In this paper, a theoretical analysis and syntheses of a parametric controller for thermo-acoustic combustion instabilities in a liquid-fueled propulsion system is developed. A generalized wave equation describes the dynamic behavior of second order nonlinear oscillations. The control algorithm is developed based on the first two modes using the time-averaged simplification of the governing coupled nonlinear system equations. The closed loop control law design is based on finding an optimal phase angle such that the heat release produced by secondary oscillatory fuel injection is out of phase with the mode’s pressure oscillations, and on finding the limits on the controller gain, to ensure the system stability. Theses gains are then optimized using three different performance indices, namely, integral of the time absolute error, ITAE, integral of the absolute error, IAE, and finally, integral of square of the error, ISE. Simulations illustrate the proposed technique capability to effectively attenuate the unwanted oscillations.

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