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The role of nonnormality in active control of combustion instability
Rahul R. Kulkarni,
Published in
2008
Abstract
Design of a linear controller for a thermoacoustic system taking the consequences of nonnormality into account is presented in this paper. The analysis is performed in the framework of the classical n-τ model of Crocco. The controllers based on classical stability analysis focuses on the stability of the individual eigenmodes of the system. However, the nonnormal nature of a thermoacoustic system which implies non-orthogonality of the eigenvectors causes redistribution of the acoustic energy between the eigenmodes even in the linear regime. Transient growth in a linearized system, even when the individual eigenvectors are decaying is an important characteristic of a nonnormal system. This short term growth amplifies the small disturbances present in the system. Traditional linear controllers based on classical linear stability analysis do not take transient growth into account. High enough amplitudes of the transient growth can cause the system to enter into the region where nonlinear effects are significant and linear controller designed would fail in this case. It is shown that, controlling the dominant mode in a nonnormal thermoacoustic system alone can cause the instability to occur at another frequency which was initially unexcited. This manifests as secondary peaks in the FFT of the evolution of the acoustic pressure and velocity. Hence, a controller based on the pole placement technique which is applicable to the transients as well as the asymptotic stability of the system designed, and its effectiveness is demonstrated with an example of a horizontal Rijke tube model. Copyright © 2008 by Kulkarni R.R. , K. Balasubramanian and R.I. Sujith.
About the journal
Journal46th AIAA Aerospace Sciences Meeting and Exhibit
Open AccessNo
Concepts (29)
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    Acoustic energy
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    ACOUSTIC PRESSURES
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    Active control
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    Combustion instabilities
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    Dominant mode
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    EIGEN MODES
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    Eigenvectors
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    Linear controllers
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    LINEAR REGIME
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    Linearized systems
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    NON-NORMALITY
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    NON-ORTHOGONALITY
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    Nonlinear effect
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    NONNORMAL
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    Pole placement technique
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    Rijke tube
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    SECONDARY PEAK
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    SHORT-TERM GROWTH
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    SMALL DISTURBANCES
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    Stability analysis
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    THERMOACOUSTIC SYSTEMS
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    TRANSIENT GROWTH
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    Aerospace engineering
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    Asymptotic stability
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    Controllers
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    Eigenvalues and eigenfunctions
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    Linear control systems
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    Linear stability analysis
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    System stability