Delayed Feedback Control Laws for Rijke Tube Thermoacoustic Instability, Synthesis, and Experimental Validation.

We approach the thermoacoustic instability problem in Rijke tubes from a mathematically novel perspective. In this benchmark experimental setting, the complex dynamic exchange between the unsteady heat release and the acoustic pressure variations creates the instability. When linearized, this behavior leads to a neutral class time-delayed dynamics with multiple independent delays, where our major contribution arrives. We aim to synthesize a series of stabilizing feedback control strategies for this dynamics. A recent mathematical paradigm, called the cluster treatment of characteristic roots (CTCR), is used to facilitate this objective. This paradigm, in essence, declares the necessary and sufficient stability conditions in the space of the system and controller parameters. The main contributions of this brief are in the first-time deployment of CTCR in the syntheses of various feedback control laws and validating experiments.