Identification of nonlinear feedback systems operating in a limit cycle

Physical processes which exhibit complex nonlinear dynamics, such as limit cycles, require careful modeling and identification. Nonlinear system identification may be the crucial initial step towards solving a signal processing or control problem. This thesis is concerned with identification of closed loop systems with forward linear dynamics and static nonlinear feedback operating in a limit cycle.;The problems of estimating the linear and nonlinear elements are treated separately. The work begins with a formulation of the problem of identifying a feedback nonlinearity from output data and from an estimate of the forward linear system for applications where feedback signals are not available. We find sufficient conditions, in terms of the estimation error, for recovery of the stable limit cycle property as well as reproduction of frequency and harmonic content of the data. We then propose the Harmonic Balance Nonlinearity Identification algorithm (HB-NID) for estimation of feedback nonlinearities for this problem, and show that it meets these objectives in the presence of mild non-idealities.;Next, Prediction Error Methods (PEM) are considered for identification of the linear dynamics from output and feedback perturbed limit cycle data. The measured signals are shown to satisfy a quasistationary property. This fact is used to prove that PEM are both convergent and consistent.;A case study on identification of nonlinear dynamics of a combustion chamber displaying pressure instabilities concludes the work. HB-NID and PEM are applied to experimental data to identify linear and nonlinear elements from a bulk mode, closed-loop model for a combustion chamber.