scholarly journals Nonlinear Dynamics and Suppressing Chaos in Magnetic Bearing System

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shun-Chang Chang
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Behavior ◽  
Magnetic Bearing ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Frequency Spectra ◽  
Loop Control ◽  
Identification Technique ◽  
Bearing System

A nonlinear mathematical model of a magnetic bearing system has been obtained by applying a modified conventional identification technique based on the principle of harmonic balance. In this study, we examined the rich nonlinear dynamics of a magnetic bearing system with closed-loop control using phase portraits, Poincaré maps, and frequency spectra. The resulting bifurcation diagram can be used to evaluate the operational range of systems employing nonlinear actuators. Estimates of the largest Lyapunov exponent based on the properties of synchronization revealed the occurrence of chatter vibration indicative of chaotic motion. Various control methods, such as the state feedback control and the injection of dither signals, were then used to quench the chaotic behavior.

scholarly journals Study on Nonlinear Dynamics and Chaos Suppression of Active Magnetic Bearing Systems Based on Synchronization

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Shun-Chang Chang
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Behavior ◽  
Nonlinear Dynamic Analysis ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Frequency Spectra ◽  
Control Approach ◽  
Chaos Suppression

This study employed a variety of nonlinear dynamic analysis techniques to explore the complex phenomena associated with a nonlinear mathematical model of an active magnetic bearing (AMB) system. The aim was to develop a method with which to assume control over chaotic behavior. The bifurcation diagram comprehensively explicates rich nonlinear dynamics over a range of parameter values. In this study, we examined the complex nonlinear behaviors of AMB systems using phase portraits, Poincaré maps, and frequency spectra. Furthermore, estimates of the largest Lyapunov exponent based on the properties of synchronization confirmed the occurrence of chatter vibration indicative of chaotic motion. Thus, the proposed continuous feedback control approach based on synchronization characteristics eliminates chaotic oscillations. Finally, some simulation results demonstrated the feasibility and efficiency of the proposed control scheme.

scholarly journals Stability, Chaos Detection, and Quenching Chaos in the Swing Equation System

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shun-Chang Chang
Keyword(s):  
Power Systems ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Equation System ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Frequency Spectra ◽  
Chaos Detection ◽  
The Rich

The main objective of this study is to explore the complex nonlinear dynamics and chaos control in power systems. The rich dynamics of power systems were observed over a range of parameter values in the bifurcation diagram. Also, a variety of periodic solutions and nonlinear phenomena could be expressed using various numerical skills, such as time responses, phase portraits, Poincaré maps, and frequency spectra. They have also shown that power systems can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. In this study, the Lyapunov exponent and Lyapunov dimension were employed to identify the onset of chaotic motion. Also, state feedback control and dither signal control were applied to quench the chaotic behavior of power systems. Some simulation results were shown to demonstrate the effectiveness of these proposed control approaches.

Destabilization of Forward Rub in Rotor Magnetic Bearing Systems Using Actively Controlled Auxiliary Bearings

2010 ◽  
Author(s):  
Iain S. Cade ◽  
M. Necip Sahinkaya ◽  
Clifford R. Burrows ◽  
Patrick S. Keogh
Keyword(s):  
Design Feature ◽  
Magnetic Bearing ◽  
Open Loop ◽  
Active Magnetic Bearing ◽  
Loop Control ◽  
Bending Mode ◽  
Operating Limits ◽  
Auxiliary Bearing ◽  
Contact Free ◽  
Bearing System

During fault conditions, rotor displacements in magnetic bearing systems may potentially exceed safety/operating limits. Hence it is a common design feature to incorporate auxiliary bearings adjacent to the magnetic bearings for the prevention of rotor/stator contact. During fault conditions the rotor may come into contact with the auxiliary bearings, which may lead to continuous rub type orbit responses. In particular, forward rub responses may become persistent. This paper advances the methodology by considering an actively controlled auxiliary bearing system. An open-loop control strategy is adopted to provide auxiliary bearing displacements that destabilize established forward rub orbit responses. A theoretical approach is undertaken to identify auxiliary bearing motion limits at which forward rub responses become unstable. Experimental validation is then undertaken using a rotor/active magnetic bearing system with an actively controlled auxiliary bearing system under piezoelectric actuation. Two different operating speeds below the first bending mode of the rotor are considered and the applied harmonic displacements of the auxiliary bearing are shown to be effective in restoring contact free levitation.

