cluster Treatment of Characteristic Roots (CTCR), which has been developed in the last few years [9][10][11][12][13]. The main contribution is the exact and exhaustive declaration of the asymptotic stability of (1) in terms of the distributed delay interval bounds by exploiting its equivalence two a lumpeddelayed system.…”

mentioning

confidence: 99%

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Non-conservative stability assessment of LTI dynamics with distributed delay using CTCR paradigm

Kammer

2015 American Control Conference (ACC)

2015

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A general class of LTI feedback control systems with a distributed delay in the feedback line is taken into account. We start with a theorem which states the equivalence of a general class of distributed delay system to a discrete delay system with multiple independent delays. While this connection has been recognized earlier, what is interesting and novel to this study is the deployment of a paradigm called The Cluster Treatment of Characteristic Roots (CTCR) for this class of systems. CTCR exhaustively declares the stability outlook of the system in the space of the delays. This capability forms a very important basis over which we can build further research connected to systems with distributed delays.

Bounds of imaginary spectra of LTI systems in the domain of two of the multiple time delays

Gao

2016

Automatica

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The stability of linear time invariant (LTI) systems with independent multiple time delays and the cluster treatment of characteristic roots (CTCR) paradigm are investigated from a new perspective. It is known that for such systems, all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays [34]. They are called kernel hypersurfaces (KH). The complete description of KH is the only prerequisite for the CTCR stability assessment procedure. As the number of delays increases, however, their evaluation becomes infeasible. Instead, we present a procedure to extract the 2-D cross-sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays. In the 2-delay domain of interest, the exact upper and lower bounds of the imaginary spectra are determined. For this, a combination of half-angle tangent representation of the characteristic equation and the Dixon resultant theory is used as the main contributions of this paper. The complete KH are obtained by sweeping the root crossing frequency in this interval. Using this knowledge CTCR creates the cross-section of the stability map in the domain of the two arbitrarily selected delays. We demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones.