Boundary PI Feedback Stabilization of Combustion Oscillations in the Rijke Tube

TY - JOUR

T1 - Boundary PI Feedback Stabilization of Combustion Oscillations in the Rijke Tube

AU - Zhang, Yu Long

AU - Liu, Shaojie

AU - Wang, Zhaohui

AU - Wang, Jun Min

AU - Li, Donghai

AU - Zhu, Min

N1 - Publisher Copyright: © 1963-2012 IEEE.

PY - 2025/4

Y1 - 2025/4

N2 - In this article, we consider the stabilization of combustion oscillations in the Rijke tube, which is modeled by a linearized wave equation with heat release fluctuation ordinary differential equation (ODE) acting as a point source term. A boundary proportional-integral (PI) feedback controller is designed to suppress the combustion oscillations. The Nyquist criterion is applied to prove that eigenvalues of the operator of the close-loop system are all located on the left-hand side of the complex plane. The closed-loop system is proved to be exponentially stable by using the Riesz basis approach. Numerical simulations are presented to verify the effectiveness of the control design. Moreover, the experimental results are obtained in an experimental Rijke tube, which validates the effectiveness of the method.

AB - In this article, we consider the stabilization of combustion oscillations in the Rijke tube, which is modeled by a linearized wave equation with heat release fluctuation ordinary differential equation (ODE) acting as a point source term. A boundary proportional-integral (PI) feedback controller is designed to suppress the combustion oscillations. The Nyquist criterion is applied to prove that eigenvalues of the operator of the close-loop system are all located on the left-hand side of the complex plane. The closed-loop system is proved to be exponentially stable by using the Riesz basis approach. Numerical simulations are presented to verify the effectiveness of the control design. Moreover, the experimental results are obtained in an experimental Rijke tube, which validates the effectiveness of the method.

KW - Combustion oscillations

KW - partial differential equation

KW - proportional-integral (PI) control

KW - Rijke tube

UR - https://www.scopus.com/pages/publications/105001959993

U2 - 10.1109/TAC.2024.3486745

DO - 10.1109/TAC.2024.3486745

M3 - Article

AN - SCOPUS:105001959993

SN - 0018-9286

VL - 70

SP - 2568

EP - 2575

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 4

ER -