Am. Annaswamy et al., IMPACT OF LINEAR COUPLING ON THE DESIGN OF ACTIVE CONTROLLERS FOR THETHERMOACOUSTIC INSTABILITY, Combustion science and technology, 128(1-6), 1997, pp. 131-180
Analysis of combustion instability has traditionally been based on the
assumption that linear coupling among acoustic modes is insignificant
. While this is reasonable when one is interested in determining the u
nstable mode frequency and growth rate, in this paper we show that thi
s assumption in a model-based active control design may lead to seriou
s errors. To explain the origin of these errors, we employ both analys
is and numerical examples to investigate the effect of linear coupling
on the resonance and antiresonance properties of a benchtop premixed
combustor in the presence of external excitation. The analysis is carr
ied our using one-dimensional flow dynamics in the presence of an osci
llating heat release source based on laminar premixed flame kinematics
, and an external actuator in the form of a loudspeaker. We show that,
for certain sensor-actuator configurations, a controller designed on
the basis of a model where linear coupling is neglected may fail to su
ppress the thermoacoustic instability when coupling is present. In the
se cases, we find that the uncoupled model fails to predict the antire
sonance damping in the system accurately and is therefore incapable of
quantifying the system response to external excitation.