Selfexcited systems arise in many applications, such as biochemical systems, mechanical systems with fluidstructure interaction, and fueldriven systems with combustion dynamics. This paper presents a Lur’e model that exhibits biased oscillations under constant inputs. The model involves arbitrary asymptotically stable linear dynamics, time delay, a washout filter, and a saturation nonlinearity. For all sufficiently large scalings of the loop transfer function, these components cause divergence under small signal levels and decay under large signal amplitudes, thus producing an oscillatory response. A biasgeneration mechanism is used to specify the mean of the oscillation. The main contribution of the paper is the presentation and analysis of a discretetime version of this model.
Identification of SelfExcited Systems Using DiscreteTime, TimeDelayed Lur’e Models
This paper considers system identification for
systems whose output is asymptotically periodic under constant
inputs. The model used for system identification is a discretetime
Lur’e model consisting of asymptotically stable linear
dynamics, a time delay, a washout filter, and a static nonlinear
feedback mapping. For sufficiently large scaling of the loop
transfer function, these components cause divergence under
small signal levels and decay under large signal amplitudes,
thus producing an asymptotically oscillatory output. A leastsquares
technique is used to estimate the coefficients of the
linear model as well as the parameters of a piecewiselinear
approximation of the feedback mapping.
 Award ID(s):
 1634709
 Publication Date:
 NSFPAR ID:
 10283703
 Journal Name:
 Proceedings of the American Control Conference
 Page Range or eLocationID:
 39293934
 ISSN:
 23785861
 Sponsoring Org:
 National Science Foundation
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