Impact of Sensor Placement on Mode Observability and LQG Control of a Thermoacoustic System

Abstract

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 Padé 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.