Experiments , Identification , and Modeling

APRIL 2015 « IEEE CONTROL SYSTEMS MAGAZINE 57 Digital Object Identifier 10.1109/MCS.2014.2384971 Date of publication: 17 March 2015 T he Rijke tube [1] is a classic experiment that is relatively simple and inexpensive to build in a typical university laboratory. Despite its construction simplicity, it can serve to illustrate a wide variety of mathematical modeling, empirical identification, verification, and feedback control techniques. As such, it is suitable for use in both advanced undergraduate and graduate control laboratory courses. The Rijke tube also serves as prototypical experiment for research and study of thermoacoustic phenomena in which heat transfer and acoustics are dynamically coupled. This experiment is perhaps the simplest illustration of the phenomenon of thermoacoustic instabilities, which typically occur whenever heat is released into gas in underdamped acoustic cavities. The heat release can be due to combustion or solid/ gas heat transfer. Under the right conditions, the coupling between the acoustic and heat release dynamics in the cavity becomes unstable. This instability manifests itself as a sustained limit cycle resulting in audible, powerful pressure oscillations. Thermoacoustic instability phenomena are most often encountered in combustors [2], [3], where the resulting powerful pressure waves are undesirable due to the danger of structural damage as well as performance degradations. In this context, they are often referred to as combustion instabilities and are notoriously difficult to model due to the additional complexity of combustion dynamics [4], [5]. One advantage of the Rijke tube is that it generates thermoacoustic instabilities without a combustion process. The absence of combustion renders the mathematical modeling EXPERIMENTS, IDENTIFICATION, AND MODELING