Limits of achievable performance of controlled combustion processes

This paper presents a fundamental limitations-based analysis to quantify limits on obtainable performance for active control of combustion (thermoacoustic) instability. Experimental data from combustor rigs and physics-based models are used to motivate the relevance of both the linear and nonlinear thermoacoustic models. For linear models, Bode integral-based analysis is used to explain peak-splitting observed in experiments. It is shown that large delay in the feedback loop and limited actuator bandwidth are the primary factors that limits the effectiveness of the active control. Explicit bounds on obtainable performance in the presence of delay, unstable dynamics, and limited controller bandwidth are obtained. A multi-input describing function framework is proposed to extend this analysis to the study of nonlinear models that also incorporate the effects of noise. The fundamental limitations are interpreted for a modified sensitivity function defined with respect to noise balance. The framework is applied to the analysis of linear thermoacoustic models with nonlinear ON-OFF actuators and Gaussian noise. The results of the analysis are well-supported by experiments and model simulations. In particular, we reproduce in model simulations and explain analytically the peak-splitting phenomenon observed in experiments.