Nonlinear feedback control of thermoacoustic oscillations in a Rijke tube

Flow disturbances could undergo transient growth to trigger thermoacoustic instability in a combustion system with non-orthogonal eigenmodes. In this work, nonlinear feedback control of thermoacoustic oscillations in a Rijke-type combustion system is considered. A generalized thermoacoustic model with distributed monopole-like actuators is proposed. To stabilize the thermoacoustic system, a Lyapunov-based nonlinear controller is developed. It is shown that the nonlinear feedback controller achieves both exponential decay of the flow disturbance energy and unity maximum transient growth.