Low-order nonlinear models of thermoacoustic instabilities and model-based control

We present three low order nonlinear models which depict limit-cycle behavior that is ubiquitous in thermoacoustic pressure oscillations. All three nonlinear models are shown to result in periodic solutions and exhibit trends similar to those observed in a bench-top combustor rig. We also analyze the behavior of a linear controller based on a model without the nonlinearities and discuss the conditions under which the controller can be successful in stabilizing the pressure despite the nonlinear mechanisms. Numerical simulations and experimental results are presented to support the nonlinear model as well as the linear controller.