A Discrete-Time, Time-Delayed Lur'e Model with Biased Self-Excited Oscillations

TL;DR

This paper analyzes a discrete-time Lur'e model with time delay and bias, demonstrating how it produces biased self-excited oscillations through a detailed stability and divergence analysis.

Contribution

It provides a novel detailed analysis of a discrete-time Lur'e model exhibiting biased self-excited oscillations with time delay and saturation nonlinearities.

Findings

Oscillations occur under certain large loop transfer scalings.

Small signals lead to divergence, large signals cause decay.

Bias mechanism sets the oscillation mean.

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 self-excited 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.