Modelling a combustion chamber acting as a Helmholtz Resonator using the two-microphones-method and design of a LQR

In this paper we introduce a novel approach to combine the Helmholtz Resonator (HR) transfer function with the well-defined two-port element method by modifying the model of a gas turbine combustor at the intersection between the combustion chamber and the exhausting outlet. Using the Two-Microphones-Method (TMM), the transfer function of the actuator is identified experimentally and incorporated into the acoustic model. The measured frequency response of the real plant confirms that the model predicts the acoustic modes of the duct and the stability of the resonance mode in case of cold flow and in case of combustion, respectively. Finally, an appropriate LQR is designed and implemented, which stabilizes the system in the unstable operating range both in the simulations and experiment.