A Time-Delayed Lur’e Model with Biased Self-Excited Oscillations

Abstract

Self-excited systems arise in many applications, such as biochemical systems, mechanical systems with fluid-structure interaction, and fuel-driven systems with combustion dynamics. This paper presents a Lur'e model that exhibits biased selfexcited oscillations under constant inputs. The model involves 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 bias-generation mechanism is used to specify the mean of the oscillation. The main contribution of the paper is a detailed analysis of a discrete-time version of this model.

Identification of Self-Excited Systems Using Discrete-Time, Time-Delayed Lur'e Models

“…Theorem 3.6 thus extends Theorem 2 in [49] to the case where the nonlinearity is piecewise-C 1 (and thus not necessarily C 1 ) and the Jacobian of the closed-loop dynamics may be singular on a set of measure zero. Finally, Theorem 3.9 has no counterpart in [50], and thus the results in the present paper provide a substantial extension of [50].…”

Self-Excited Dynamics of Discrete-Time Lur'e Systems

“…The contribution of the present paper is to prove that this model structure yields self-excited oscillations for sufficiently large scalings of the asymptotically stable dynamics. A preliminary study of self-excited oscillations in a similar discrete-time Lur'e model was performed in [17]. However, the present paper goes far beyond [17] in breadth and depth of the analysis of these systems.…”

“…A preliminary study of self-excited oscillations in a similar discrete-time Lur'e model was performed in [17]. However, the present paper goes far beyond [17] in breadth and depth of the analysis of these systems.…”