Experiments in Control and Anti-Control of Chaos in a Dry Friction Oscillator

2003 ◽  
Vol 9 (3-4) ◽  
pp. 387-397 ◽  
Author(s):  
Francis C. Moon ◽  
Anil J. Reddy ◽  
William T. Holmes
Keyword(s):  
Dry Friction ◽  
Normal Force ◽  
Control Method ◽  
Unstable Periodic Orbits ◽  
Mechanical Oscillator ◽  
Chaotic State ◽  
Control Of Chaos ◽  
Magnetic Actuator ◽  
Friction Oscillator ◽  
Proportional Feedback

We describe a mechanical oscillator with a dry friction nonlinearity and feedback control. It is shown to exhibit both control of chaos, i.e., the stabilization of unstable periodic orbits in a strange attractor, as well as anti-control of chaos. Anti-control of chaos is the use of feedback to drive a nonlinear system into a chaotic state near a periodic motion. The addition of noise or dither onto periodic oscillations can often be useful in engineering devices. The control and anti-control method is based on “ occasionally proportional feedback” developed by Hunt as an extension of the well-known OGY theory of the control of chaos. In this work, the control is effected by changing the normal force of the dry friction element using a magnetic actuator.

DELAYED FEEDBACK CONTROL OF CHAOTIC SYSTEMS WITH DRY FRICTION

2002 ◽  
Vol 12 (08) ◽  
pp. 1877-1883 ◽  
Author(s):  
UGO GALVANETTO
Keyword(s):  
Dry Friction ◽  
Chaotic Systems ◽  
Control Method ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Chaotic Attractors ◽  
Unstable Periodic Orbits ◽  
Numerical Techniques ◽  
The Stability ◽  
Time Delayed Feedback

This paper describes some numerical techniques to control unstable periodic orbits embedded in chaotic attractors of a particular discontinuous mechanical system. The control method is a continuous time delayed feedback that modifies the stability of the orbit but does not affect the orbit itself.

Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method

2015 ◽  
pp. 259-278 ◽  
Author(s):  
Hassène Gritli ◽  
Safya Belghith ◽  
Nahla Khraief
Keyword(s):  
Fixed Point ◽  
Poincaré Map ◽  
Control Method ◽  
Poincare Map ◽  
Mechanical Oscillator ◽  
Control Of Chaos ◽  
Impact Oscillator ◽  
Control Approach ◽  
Rigid Constraint ◽  
The Impact

This chapter deals with the control of chaos exhibited in the behavior of a one-degree-of-freedom impact mechanical oscillator with a single rigid constraint. The mathematical model of such impact oscillator is represented by an impulsive hybrid linear non-autonomous dynamics. The proposed control approach is based chiefly on the OGY method. First, an analytical expression of a constrained controlled Poincaré map is derived. Secondly, the linearized controlled Poincaré map around the fixed point of the constrained map is determined. Relying on the linearized map, a state feedback controller is designed. It is shown that the proposed control strategy is efficient for the control of chaos for the desired fixed point and for the fixed parameter. It is shown also that, by changing the system parameter, the behavior of the impact mechanical oscillator changes radically. Thus, the drawback of the developed OGY control method is revealed and some remedies are given.

Non-reversible dry friction oscillator: Design and measurements

1999 ◽  
Vol 213 (5) ◽  
pp. 527-534 ◽  
Author(s):  
M Wiercigroch ◽  
V. W. T. Sin ◽  
Z. F. K. Liew
Keyword(s):  
Dry Friction ◽  
Normal Force ◽  
Calibration Procedure ◽  
Friction Characteristics ◽  
Design Choice ◽  
Wide Range ◽  
Friction Oscillator ◽  
Set Up ◽  
Clamping Device ◽  
The Mathematical Model

A Coulomb oscillator with a variable normal force has been designed and manufactured to carry out a wide range of experimental dynamic analysis, especially the study of the non-reversibility of dry friction characteristics. The design choice was based on the criteria of accuracy of the mathematical model and flexibility in terms of parameter changes such as the natural frequency of the system, coefficient of friction and normal force. The system consists of a block mass attached to two coil springs and a dry frictional damper in which the friction force is varied by a pneumatic actuator. This allows a constant pressure between sliding surfaces to be maintained. The experimental set-up, the calibration procedure for the clamping device and typical results are presented. Experimental non-reversible dry friction characteristics are discussed.

