Feedback control of thermoacoustic oscillation transient growth of a premixed Laminar flame

Abstract

Transient growth of combustion-excited oscillations could trigger thermoacoustic instability in a combustion system with nonorthogonal eigenmodes. In this work, feedback control of transient growth of combustion-excited oscillation in a simplified thermoacoustic system with Dirichlet boundary conditions is considered. For this a thermoacoustic model of a premixed laminar flame with an actuator is developed. It is formulated in state-space by expanding acoustic disturbances via Galerkin series and linearizing flame model and recasting it into the classical time-lag N-τ for controllers implementation. As a linear-quadratic-regulator (LQR) controller is implemented, the system becomes asymptotically stable. However, it is associated with transient growth of thermoacoustic oscillations, which may potentially trigger combustion instability. To eliminate the oscillations transient growth, a strict dissipativity controller is then implemented. Comparison is then made between the performances of these controllers. It is found that the strict dissipativity controller achieves both exponential decay of the oscillations and unity maximum transient growth.