Robust and Adaptive Nonlinear Regulation of Thermoacoustic Oscillations in Rijke-Type Systems

Nonlinear control of self-excited oscillations in a Rijke-type thermoacoustic system is considered. A commonly used thermoacoustic model with a number of monopole-like actuators is first introduced. The model is expressed in a nonlinear control-oriented form, which includes unmodeled nonlinearities and parametric uncertainty in both the thermoacoustic dynamics and in the actuator dynamics. A robust and adaptive nonlinear control law is developed to compensate for the parametric uncertainty and unmodeled nonlinearities. Challenges in the control design include input-multiplicative parametric uncertainty. This challenge is mitigated through careful algebraic manipulation in the regulation error system development along with a Lyapunov-based adaptive law. A rigorous Lyapunov-based stability analysis is used to prove that the nonlinear controller achieves asymptotic regulation of an uncertain thermoacoustic system with multiple modes.