Abstract
Lur’e systems are dynamical systems that are characterized by the feedback interconnection between a linear, time-invariant system and a feedback nonlinearity. Lur’e systems have been used to characterize the dynamics of several systems including gas turbine combustors and self-oscillatory systems. In this paper, we introduce an Identification algorithm for Lur’e systems with hysteretic feedback nonlinearities. We assume that the input to the Lur’e system is an unknown constant signal, and the linear dynamics have nonzero initial conditions. First, we use least squares with a transfer function model to identify the linear dynamics of the Lur’e system. Then, we use the identified linear dynamics along with the measured output to construct an estimate of the hysteretic nonlinearity. We show numerical examples to illustrate the proposed approach.
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