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.

scholarly journals Controlling Chaos through Period-Doubling Bifurcations in Attitude Dynamics for Power Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shun-Chang Chang
Keyword(s):  
Power Systems ◽  
Control Method ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Lyapunov Stability Theory ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Frequency Spectra ◽  
Controlling Chaos ◽  
Period Doubling Bifurcations

This paper addresses the complex nonlinear dynamics involved in controlling chaos in power systems using bifurcation diagrams, time responses, phase portraits, Poincaré maps, and frequency spectra. Our results revealed that nonlinearities in power systems produce period-doubling bifurcations, which can lead to chaotic motion. Analysis based on the Lyapunov exponent and Lyapunov dimension was used to identify the onset of chaotic behavior. We also developed a continuous feedback control method based on synchronization characteristics for suppressing of chaotic oscillations. The results of our simulation support the feasibility of using the proposed method. The robustness of parametric perturbations on a power system with synchronization control was analyzed using bifurcation diagrams and Lyapunov stability theory.

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.

Bifurcation, routes to chaos, and synchronized chaos of electromagnetic valve train in camless engines

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Shun-Chang Chang
Keyword(s):  
Numerical Simulations ◽  
Robustness Analysis ◽  
Period Doubling ◽  
Valve Train ◽  
Phase Portraits ◽  
Control Technique ◽  
Nonlinear Phenomena ◽  
Parametric Perturbation ◽  
Frequency Spectra ◽  
Electromagnetic Valve

AbstractThe main objects of this paper focus on the complex dynamics and chaos control of an electromagnetic valve train (EMV). A variety of periodic solutions and nonlinear phenomena can be expressed using various numerical techniques such as time responses, phase portraits, Poincaré maps, and frequency spectra. The effects of varying the system parameters can be observed in the bifurcation diagram. It shows that this system can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. Lyapunov exponents and Lyapunov dimensions are employed to confirm chaotic behavior for EMV. A proposed continuous feedback control method based on synchronization characteristics eliminated chaotic oscillations. Numerical simulations are utilized to verify the feasibility and efficiency of the proposed control technique. Finally, some robustness analysis of parametric perturbation on EMV system with synchronization control is confirmed by Lyapunov stability theory and numerical simulations.

scholarly journals Discrete-Time Predator-Prey Interaction with Selective Harvesting and Predator Self-Limitation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhihua Chen ◽  
Qamar Din ◽  
Muhammad Rafaqat ◽  
Umer Saeed ◽  
Muhammad Bilal Ajaz
Keyword(s):  
Discrete Time ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
State Feedback Control ◽  
Time Model ◽  
Predator Prey ◽  
Selective Harvesting ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction

Selective harvesting plays an important role on the dynamics of predator-prey interaction. On the other hand, the effect of predator self-limitation contributes remarkably to the stabilization of exploitative interactions. Keeping in view the selective harvesting and predator self-limitation, a discrete-time predator-prey model is discussed. Existence of fixed points and their local dynamics is explored for the proposed discrete-time model. Explicit principles of Neimark–Sacker bifurcation and period-doubling bifurcation are used for discussion related to bifurcation analysis in the discrete-time predator-prey system. The control of chaotic behavior is discussed with the help of methods related to state feedback control and parameter perturbation. At the end, some numerical examples are presented for verification and illustration of theoretical findings.

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.

Bifurcation Analysis of a Power System Model with Three Machines and Four Buses

2016 ◽  
Vol 26 (05) ◽  
pp. 1650082 ◽  
Author(s):  
Yu Chang ◽  
Xiaoli Wang ◽  
Dashun Xu
Keyword(s):  
Power Systems ◽  
Power System ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Period Doubling ◽  
Bifurcation Phenomena ◽  
Fold Bifurcation ◽  
Approximate Expressions

The bifurcation phenomena in a power system with three machines and four buses are investigated by applying bifurcation theory and harmonic balance method. The existence of saddle-node bifurcation and Hopf bifurcation is analyzed in time domain and in frequency domain, respectively. The approach of the fourth-order harmonic balance is then applied to derive the approximate expressions of periodic solutions bifurcated from Hopf bifurcations and predict their frequencies and amplitudes. Since the approach is valid only in some neighborhood of a bifurcation point, numerical simulations and the software Auto2007 are utilized to verify the predictions and further study bifurcations of these periodic solutions. It is shown that the power system may have various types of bifurcations, including period-doubling bifurcation, torus bifurcation, cyclic fold bifurcation, and complex dynamical behaviors, including quasi-periodic oscillations and chaotic behavior. These findings help to better understand the dynamics of the power system and may provide insight into the instability of power systems.

