LMS algorithm for adaptive control of combustion oscillations

Self-excited oscillations of a ducted flame, bunting in the wake of a bluff-body flame-holder, are considered. The non-linear kinematic model used here to describe these oscillations calculates the influence of the velocity fluctuations on the shape of the flame surface, and hence on the heat release rate. It is easy and quick to vary parameters in our model, and therefore a theoretical and numerical adaptive control strategy is developed, aiming at eliminating the flame instabilities. The control is based on an IIR filter, its coefficients being optimised by the LMS algorithm Some system identification (SI) is necessary because the output of the adaptive filter does not interfere directly with the combustion oscillations, but only through a transfer function. Our control strategy, carried out with an on-line SI, gives very satisfactory results, and several new ideas are developed. Firstly it is shown that, in the LMS algorithm running the controller, a term, usually neglected without mathematical justification, must be included in the gradient estimate in order to suppress the oscillations. Secondly, a new LMS-based on-line SI procedure, using an additional random noise and global quantities available in an experiment, is described and tested successfully in our numerical simulation. Finally, an efficient method to overcome the IIR instability is implemented, and our controller proves successful at reducing the pressure oscillations both under varying operating conditions and in the presence of a background noise.