Abstract
Abstract This paper proposes an observer for the electrically heated vertical Rijke tube, using a model capable of inciting thermoacoustic instabilities. The model consists of linear, distributed acoustics coupled with nonlinear, lumped heat release. Using a boundary pressure measurement taken at the bottom end of the tube, the observer is designed by copying the system model and reconstructing both the bottom and top boundary conditions, the former exactly and the latter with an error that is shown to be converge to zero exponentially. It is proven that the observer produces state estimates that converge to their correct values asymptotically. Furthermore, it is shown the state estimation errors stay bounded when there is a modelling error in the boundary acoustic impedance. The proposed observer is simulated and compared to two alternative observers.
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