Factors that limit control effectiveness in self-excited noise driven combustors

This thesis considers what limits control effectiveness in self-excited, noise driven, combustors using a full Strouhal number thermo-acoustic model with the ultimate aim of learning how to design combustors to be responsive to feedback control of combustion instabilities. The inclusion of time delays in the volumetric heat release perturbation models create unique behavioral characteristics which are not properly reproduced within current low Strouhal number thermo-acoustic models used for feedback control. New analysis tools using probability density functions are introduced in this thesis which enable exact expressions for the statistics of a time delayed system. Additionally, preexisting tools from applied mathematics and control theory for spectral analysis of time delay systems are introduced to the combustion community. These new analysis tools can be used to extend sensitivity function analysis used in control theory to explain limits to control effectiveness in self-excited combustors. The control effectiveness of self-excited combustors with actuator constraints are found to be most sensitive to the location of non-minimum phase zeros. Modeling the non-minimum phase zeros correctly require accurate volumetric heat release perturbation models. Designs that removes non-minimum phase zeros are more likely to have poles in the right hand complex plane. As a result, unstable combustors are inherently more responsive to feedback control.