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Active control of longitudinal pressure oscillations in a combustion chamber is studied theoretically by means of a low order model obtained by systematic reduction from a complete representation. The formulation is based on the derivation of a generalized wave equation that accommodates the effects of mean flow, combustion, noise and control action. By using spatial averaging, the equations describing the dynamics of the chamber are reduced to a set of coupled ordinary differential equations, representing the motions of a system of coupled oscillators. The form of the resulting equations is particularly convenient for model reduction and for introducing feedback control terms, while retaining all physical processes. The oscillator equations are then rewritten in state-space form. Simulations are carried out to investigate in a unified fashion various aspects of the problem. These include the influences of noise, parameter uncertainties, unmodeled modes and a single timedelay. A criterion is derived that guarantees stability of the controlled closed-loop system in the presence of those quantities. The particular controller used here is based on a standard LQR design, but any design technique can be used as long as the stability criterion is fulfilled.

Active feedback control of combustor dynamics with time delay and noise