Active control of nonlinear pressure oscillations in combustion chambers

A theoretical analysis of active control of nonlinear acoustic instabilities in combustion chambers is developed in this article. The formulation starts with a generalized wave equation that describes the dynamic behavior of second-order nonlinear oscillations with distributed feedback actions. Control inputs are provided by the burning of the injected secondary fuel in the chamber, with its instantaneous mass flow rate modulated by a proportional-plus-integral (PI) controller located between the pressure sensor and the fuel injection mechanism. Various nonlinear-stability characteristics, including the existence and stability of limit cycles, are studied analytically using the method of time averaging. In addition, an optimization procedure is developed for selecting controller gains.