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

Two-Frequency Oscillation With Combined Coulomb and Viscous Frictions

2002 ◽  
Vol 124 (4) ◽  
pp. 537-544 ◽  
Author(s):  
Gong Cheng ◽  
Jean W. Zu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Single Frequency ◽  
Friction Oscillator ◽  
One Stop ◽  
Frequency Excitation ◽  
Stop Motion ◽  
The One ◽  
Coulomb Dry Friction ◽  
Mass Spring

In this paper, a mass-spring-friction oscillator subjected to two harmonic disturbing forces with different frequencies is studied for the first time. The friction in the system has combined Coulomb dry friction and viscous damping. Two kinds of steady-state vibrations of the system—non-stop and one-stop motions—are considered. The existence conditions for each steady-state motion are provided. Using analytical analysis, the steady-state responses are derived for the two-frequency oscillating system undergoing both the non-stop and one-stop motions. The focus of the paper is to study the influence of the Coulomb dry friction in combination with the two frequency excitations on the dynamic behavior of the system. From the numerical simulations, it is found that near the resonance, the dynamic response due to the two-frequency excitation demonstrates characteristics significantly different from those due to a single frequency excitation. Furthermore, the one-stop motion demonstrates peculiar characteristics, different from those in the non-stop motion.

ZERO-CROSS INSTANTANEOUS STATE SETTING FOR CONTROL OF A BIFURCATING H-BRIDGE INVERTER

2007 ◽  
Vol 17 (10) ◽  
pp. 3571-3575 ◽  
Author(s):  
SATOSHI AKATSU ◽  
HIROYUKI TORIKAI ◽  
TOSHIMICHI SAITO
Keyword(s):  
Pulse Width Modulation ◽  
Control Method ◽  
Period Doubling ◽  
Current Mode ◽  
Nonlinear Phenomena ◽  
Unstable Periodic Orbits ◽  
Bifurcation And Chaos ◽  
Zero Crossing ◽  
Modulation Signal ◽  
A Current

This paper studies stabilization of low-period unstable periodic orbits (UPOs) in a simplified model of a current mode H-bridge inverter. The switching of the inverter is controlled by pulse-width modulation signal depending on the sampled inductor current. The inverter can exhibit rich nonlinear phenomena including period doubling bifurcation and chaos. Our control method is realized by instantaneous opening of inductor at a zero-crossing moment of an objective UPO and can stabilize the UPO instantaneously as far as the UPO crosses zero in principle. Typical system operations can be confirmed by numerical experiments.

scholarly journals Detecting and stabilizing periodic orbits of chaotic Henon map through predictive control

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu
Keyword(s):  
Periodic Orbits ◽  
Predictive Control ◽  
Nonnegative Integer ◽  
Strange Attractor ◽  
Discrete System ◽  
Control Method ◽  
Nonlinear Mapping ◽  
Unstable Periodic Orbits ◽  
Hénon Map ◽  
Henon Map

The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.

EXPERIMENTAL VERIFICATION OF PYRAGAS’S CHAOS CONTROL METHOD APPLIED TO CHUA’S CIRCUIT

1994 ◽  
Vol 04 (06) ◽  
pp. 1703-1706 ◽  
Author(s):  
P. CELKA
Keyword(s):  
Periodic Orbits ◽  
Experimental Verification ◽  
Chaos Control ◽  
Control Method ◽  
Experimental Results ◽  
Experimental Setup ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit

We have built an experimental setup to apply Pyragas’s [1992, 1993] control method in order to stabilize unstable periodic orbits (UPO) in Chua’s circuit. We have been able to control low period UPO embedded in the double scroll attractor. However, experimental results show that the control method is useful under some restrictions we will discuss.

CONTROL OF n-SCROLL CHUA'S CIRCUIT

2009 ◽  
Vol 19 (11) ◽  
pp. 3813-3822 ◽  
Author(s):  
ABDELKRIM BOUKABOU ◽  
BILEL SAYOUD ◽  
HAMZA BOUMAIZA ◽  
NOURA MANSOURI
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Predictive Control ◽  
Control Method ◽  
Sufficient Conditions ◽  
Chua’S Circuit ◽  
Unstable Periodic Orbits ◽  
Chua's Circuit ◽  
Necessary And Sufficient

This paper addresses the control of unstable fixed points and unstable periodic orbits of the n-scroll Chua's circuit. In a first step, we give necessary and sufficient conditions for exponential stabilization of unstable fixed points by the proposed predictive control method. In addition, we show how a chaotic system with multiple unstable periodic orbits can be stabilized by taking the system dynamics from one UPO to another. Control performances of these approaches are demonstrated by numerical simulations.

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