scholarly journals Stability, Bifurcation, and Quenching Chaos of a Vehicle Suspension System

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Chun-Cheng Chen ◽  
Shun-Chang Chang
Keyword(s):  
Chaotic Motion ◽  
Control Method ◽  
Homoclinic Orbits ◽  
Suspension System ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Frequency Spectra ◽  
The Road ◽  
Dynamics And Control ◽  
Vehicle Suspension System

This study investigated the dynamics and control of a nonlinear suspension system using a quarter-car model that is forced by the road profile. Bifurcation analysis used to characterize nonlinear dynamic behavior revealed codimension-two bifurcation and homoclinic orbits. The nonlinear dynamics were determined using bifurcation diagrams, phase portraits, Poincaré maps, frequency spectra, and Lyapunov exponents. The Lyapunov exponent was used to identify the onset of chaotic motion. Finally, state feedback control was used to prevent chaotic motion. The effectiveness of the proposed control method was determined via numerical simulations.

Nonlinear dynamics and chaos

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Chaotic Behavior ◽  
Phase Portraits ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Kam Theorem ◽  
Physical Systems ◽  
Nonlinear Dynamics And Chaos ◽  
Iterative Maps

Simple maps and dynamical systems are used to explore chaos in nature. The discussion starts with a review of the properties of nonlinear ordinary differential equations, including the useful concepts of phase portraits, fixed points, and limit cycles. These notions are developed further in an examination of iterative maps that reveal chaotic behavior. Next, the damped driven oscillator is used to illustrate the Lyapunov exponent that can be used to quantify chaos. The famous KAM theorem on the conditions under which chaotic behavior occurs in physical systems is also presented. The principle is illustrated with the Hénon-Heiles model of a star in a galactic environment and billiard models that describe the motion of balls in closed two-dimensional regions.

Detecting Parameter Changes Using Experimental Nonlinear Dynamics and Chaos

1996 ◽  
Vol 118 (3) ◽  
pp. 375-383 ◽  
Author(s):  
R. S. Chancellor ◽  
R. M. Alexander ◽  
S. T. Noah
Keyword(s):  
Nonlinear Dynamics ◽  
Periodic Orbits ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
Unstable Periodic Orbits ◽  
Bifurcation Diagrams ◽  
Frequency Spectra ◽  
Nonlinear Dynamics And Chaos ◽  
Chaotic Nature ◽  
Parameter Values

A method of detecting parameter changes using analytical and experimental nonlinear dynamics and chaos is applied to a piecewise-linear oscillator. Experimental data show the chaotic nature of the system through phase portraits, Poincare´ maps, frequency spectra and bifurcation diagrams. Unstable periodic orbits were extracted from each chaotic time series obtained from the system with six different parameter values. Movement of the unstable periodic orbits in phase space is used to detect parameter changes in the system.

ON STICK–SLIP HOMOCLINIC CHAOS AND BIFURCATIONS IN A MECHANICAL SYSTEM WITH DRY FRICTION

2001 ◽  
Vol 11 (07) ◽  
pp. 2019-2029 ◽  
Author(s):  
B. R. PONTES ◽  
V. A. OLIVEIRA ◽  
J. M. BALTHAZAR
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Chaotic Behavior ◽  
Prediction Method ◽  
Phase Portraits ◽  
Frequency Spectra ◽  
Stick Slip ◽  
Potential Wells ◽  
Homoclinic Chaos ◽  
Belt System

In this paper we consider a self-excited mechanical system by dry friction in order to study the bifurcational behavior of the arisen vibrations. The oscillating system consists of a mass block-belt-system which is self-excited by static and Coulomb friction. We analyze the system behavior numerically through bifurcation diagrams, phase portraits, frequency spectra and Poincaré maps, which show the existence of nonhomoclinic and homoclinic chaos and a route to homoclinic chaos. The homoclinic chaos is also analyzed analytically via the Melnikov prediction method. The system dynamic is characterized by the existence of two potential wells in the phase plane which exhibit rich bifurcational and chaotic behavior.

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