It is well-known that phase-shifting controllers used for active combustion control must be manually adjusted in order to maintain control over a broad range of operating combustor operating conditions. If one assumes that the thermoacoustic instabilities are linearly stabilizable, then what is needed is a method to determine, and ultimately predict, the frequency response of the plant for any range of operating conditions, so the controller design can be automatically updated to track the changing plant gain/phase relationships that are observed with changing heat release. A unique test-based, design process has been proposed to predict the gain/phase characteristics required of a proportional, phase-shifting controller that can stabilize the thermoacoustic instabilities. In this paper, that process is used to automate the design of a fixed-gain feedback controller that limits the amplitudes of any feedback induced instabilities (to some pre-specified level) while providing the best control of the targeted limit cycling pressure oscillations.
The paper describes how a neural network was trained, using the suggested design process, to predict the frequency response of the thermoacoustics in a tube combustor at frequencies adjacent to the limit cycle frequency using certain operating conditions that included a sparsely-sampled temperature profile, total air/fuel flow rate, and equivalence ratio. The neural net training was performed using complex valued, open-loop frequency response function data as the desired signal with the previously mentioned operating conditions as the input signals. (The open loop data was collected for a narrow frequency range surrounding the limit cycle instability by performing a sine dwell at discrete frequencies). Once the neural network was trained, it was used to predict the approximate phase and gain margins as a function of temperature and flow conditions. The margins were then used to automatically update and design a fixed shape feedback controller having the proper phase and magnitude to ensure stability and control in the face of changing operating conditions. A companion paper describes the methodology that underlies the automated design of the feedback controller gain and phase delay.
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