Feedback control of combustion instabilities from within limit cycle oscillations using H-infinity loop-shaping and the nu-gap metric

摘要

Combustion instabilities arise due to a two-way coupling between acoustic waves and unsteady heat release. Oscillation amplitudes successively grow, until nonlinear effects cause saturation into limit cycle oscillations. Feedback control, in which an actuator modifies some combustor input in response to a sensor measurement, can suppress combustion instabilities. Linear feedback controllers are typically designed using linear combustor models. However, when activated from within limit cycle, the linear model is invalid and such controllers are not guaranteed to stabilise. This work develops a feedback control strategy guaranteed to stabilise from within limit cycle oscillations. A low order model of a simple combustor, exhibiting the essential features of more complex systems, is presented. Linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame. The latter is determined numerically using a level set approach. Its implication is that the open loop transfer function (OLTF) needed for controller design varies with oscillation level. The difference between the mean and the rest of OLTFs is characterised using the ν-gap metric, providing the minimum required “robustness margin” for an H∞ loop-shaping controller. Such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations.