H _∞ loop-shaping control of azimuthal combustion instabilities in annular combustors

Lean combustion technique and annular geometries are preferred in aero-engines and gas turbines, which however may lead to azimuthal combustion instabilities. Active control can be used to stabilize combustion instabilities. Due to its easy use, linear feedback controllers embedded with linear flame response models under weak perturbation amplitude are typically preferred. However, flame responses to oncoming disturbances are typically nonlinear; such controllers are not guaranteed to stabilize. Model-based control strategies generally focus on axisymmetric cases, even though symmetry breaking of azimuthal thermoacoustic modes often occurs in annular combustors. This work uses an improved thermoacoustic model to simulate combustion instabilities within annular combustors, providing a platform on which control strategies development can be performed. The improved model takes into account the nonlinear flame response and the symmetry breaking of azimuthal modes. Single-input single-output control strategies targeting on these nonlinear instabilities are developed in this work. Such controllers can achieve stability for linear and nonlinear fluctuations as well as in symmetric and non-axisymmetric cases. The controllers adopt the (Formula presented.) loop-shaping control strategy and a satisfactory robust performance is obtained.