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 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.

Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium

2016 ◽  
Vol 26 (02) ◽  
pp. 1650031 ◽  
Author(s):  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Tomasz Kapitaniak
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Exponents ◽  
Chaotic Systems ◽  
Poincaré Map ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Equilibrium System ◽  
Frequency Spectra ◽  
Chaotic Flows ◽  
New System

Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new system is investigated through numerical simulations such as phase portraits, Lyapunov exponents, Poincaré map, and frequency spectra. Furthermore, the feasibility of such a system is verified through circuital implementation.

LATERAL AND TORSIONAL VIBRATIONS OF A TWO-DISK ROTOR-STATOR SYSTEM WITH AXIAL CONTACT/RUBS

2009 ◽  
Vol 01 (02) ◽  
pp. 305-326 ◽  
Author(s):  
KUNPENG ZHANG ◽  
QIAN DING
Keyword(s):  
Numerical Simulations ◽  
Dry Friction ◽  
Contact Forces ◽  
Phase Portraits ◽  
Torsional Vibrations ◽  
Frequency Spectra ◽  
Friction Forces ◽  
Coupled Equations ◽  
Dynamical Behaviors ◽  
Disk Contact

The dynamics of a rotor system with axial contact/rub events between the disks and stator are investigated by numerical simulations. The formula for determining the contact/rub points, axial contact forces and dry friction forces are deduced. To account for their influence, the axial contact forces are substituted by equivalent forces acting at the disk centers, based on the equivalent moment rule. One-parametric model is used to estimate the contact-induced dry friction forces. The coupled equations of lateral and torsional motions of rotor and the lateral motion of disk are then established. Numerical simulations are carried out to reveal the lateral and torsional vibrations for both two-disk contact/rubs with different axial clearances, and one disk contact/rubs. Bifurcation diagrams, orbits, phase portraits, amplitude-frequency spectra and Poincaré maps are adopted to demonstrate the dynamical behaviors of the system. The results show that though both the lateral and torsional vibrations can reflect the influences of contact/rubs on rotor dynamics, the spectrum analyses of the torsional vibrations are more suitable to determine straight the extent of their effect.

Hunting Cooperation in a Discrete-Time Predator–Prey System

2018 ◽  
Vol 28 (07) ◽  
pp. 1850083 ◽  
Author(s):  
Saheb Pal ◽  
Nikhil Pal ◽  
Joydev Chattopadhyay
Keyword(s):  
Numerical Simulations ◽  
Discrete Time ◽  
Period Doubling ◽  
Phase Portraits ◽  
Predator Population ◽  
Predator Prey ◽  
Prey System ◽  
Cooperation Rate ◽  
Route To Chaos ◽  
The Impact

The present paper mainly investigates the impact of hunting cooperation in a discrete-time predator–prey system through numerical simulations. We show that without hunting cooperation, an increase in the growth rate of prey population produces chaotic dynamics. We also show that hunting cooperation has the potential to modify the well-known period-doubling route to chaos by reverse period-halving bifurcations and makes the system stable. However, very high hunting cooperation can be detrimental and populations go to extinction. We observe that hunting cooperation induces strong demographic Allee effect in the system, where predator population persists due to hunting cooperation and would go to extinction without hunting cooperation. We perform extensive numerical simulations of the system and draw phase portraits, bifurcation diagrams, maximum Lyapunov exponents, two-parameter stability regions. We also observe the occurrence of flip and Neimark–Sacker bifurcations by taking the hunting cooperation rate as a bifurcation parameter.

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 Study on Nonlinear Phenomena in Buck-Boost Converter with Switched-Inductor Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Hongchen Liu ◽  
Shuang Yang
Keyword(s):  
Period Doubling ◽  
Boost Converter ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Mapping Model ◽  
Tangent Bifurcation ◽  
Value Range ◽  
The Time Domain ◽  
Intermittent Chaos ◽  
Voltage Conversion

