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This article examines the degree to which optimizing a Rijke tube experiment can improve the accuracy of thermoacoustic model parameter estimation, thereby facilitating robust stability control. We use a one-dimensional thermoacoustic model to describe the combustion dynamics in a Rijke tube. This model contains two unknown parameters that relate velocity perturbations to heat release rate oscillations, namely, a time delay τ and amplification factor β. The parameters are estimated from experiments where the system input is the acoustic excitation from a loudspeaker and the output is the pressure response captured by a microphone. Our work is grounded in the insight that optimizing an experiment’s design for higher Fisher identifiability leads to more accurate parameter estimates. The novel goal of this paper is to apply this insight in the laboratory using a flame-driven Rijke tube setup. For comparison purposes, we conduct a benchmark experiment with a broadband chirp signal as the excitation input. Next, we excite the Rijke tube at two frequencies optimized for Fisher identifiability. Repeats of both experiments show that the optimal experiment achieves parameter estimates with uncertainties at least one order of magnitude smaller than the benchmark. With smaller parameter estimate uncertainties, an LQG controller designed to attenuate combustion instabilities is able to achieve stronger robustness guarantees, quantified in terms of closed-loop structured singular values that account for parameter estimation uncertainty. 

This paper investigates the effect of sensor placement on the observability and LQG control of a thermoacoustic model. This model describes combustion instability in a one-dimensional combustor, called a Rijke tube. The transfer function describing this model is transcendental because of the time delay terms in the heat release dynamics. We apply Pade approximation to achieve a finite-dimensional transfer function and truncate the system by neglecting states with low Hankel singular values. We then analyze the impact of the placement and number of sensors on the observability of each mode of the resulting reduced-order model. Next, we design an LQG controller for suppressing pressure oscillations in the simplified thermoacoustic system. We find that placing sensors near the model's pressure nodes slows down the rate at which LQG control attenuates pressure oscillations, increases the control effort required for this attenuation, and worsens the controller's robustness. 

This paper presents the design of a thermoacoustically unstable combustor experiment for identifiability. We examine the impact of sensor placement, flame location, and acoustic excitation frequency on the Fisher identifiability of a one-dimensional combustion stability model’s parameters.The model uses linear delay differential equations to describe both the acoustics and heat release dynamics in a laboratory combustor called a Rijke tube. We derive analytic expressions for the frequency-domain Fisher identifiability of the model’s parameters. This leads to two key insights. First, excitation frequency, flame location, and sensor placement all have a significant impact on parameter identifiability. Second, the optimal excitation frequencies for identifiability are not strong functions of sensor placement but change with flame location. Building on these insights, the paper concludes by using a genetic algorithm to optimize the design of a Rijke tube experiment for thermoacoustic model identifiability.