MODEL BASED CONTROL OF NONLINEAR COMBUS- TION INSTABILITIES

Lean premixed combustion chambers are susceptible to combustion instabilities arising from the coupling between the heat release rate perturbations and the acoustic disturbances. These instabilities are generally harmful. Active feedback control can be used to interrupt the coupling between the acoustic waves and unsteady heat release and prevent or suppress instability. The design of most types of controller requires prior knowledge of how the combustor responds to actuation -the "open loop transfer function" (OLTF). This includes the flame response to oncoming flow disturbances, which becomes non-linear at larger amplitudes. Saturation of the heat release rate amplitude or a phase lag change relative to the acoustic pressure as the modulation level increases has been confirmed to occur experimentally in many cases. This may cause the dominant unstable frequency to change, which in turn alters the OLTF and makes the design of controller more complicated. A flame describing function model is proposed in this paper to account for the non-linearities of the heat release rate amplitude. This flame model is applied to a model combustor. The ν-gap metric is used to quantify the deviation of the set of OLTFs for different disturbance levels from the selected transfer function for the controller design. This provides us a bound on the minimum required "robustness stability margin" for an H ∞ loop shaping controller. Such a controller is synthesized, and it is confirmed that as long as the ν-gap is smaller than the stability margin, the robust controller is guaranteed to stabilize the combustor for all possible flame responses