Boundary PI Feedback Stabilization of Combustion Oscillations in the Rijke Tube

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.