Delayed Feedback Control of Chaos in an Electronic Double-Scroll Oscillator

1994 ◽  
Vol 49 (9) ◽  
pp. 843-846 ◽  
Author(s):  
A. Kittel ◽  
J. Parisi ◽  
K. Pyragas ◽  
R. Richter
Keyword(s):  
Feedback Control ◽  
Delay Time ◽  
Output Signal ◽  
Chaos Control ◽  
Electronic Circuit ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Control Of Chaos ◽  
The Difference

Abstract We present experimental results on stabilizing unstable periodic orbits of an autonomous chaos oscillator based on a simple electronic circuit. Control is achieved by applying the difference between the actual and a delayed output signal of the oscillator. The quality of chaos control can be measured via the strength of perturbation. The dependence on the delay time shows a characteristic resonance-type behavior.

Delayed feedback control of chaos by self-adapted delay time

1995 ◽  
Vol 198 (5-6) ◽  
pp. 433-436 ◽  
Author(s):  
A. Kittel ◽  
J. Parisi ◽  
K. Pyragas
Keyword(s):  
Feedback Control ◽  
Delay Time ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Control Of Chaos

Delayed feedback control of chaos

2006 ◽  
Vol 364 (1846) ◽  
pp. 2309-2334 ◽  
Author(s):  
Kestutis Pyragas
Keyword(s):  
Feedback Control ◽  
Feedback Loop ◽  
Theoretical Models ◽  
Practical Method ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Control Of Chaos ◽  
Current State ◽  
Time Delayed Feedback

Time-delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The method is based on applying feedback perturbation proportional to the deviation of the current state of the system from its state one period in the past, so that the control signal vanishes when the stabilization of the target orbit is attained. A brief review on experimental implementations, applications for theoretical models and most important modifications of the method is presented. Recent advancements in the theory, as well as an idea of using an unstable degree of freedom in a feedback loop to avoid a well-known topological limitation of the method, are described in detail.

scholarly journals Tunable Real Space Transfer Oscillator by Delayed Feedback Control of Chaos

1995 ◽  
Vol 50 (2-3) ◽  
pp. 117-124 ◽  
Author(s):  
D. P. Cooper ◽  
E. Schöll
Keyword(s):  
Delay Time ◽  
Chaotic Attractor ◽  
Real Space ◽  
Small Time ◽  
Delayed Feedback ◽  
Self Control ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Control Of Chaos ◽  
Real Space Transfer

Abstract It is demonstrated numerically that by using Pyragas' method of chaos self-control a stable semiconductor oscillator can be designed based on driven real-space transfer oscillations in a modulation-doped heterostructure. By application of a small time-continuous delayed feedback voltage control signal, different unstable periodic orbits embedded in the chaotic attractor can be stabilized. Thus different modes of self-generated periodic voltage oscillations can be selected by choosing an appropriate delay time. This provides tunability to different discrete frequencies.

Chaos Control in Single Mode Approximation of T-AFM Systems Using Nonlinear Delayed Feedback Based on Sliding Mode Control

2007 ◽  
Author(s):  
Hoda Sadeghian ◽  
Mehdi Tabe Arjmand ◽  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Feedback Control ◽  
High Performance ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Single Mode ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Model Parameters ◽  
Unstable Periodic Orbits ◽  
Single Mode Approximation

The taping mode Atomic Force Microscopic (T-AFM) can be properly described by a sinusoidal excitation of its base and nonlinear potential interaction with sample. Thus the cantilever may cause chaotic behavior which decreases the performance of the sample topography. In this paper a nonlinear delayed feedback control is proposed to control chaos in a single mode approximation of a T-AFM system. Assuming model parameters uncertainties, the first order Unstable Periodic Orbits (UPOs) of the system is stabilized using the sliding nonlinear delayed feedback control. The effectiveness of the presented methods is numerically verified and the results show the high performance of the controller.

BIFURCATION CONTROL OF A PARAMETRIC PENDULUM

2012 ◽  
Vol 22 (05) ◽  
pp. 1250111 ◽  
Author(s):  
ALINE S. DE PAULA ◽  
MARCELO A. SAVI ◽  
MARIAN WIERCIGROCH ◽  
EKATERINA PAVLOVSKAIA
Keyword(s):  
Chaos Control ◽  
Control Method ◽  
Excitation Frequency ◽  
Period Doubling ◽  
Bifurcation Control ◽  
Period Doubling Bifurcation ◽  
Delayed Feedback Control ◽  
Unstable Periodic Orbits ◽  
Parametric Pendulum ◽  
Feedback Control Method

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

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