An analytically tractable model for combustion instability

Bouziani, Fethi; Landau, Ioan Doré; Voda-Besancon, A.; Bitmead, Robert R.

doi:10.1109/cdc.2005.1583355

Cited by 7 publications

(15 citation statements)

References 15 publications

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“…The model in [1] features in the feedback loop a cascade of a : differentiator -delay -static nonlinear characteristic -low pass filter -differentiator. An analytically tractable model for [1] has been proposed in [17] based on coupled Van der Pol equations. The block diagram of the model is shown in Figure 1, where w1 and w2 are the natural radian frequencies of the first and second resonators respectively and which can have arbitrary values with some modest provisions to be developed, E is a small positive quantity.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a tractable model for combustion instability: the effect of delay and low pass filtering

Bouziani¹,

Landau²,

Bitmead

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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In this paper a new analytically tractable model for combustion instability is proposed. The model is based on two coupled resonators in a feedforward path, and a feedback path composed of a delay, generalized Van der Pol term and a low pass filter. The model is analyzed and approximated using a refined Krylov-Bogoliubov (K-B) method. The analysis shows that the model captures the phenomenon of two coexisting oscillating modes which has been noted in combustion instability in [1], [2]. Conditions for the occurrence of various operation regimes have been established. The importance of delay and low pass filtering is discussed in this article. A frequency domain comparison between K-B approximations and the true outputs of the model has been provided in the end of the paper.

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Section: Introductionmentioning

confidence: 99%

Analysis of a tractable model for combustion instability: the effect of delay and low pass filtering

Bouziani¹,

Landau²,

Bitmead

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hence, we limit our study here to case 1. This is new and have clear practical implication when compared with [18].…”

Section: Lemma 3 Consider the Expression (18) And The Assumptions 1 mentioning

confidence: 99%

“…Indeed, the expression (21) correspond to linear combinations of frequencies ω 1 and ω 2 present in the development of f and the expressions (22) and (23) are the gain and phase introduced by the delay plus differentiator block and filtering, respectively. Proof: substituting approximations (19) in expression (18), one getṡ…”

Section: Assumption 1 For Small Time Delay τ the Quantitiesmentioning

confidence: 99%

“…The relationship between coupled Van der Pol equations and combustion instabilities model of Dunstan and Bitmead [11] has been discussed in [18]. A system of two coupled Van der Pol equations has been considered as a basic model for combustion instabilities…”

Section: Combustion Instability Modelmentioning

confidence: 99%

“…The model has been successfully analyzed using Krylov-Bogoliubov approach in [18]. However, this model does not include the cascade differentiator -delay and the low pass filter (existing in Dunstan and Bitmead model [11]).…”

Section: Combustion Instability Modelmentioning

confidence: 99%

See 2 more Smart Citations

A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations

Landau¹,

Bouziani²,

Bitmead

Analysis and Design of Nonlinear Control Systems

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PreludeIt is a great pleasure for us to contribute to this book dedicated to Alberto Isidori on the occasion of his sixty fifth birthday. It is also, for the first author, the occasion to acknowledge a very long period of useful and pleasant exchange which started in 1973 (bilinear systems) and has continued through the years on various specific subjects.The important contributions of Albereto Isidori in the control of nonlinear systems have had a tremendous impact in the control community. Feedback linearization was one of the important subjects developed by Alberto. While the oscillatory nonlinear system considered in this contribution requires specific techniques for its analysis, still a feedback linearization is used for quenching the oscillations.

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On the dynamics of flame images identified through computer vision and modal methods

Chui

Neto

Trigo

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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Combustion processes in industrial furnaces pose challenging difficulties when one attempts to model flame. Chemical and physical phenomena interact and affect flame behavior in such a complex way that several different approaches have been under development to tackle the modeling problem. Flame instabilities could potentially harm safety operation of the furnace. Ultimate goal of flame control is to develop means to actuate over the flame state in order to avoid dangerous situations. A critical step towards this objective is to come up with a reliable model for the flame, so that control theory could be applied to automatically maintain flame state within safe standards. This work proposes a methodology to model the dynamics of flames through computer vision to acquire and process flame images in order to extract image features evolution in time. Then, a dynamic model is identified through random decrement algorithm and Ibrahim time domain method, which are operational modal analysis techniques, together with a random contribution. Flames from seven different combustion conditions were modeled by such methodology, and their estimated values were compared with experimental data for validation. Results show that estimated and experimental data possess a high degree of correlation, thus confirming the viability of the proposed dynamic model of flames.

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An analytically tractable model for combustion instability

Abstract: Abstract-A system of two coupled Van der Pol equations is considered as a model for combustion instability. This system is analyzed using the Krylov-Bogoliubov method. The results of the analysis are compared with simulation results and with data obtained from a combustion system.

Cited by 7 publications

References 15 publications

Analysis of a tractable model for combustion instability: the effect of delay and low pass filtering

Analysis of a tractable model for combustion instability: the effect of delay and low pass filtering

A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations

On the dynamics of flame images identified through computer vision and modal methods

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