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.