Boundary Feedback Control of Unstable thermoacoustic Oscillations in the Rijke Tube

The problem of boundary stabilization of thermoacoustic oscillations is investigated. The Rijke tube is used as prototype system to study such phenomena. We consider that this system is modelled as a 2 x 2 linear first-order hyperbolic system that behaves like a wave equation with the control variable at one boundary condition. Our control approach is based on employing characteristic coordinates to convert the system into a system of two delay elements. Analysing the periodicity of the solution of these equations a discrete transfer function is obtained. This enable us to employ a discrete time domain control design to guarantee the exponential stability of the closed-loop system. The performance of the controller is evaluated through simulation results.