Boundary control of a Rijke Tube using irrational transfer functions with experimental validation

Abstract

This paper is concerned with boundary stabilization of thermoacoustic oscillations in the Rijke tube. This system consists of a vertical tube open in both ends and a heater placed in the lower half of the tube. A speaker placed under the tube is used as actuator while a microphone placed near the top of the tube provides the pressure measurement. To study this problem we consider that the mathematical model takes the form of two interconnected compartments: one for the cold zone and other for the hot zone. The control input is applied on the left boundary condition of the cold zone. From this model we derive an irrational transfer function to design a stabilizing boundary control in the frequency domain. In particular, we derive necessary and sufficient conditions for the input-output stability through the use of Nyquist-type test. Experimental results show the effectiveness and real-life applicability of the method.