This study presents an intersection of two seemingly separate areas of research frontiers, “prediction and control of thermoacoustic instability” and “stability analysis of neutral-class linear-time-invariant (LTI) and time-delayed systems (TDS)”. The former is a coveted capability which has been elusive to the scientific community over 1½ centuries. Analytical capabilities have been limited due to the complex physics invoking the “combustion” phenomenon. Most available results rely on accumulated empirical knowledge. In this paper we consider a benchmark combustion test platform, which is known as Rijke’s tube. Its representation is simplified to an LTI neutral TDS, stability of which is assessed using a recent mathematical paradigm called the Cluster Treatment of Characteristic Roots (CTCR). CTCR provides a unique non-conservative and exhaustive stability declaration for a Rijke’s tube within the space of its parameters, naturally, under some simplifying assumptions. For those operating conditions which induce instability, we also propose a conventional and simple control strategy which can recover stability. This method is also analyzed using the CTCR paradigm for the first time.
- Dynamic Systems and Control Division
Stability and Control of a Thermoacoustic Device: The Rijke’s Tube
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Olgac, N, Zalluhoglu, U, & Kammer, AS. "Stability and Control of a Thermoacoustic Device: The Rijke’s Tube." Proceedings of the ASME 2014 Dynamic Systems and Control Conference. Volume 2: Dynamic Modeling and Diagnostics in Biomedical Systems; Dynamics and Control of Wind Energy Systems; Vehicle Energy Management Optimization; Energy Storage, Optimization; Transportation and Grid Applications; Estimation and Identification Methods, Tracking, Detection, Alternative Propulsion Systems; Ground and Space Vehicle Dynamics; Intelligent Transportation Systems and Control; Energy Harvesting; Modeling and Control for Thermo-Fluid Applications, IC Engines, Manufacturing. San Antonio, Texas, USA. October 22–24, 2014. V002T33A001. ASME. https://doi.org/10.1115/DSCC2014-5888
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