System Identi cation for Limit Cycling Systems : A Case Study forCombustion Instabilities

This paper presents a case study in system identiication for limit cycling systems. The focus of the paper is on (a) the use of a model structure derived from physical considerations and (b) the use of algorithms for the identiication of component subsystems of this model structure. The physical process used in this case study is that of a reduced order model for combustion instabilities for lean premixed systems. The identiication techniques applied in this paper are the use of linear system identiication tools (prediction error methods), time delay estimation (based on Kalman lter harmonic estimation methods) and qualitative validation of model properties using harmonic balance and describing function methods. The novelty of the paper, apart from its practical application, is that closed loop limit cycle data is used together with a priori process structural knowledge to identify both linear dynamic forward and nonlinear feedback paths. Future work will address the reenement of the process presented in this paper, the use of alternative algorithms and also the use of control approaches for the validated model structure obtained from this paper.

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