Active Control of Combustion Instabilities with Distributed Actuators

A theoretical analysis of the active control of combustion instabilities with spatially distributed actuators is presented in this paper. The model simulates unsteady motions in a combustion chamber, with feedback control produced by the injection of secondary fuel into the chamber. The mass flow rate of the injected fuel is modulated by a proportional-plus-integral (PI) controller between the sensor and the fuel injector. The formulation is based on a generalized wave equation which accomodates all influences of combustion, mean flow, and acoustic oscillation on the system behavior. Control actions arising from the distributed combustion of the fuel are modeled by an assembly of point actuators; the power output of each acuator is determined by its position, the local burning characteristics of the fuel, and the time delay with respect to the instant of fuel injection. The analysis and design of both analog and digital PI controllers are presented. The stability of the system has been examined by means of the frequency-domain method developed by Nyiquist. In addition, a formulation is constructed to determine the eigenvalues of the closed-loop system in discrete time. Several aspects of the distributed control processes, including the relationships among time delays, actuator dimension, controller gains, and combustion response, are investigated systematically.