Adaptive stabilization of nonlinear acoustic oscillations in combustion chambers

We present a self-tuning scheme for adapting the parameters of a PI controller proposed by Fung-Yang (1992) for stabilization of a Culick-type model of nonlinear acoustic oscillations in combustion chambers. Our adaptation criterion is Lyapunov-based. We focus on a two-mode model and develop a design based on an assumption that the amplitudes of the two modes are available for measurement. The adaptation mechanism is designed to stabilize both modes and prevent the phenomenon observed by Billoud et al. (1992) whose adaptive controller stabilizes the first but destabilizes the second mode. We also prove that the adaptation mechanism is robust to a time delay inherent to the actuation approach via heat release. We also develop an adaptation scheme which employs only one pressure sensor. Our approach is based on the idea to use the squares of the pressure and its derivative. Simulations illustrate the capability of the scheme to attenuate limit cycles without the knowledge of the growth coefficients