State-feedback control of longitudinal combustion instabilities

Active control of longitudinal pressure oscillations in combustion chambers has been studied theoretically by means of a digital state-feedback control technique. The formulation is based on a generalized wave equation that accommodates all influences of combustion, mean flow, unsteady motions, and control actions. Following a procedure equivalent to the Galerkin method, a system of ordinary differential equations governing the amplitude of each oscillatory mode is derived for the controller design. The control actions are provided by a finite number of point actuators, with instantaneous chamber conditions monitored by multiple sensors. Several important control aspects, including sampling period, locations of sensors and actuators, controllability, and observability, have been investigated systematically. As a specific example, the case involving two controlled and two residual (uncontrolled) modes is studied.