On the identification of a nonlinear function in a feedback loop

Many models of systems important in practice have the form of an interconnection of a known linear model and an unknown nonlinear function. One example of such a system is a model of thermoacoutic instability affecting gas turbine engines and rockets (so-called thermoacoustic feedback loop). In this paper, we propose a computationally attractive algorithm for identifying static nonlinearity in a thermoacoustic feedback loop which is either in a limit cycle or is being driven by Gaussian noise. The algorithm is based upon functional analytic treatment of the describing function method and lends itself nicely to a class of limit cycling or noise driven feedback systems where the nonlinearity is of a special type. We present examples as well as a simulations with the thermoacoustic feedback loop as an application of the identification algorithm.