Ламинарный хаос в связанных системах с запаздыванием

The possibility of the existence of laminar chaos in coupled time-delayed feedback systems is investigated. The cases of unidirectional and mutual coupling of time-delay systems are considered. It is shown for the first time that laminar chaos can exist not only in a system with a variable delay time, but also in a system with a constant delay time, if it is coupled with a system in the regime of laminar chaos.

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Introduction

Delay-Adaptive Linear Control ◽

10.23943/princeton/9780691202549.003.0001 ◽

2020 ◽

pp. 1-16

Author(s):

Yang Zhu ◽

Miroslav Krstic

Keyword(s):

Time Delay ◽

Linear Time ◽

Delay Systems ◽

Engineering Practice ◽

Time Delay Systems ◽

Feedback Systems ◽

Deviating Argument ◽

Linear Time Invariant ◽

Feedback Laws ◽

Input Delays

This introductory chapter provides an overview of time-delay systems. Time-delay systems, also called systems with after-effect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations, are ubiquitous in practice. Some representative examples are found in chemical industry, electrical and mechanical engineering, biomedical engineering, and management and traffic science. The most common forms of time delay in dynamic phenomena that arise in engineering practice are actuator and sensor delays. Due to the time it takes to receive the information needed for decision-making, to compute control decisions, and to execute these decisions, feedback systems often operate in the presence of delays. The chapter then illustrates the possible methods in control of time-delay systems. This book develops adaptive and robust predictor feedback laws for the compensation of the five uncertainties for general linear time-invariant (LTI) systems with input delays.

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Ламинарный хаос в генераторе с запаздывающей обратной связью

Письма в журнал технической физики ◽

10.21883/pjtf.2020.09.49366.18218 ◽

2020 ◽

Vol 46 (9) ◽

pp. 16

Author(s):

Д.Д. Кульминский ◽

В.И. Пономаренко ◽

М.Д. Прохоров

Keyword(s):

Delay Time ◽

Nonlinear Function ◽

Harmonic Signal ◽

Delayed Feedback ◽

Radio Engineering ◽

First Time ◽

Time Delayed Feedback

For the first time, the phenomenon of laminar chaos is experimentally studied in a radio engineering generator with time-delayed feedback, the delay time of which is modulated by an external harmonic signal. Regions of various regimes of laminar chaos are constructed on the plane of the parameters of modulating signal. The nonlinear function of generator is reconstructed in the regime of laminar chaos.

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Comparison of TDC Circuit Design Method to Constant Delay Time

Journal of information and communication convergence engineering ◽

10.6109/jicce.2010.8.4.461 ◽

2010 ◽

Vol 8 (4) ◽

pp. 461-465

Author(s):

Jin-Ho Choi

Keyword(s):

Circuit Design ◽

Delay Time ◽

Design Method ◽

Constant Delay ◽

Constant Delay Time

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Stability and Performance of First-Order Linear Time-Delay Feedback Systems: An Eigenvalue Approach

Journal of Control Science and Engineering ◽

10.1155/2011/719730 ◽

2011 ◽

Vol 2011 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Shu-An He ◽

I-Kong Fong

Keyword(s):

Time Delay ◽

Linear Time ◽

Delay System ◽

Feedback Stabilization ◽

Delay Systems ◽

Lambert Function ◽

Time Delay Systems ◽

Feedback Systems ◽

Order Linear ◽

First Order

Linear time-delay systems with transcendental characteristic equations have infinitely many eigenvalues which are generally hard to compute completely. However, the spectrum of first-order linear time-delay systems can be analyzed with the Lambert function. This paper studies the stability and state feedback stabilization of first-order linear time-delay system in detail via the Lambert function. The main issues concerned are the rightmost eigenvalue locations, stability robustness with respect to delay time, and the response performance of the closed-loop system. Examples and simulations are presented to illustrate the analysis results.

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