Linear theory of active control of pressure oscillations in combustion chambers

Active control of longitudinal pressure oscillations in combustion chambers has been studied theoretically using a digital state-feedback control technique. The formulation is based on a generalized wave equation which accommodates various influences on combustion, mean flow, unsteady motions, and contol actions. After a procedure equivalent to the Galerkin method, a system of ordinary differential equation governing the amplitude of each oscillatory mode is derived, serving as a basis for the controller design. The control actions is provided by a finite number of point acutators, with the instantaneous chamber conditions monitored by a few sensors. Several important control aspects such as sampling period, locations of sensors and controllers, controllability and observabi1ity have been investigated. As a specific example, the case involving two controlled and two residual (uncontrolled) modes is studied. The control and observation spillover phenomena due to the residual modes are clearly demonstrated.