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

• 成果类型: Article
• 署名作者: Wilhelmsen, Nils Christian A.; Di Meglio, Florent
• 署名单位: Universite PSL; MINES ParisTech
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3392445
• 发表日期: 2024
• 页码: 7556-7571
• 关键词: Combustion; fires; observers; Ducts; Acoustics; Output feedback; oscillators; Backstepping; combustion; Control; coupled PDE-ODE; Distributed parameter systems; observer; thermoacoustic instabilities; time delays

摘要

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 x 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.