Acoustic Boundary Output Feedback Stabilization of Dynamic $n-\tau$ Model Flame via Duct With Variable Cross Section

Nils Christian A. Wilhelmsen, Florent Di Meglio

Abstract: We propose an output feedback controller to stabilize thermoacoustic instabilities in a duct with variable cross section, by actuating and sensing the acoustic boundary opposite from the flame. A linear parametric state-space model, taking into account both time-delay effects from the classical $n-\tau$ model and low-pass filtering effects, models the flame subsystem. For the acoustics, a distributed model taking into account variations in the cross-sectional area along the duct is developed and written as a $2\times 2$ linear hyperbolic partial differential equation (PDE) system. Next, a full-state feedback control law is proposed, designed by first mapping the considered plant into a simplified partial differential equation - ordinary differential equation (PDE-ODE) cascade, for which control design is a solved problem. Subsequently, the observer is designed by mapping the estimation error dynamics directly into a stable target PDE-ODE cascade. Combining the full-state feedback control law and observer, we arrive at an output feedback controller. A simulation example to demonstrate the theory is presented, where the full-state feedback controller, observer, and output feedback controller are shown to stabilize and estimate the pressure, velocity, and heat release rate.

External IDs:doi:10.1109/tac.2024.3392445