Quenching oscillations in combustion instabilities using model-based closed-loop multiplicative control

Abstract

This papers deals with active control of combustion instabilities through measurement and feedback of pressure oscillations. The measurement is used to construct a multiplicative feedback control. The aim of such a control is to quench the oscillations associated with the instability associated with lean pre-mixed combustion. This quenching is analyzed using the Krylov-Bogoliubov approach applied to a tractable gray-box model of the underlying process and fitted using experimental data. A linear and a nonlinear feedback law are considered and conditions for quenching the oscillations established. Both give successful results verified by the simulation tests.

Analysis of Control Relevant Coupled Nonlinear Oscillatory Systems

“…The negative stiffness situation is encountered in inverted pendulum problem driven by vertical excitation [17], and the negative damping situation is encountered combustion instabilities models [7,4].…”

On the dynamics of flame images identified through computer vision and modal methods

“…A particular model from a second-order ordinary differential equation that combines heat released by the flame and acoustic pressure generated by the combustion process inside the chamber received special attention over the last decades [3][4][5][6][7][8][9][10][11][12]. It is important to notice that the works of Bouziani et al [8][9][10] and Landau et al [3] culminated in an analytically tractable model with a Van der Pol-based formulation that could explain the coexistence of two distinct nonharmonic frequencies that were observed experimentally. Although these researches have brought remarkable results on proposing a model that could explain the dynamics of the flame, it is valid only for a narrow band of equivalence ratio values and there are some difficulties related to obtaining model's parameters that still limit its application.…”

A Nonlinear Model for Combustion Instability: Analysis and Quenching of the Oscillations

“…Using (26), property (20) and notation (22), one arrives at (24). Result (24) yields the frequency set…”

“…Two types of control law can be considered, one linear the other nonlinear. The linear law need the availability of x 1 and x 2 which can be obtained by using appropriate band pass filters [20]. Here we are interested on the non-linear feedback which use the pressure measurement (p = x 1 + x 2 ), since it gives effective results and is subject to less constrains.…”