Nonlinear feedback control of self-sustained thermoacoustic oscillations

Acoustic disturbances could undergo transient growth to trigger thermoacoustic instability in a combustion system with non-orthogonal eigenmodes, even with stable eigenvalues and in the presence of conventional linear controllers. In this work, nonlinear feedback control of thermoacoustic oscillations in a Rijke-type combustion system is considered. A thermoacoustic model with distributed monopole-like actuators is presented. To stabilize the thermoacoustic system, a nonlinear feedback controller is developed. It is shown that the feedback controller achieves both exponential decay of the flow disturbance energy and unity maximum transient growth. The performance of the controller is illustrated with two systems: one associated with one mode and one actuator, and the other with two modes and two actuators. The successful demonstration indicates that the developed nonlinear controller has the potential to be applied to combustion systems with multiple modes.