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 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 Nonlinear Dynamic Analysis and Chaos Prediction of Grinding Motorized Spindle System

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Weitao Jia ◽  
Feng Gao ◽  
Yan Li ◽  
Wenwu Wu ◽  
Zhongwei Li
Keyword(s):  
Nonlinear Dynamic ◽  
High Speed ◽  
Chaotic Behavior ◽  
Nonlinear Dynamic Analysis ◽  
Phase Portraits ◽  
Impact Factors ◽  
Nonlinear Dynamic Model ◽  
Motorized Spindle ◽  
Spindle System ◽  
The Impact

The paper determines the impact factors of dynamics of a motorized spindle rotor system due to high speed: centrifugal force and bearing stiffness softening. A nonlinear dynamic model of the grinding motorized spindle system considering the above impact factors is constructed. Through system simulation including phase portraits and Poincaré map, the periodic behavior and chaotic behavior of the nonlinear grinding motorized spindle system are revealed. The threshold curve of chaos motion is obtained through the Melnikov method. The conclusion can provide a theoretical basis for researching deeply the dynamic behaviors of the grinding motorized spindle system.

Analysis of Nonlinear Dynamics for a Rotor-Active Magnetic Bearing System With Time-Varying Stiffness: Part I — Formulation and Local Bifurcations

2003 ◽  
Author(s):  
Wei Zhang ◽  
Jean W. Zu
Keyword(s):  
Nonlinear Dynamics ◽  
Steady State ◽  
Transient State ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Quasiperiodic Solutions ◽  
Local Bifurcations ◽  
Averaged Equations ◽  
Amb System

In this two-part paper, we investigate nonlinear dynamics in the rotor-active magnetic bearings (AMB) system with 8-pole legs and the time-varying stiffness. The model of parametrically excited two-degree-of-freedom nonlinear system with the quadratic and cubic nonlinearities is established to explore the periodic and quasiperiodic motions as well as the bifurcations and chaotic dynamics of the system. The method of multiple scales is used to obtain the averaged equations in the case of primary parameter resonance and 1/2 subharmonic resonance. In Part I of the companion paper, numerical approach is applied to the averaged equations to find the periodic, quasiperiodic solutions and local bifurcations. It is found that there exist 2-period, 3-period, 4-period, 5-period, multi-period and quasiperiodic solutions in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The catastrophic phenomena for the amplitude of nonlinear oscillations are first observed in the rotor-AMB system with 8-pole legs and the time-varying stiffness. The procedures of motion from the transient state chaotic motion to the steady state periodic and quasiperiodic motions are also found. The results obtained here show that there exists the ability of autocontrolling transient state chaos to the steady state periodic and quasiperiodic motions in the rotor-AMB system with 8-pole legs and the time-varying stiffness.

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.

Analysis of Nonlinear Dynamics of a Rotor-Active Magnetic Bearing System With 16-Pole Legs

2017 ◽  
Author(s):  
Ruiqin Wu ◽  
Wei Zhang ◽  
Ming Hui Yao
Keyword(s):  
Nonlinear Dynamics ◽  
Perturbation Method ◽  
Primary Resonance ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Chaotic Motions ◽  
Dimensionless Equation ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation

In this paper, we use the asymptotic perturbation method to analyze the nonlinear dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs. The motion governing equation is derived by using classical Newton law. The resulting dimensionless equation of motion for the system is expressed as a two-degree-of-freedom system including the parametric excitation, quadratic and cubic nonlinearities. The asymptotic perturbation method is used to obtain the averaged equation when the primary resonance and 1/2 sub-harmonic resonance are taken into consideration. From the averaged equations obtained, numerical simulations are presented to investigate the modulation of vibration amplitudes of the rotor-AMB system. Based on a specific set of parameters, it is found that there exist the periodic, quasi-periodic and chaotic motions in the modulated amplitude of the rotor in the system.

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.

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.

Structural static stability and dynamic chaos of active electromagnetic bearing systems: Analytical investigations and numerical simulations

2016 ◽  
Vol 24 (24) ◽  
pp. 5774-5793 ◽  
Author(s):  
Alexandre Kongne Mando ◽  
David Yemélé ◽  
Wilfried Takam Sokamte ◽  
Anaclet Fomethe
Keyword(s):  
Chaotic Behavior ◽  
State Diagram ◽  
Transient State ◽  
Static Stability ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
System A ◽  
Inner Radius ◽  
Localized Excitations ◽  
The Stability

The complete nonlinear dynamics of an active magnetic bearing (AMB) with proportional and derivative controller is revisited analytically. Through the stability analysis of the second-order nonlinear differential equation governing the dynamics of the system, a state diagram is obtained in the proportional gain and precontrol current space. This diagram is fundamental and may help in making important design decisions namely in the identification of a controller for the complete range of the rotor mass, in order to ensure structural stability. In particular, we find that there exists a threshold for the proportional gain whose expression depends both on the inner radius of the bearing and on the bias current, and below which no stable dynamics of the system can occur. In the operating range, we show that the system exhibits a rich dynamics characterized by the possibility for the existence of many kinds of nonlinear localized excitations in the transient state, which may lead to an irregular or a chaotic behavior of the shaft. In this regime, the expressions of the critical running speed obtained by means of the Melnikov theory indicate its dependence on the AMB characteristic parameters.

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.

Sign in / Sign up

Export Citation Format

Share Document