Feedback Control of Rijke-Type Thermoacoustic Oscillations Transient Growth

Abstract

Non-normality can lead to acoustic disturbances transient growth in linearly stable thermoacoustic systems. This can cause small-amplitude disturbances to grow into limit cycle oscillations and the systems become nonlinearly unstable. Such self-excited limit cycle oscillations are detrimental to the land-based gas turbine and aero-engines. In this work, we demonstrate the conventional controllers such as linear quadratic regulator (LQR) fail in eliminating the transient energy growth, which has great potential to trigger thermoacoustic instability. To minimize the acoustic disturbances transient growth, a transient growth controller (TGC) is designed by considering the non-normality effect. The performance of the conventional controllers and TGC is performed and compared in a horizontal thermoacoustic system with Dirichlet boundary conditions and monopole-like actuators implemented. An acoustically compact heat source is confined and modelled as time-lag formulation. The TGC controller is shown to be able to not only stabilize the thermoacoustic system but also minimize the transient energy growth.