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.

Intermittent Chaotic Dynamics of Rail Axle Supported by Roller Bearings

2009 ◽  
Author(s):  
S. P. Harsha ◽  
C. ‘Nat’ Nataraj
Keyword(s):  
High Speed ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Radial Clearance ◽  
High Speed Rail ◽  
Frequency Spectra ◽  
Roller Bearings ◽  
Nonlinear Springs ◽  
Rolling Elements

In this paper, intermittent chaotic analysis of high speed rail axle supported by roller bearings has been analyzed. In the analytical formulation, the contacts between rolling elements and races are considered as nonlinear springs, whose stiffness values are obtained by using Hertzian elastic contact deformation theory. The results show the appearance of instability and chaos in the dynamic response as the speed of the axle-bearing system is changed. Period doubling and mechanism of intermittency have been observed which lead to chaos. The appearance of regions of periodic, sub-harmonic and chaotic behavior is seen to be strongly dependent on the radial clearance. Poincare´ maps, time response and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation

2020 ◽  
Vol 31 (04) ◽  
pp. 2050059
Author(s):  
Asit Saha ◽  
Amiya Das
Keyword(s):  
Nonlinear Wave ◽  
Chaotic Behavior ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Phase Portraits ◽  
Phase Plane Analysis ◽  
Linear Coefficient ◽  
Wave Solutions ◽  
Nonlinear Wave Solutions

Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the first time in the literature. Bifurcation of phase portraits of the unperturbed GNWS equation is dispensed using phase plane analysis through symbolic computation and it shows stable oscillation of the traveling waves. Chaotic behavior of the perturbed GNWS equation is obtained by applying different computational tools, like phase plot, time series plot, Poincare section, bifurcation diagram and Lyapunov exponent. A period-doubling bifurcation behavior to chaotic behavior is shown for the perturbed GNWS equation and again it shows chaotic to periodic motion through inverse period-doubling bifurcation. The perturbed GNWS equation also shows chaotic motion through a sequence of periodic motions (period-1, period-3 and period-5) depending on the variation of the parameter of linear coefficient. Thus, the parameter of linear coefficient plays the role of a controlling parameter in the chaotic dynamics of the perturbed GNWS equation.

scholarly journals Circuit Implementation of a Modified Chaotic System with Hyperbolic Sine Nonlinearities Using Bi-Color LED

Technologies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 15
Author(s):  
Christos K. Volos ◽  
Lazaros Moysis ◽  
George D. Roumelas ◽  
Aggelos Giakoumis ◽  
Hector E. Nistazakis ◽  
...  
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Original System ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
Circuit Realization ◽  
Hyperbolic Sine ◽  
Route To Chaos ◽  
Sine Functions

In this paper, a chaotic three dimansional dynamical system is proposed, that is a modification of the system in Volos et al. (2017). The new system has two hyperbolic sine nonlinear terms, as opposed to the original system that only included one, in order to optimize system’s chaotic behavior, which is confirmed by the calculation of the maximal Lyapunov exponents and Kaplan-Yorke dimension. The system is experimentally realized, using Bi-color LEDs to emulate the hyperbolic sine functions. An extended dynamical analysis is then performed, by computing numerically the system’s bifurcation and continuation diagrams, Lyapunov exponents and phase portraits, and comparing the numerical simulations with the circuit simulations. A series of interesting phenomena are unmasked, like period doubling route to chaos, coexisting attractors and antimonotonicity, which are all verified from the circuit realization of the system. Hence, the circuit setup accurately emulates the chaotic dynamics of the proposed system.

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