Abstract: In order to reduce NOx emissions in aero-engine combustion chambers, lean premixed pre-vaporized combustion technology is widely used, which will lead to combustion instability more frequently. The energy of combustion instability of aero-engine comes from the combustion of propellant, and thermoacoustic instability is the main form of combustion instability. In order to suppress the thermoacoustic instability, firstly, the influence of flame combustion response on the system is considered based on the Culick model, and the mathematical model of thermoacoustic instability with state delay is derived. Secondly, based on the derived model, the influence of the convection time from fuel injection to heat release from combustion on the stability of the thermoacoustic system is explored, then a back-stepping active control method with prescribed performance is designed, and the upper bound of the convection time is obtained under the premise of ensuring the prescribed performance of the system. Finally, it is verified from both theoretical analysis and simulation results that the active control method can make the pressure oscillation of the thermoacoustic instability system converge asymptotically and satisfy the prescribed performance with time-delay robustness.

Key words: thermoacoustic instability, state-delay, prescribed performance control, backstepping, robust control