The switched-inductor structure can be inserted into a traditional Buck-Boost converter to get a high voltage conversion ratio. Nonlinear phenomena may occur in this new converter, which might well lead the system to be unstable. In this paper, a discrete iterated mapping model is established when the new Buck-Boost converter is working at continuous conduction current-controlled mode. On the basis of the discrete model, the bifurcation diagrams and Poincare sections are drawn and then used to analyze the effects of the circuit parameters on the performances. It can be seen clearly that various kinds of nonlinear phenomena are easy to occur in this new converter, including period-doubling bifurcation, border collision bifurcation, tangent bifurcation, and intermittent chaos. Value range of the circuit parameters that may cause bifurcations and chaos are also discussed. Finally, the time-domain waveforms, phase portraits, and power spectrum are obtained by using Matlab/Simulink, which validates the theoretical analysis results.

scholarly journals Zero Average Surface Controlled Boost-Flyback Converter

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 57
Author(s):  
Juan-Guillermo Muñoz ◽  
Fabiola Angulo ◽  
David Angulo-Garcia
Keyword(s):  
Duty Cycle ◽  
Period Doubling ◽  
Power Converter ◽  
Control Technique ◽  
Average Surface ◽  
Flyback Converter ◽  
Stable Period ◽  
Period 2 ◽  
Wide Range ◽  
The Right

The boost-flyback converter is a DC-DC step-up power converter with a wide range of technological applications. In this paper, we analyze the boost-flyback dynamics when controlled via a modified Zero-Average-Dynamics control technique, hereby named Zero-Average-Surface (ZAS). While using the ZAS strategy, it is possible to calculate the duty cycle at each PWM cycle that guarantees a desired stable period-1 solution, by forcing the system to evolve in such way that a function that is constructed with strategical combination of the states over the PWM period has a zero average. We show, by means of bifurcation diagrams, that the period-1 orbit coexists with a stable period-2 orbit with a saturated duty cycle. While using linear stability analysis, we demonstrate that the period-1 orbit is stable over a wide range of parameters and it loses stability at high gains and low loads via a period doubling bifurcation. Finally, we show that, under the right choice of parameters, the period-1 orbit controller with ZAS strategy satisfactorily rejects a wide range of disturbances.

Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

2005 ◽  
Vol 128 (3) ◽  
pp. 282-293 ◽  
Author(s):  
J. C. Chedjou ◽  
K. Kyamakya ◽  
I. Moussa ◽  
H.-P. Kuchenbecker ◽  
W. Mathis
Keyword(s):  
Electronic Circuit ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Electromechanical System ◽  
Phase Portraits ◽  
Coupling Coefficients ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
Design Engineers

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

Nonlinear Dynamics of an Imperfect Microbeam Under an Axial Load and Electric Excitation

2011 ◽  
Author(s):  
Laura Ruzziconi ◽  
Mohammad I. Younis ◽  
Stefano Lenci
Keyword(s):  
Nonlinear Dynamics ◽  
Microelectromechanical Systems ◽  
Complex Dynamics ◽  
Nonlinear Behavior ◽  
Single Mode ◽  
Phase Portraits ◽  
Nonlinear Phenomena ◽  
Theoretical Point ◽  
Initial Shape ◽  
Electric Excitation

This study is motivated by the growing attention, both from a practical and a theoretical point of view, toward the nonlinear behavior of microelectromechanical systems (MEMS). We analyze the nonlinear dynamics of an imperfect microbeam under an axial force and electric excitation. The imperfection of the microbeam, typically due to microfabrication processes, is simulated assuming the microbeam to be of a shallow arched initial shape. The device has a bistable static behavior. The aim is that of illustrating the nonlinear phenomena, which arise due to the coupling of mechanical and electrical nonlinearities, and discussing their usefulness for the engineering design of the microstructure. We derive a single-mode-reduced-order model by combining the classical Galerkin technique and the Pade´ approximation. Despite its apparent simplicity, this model is able to capture the main features of the complex dynamics of the device. Extensive numerical simulations are performed using frequency response diagrams, attractor-basins phase portraits, and frequency-dynamic voltage behavior charts. We investigate the overall scenario, up to the inevitable escape, obtaining the theoretical boundaries of appearance and disappearance of the main attractors. The main features of the nonlinear dynamics are discussed, stressing their existence and their practical relevance. We focus on the coexistence of robust attractors, which leads to a considerable versatility of behavior. This is a very attractive feature in MEMS applications. The ranges of coexistence are analyzed in detail, remarkably at high values of the dynamic excitation, where the penetration of the escape (dynamic pull-in) inside the double well may prevent the safe jump between the attractors.

scholarly journals DESIGN OF TIME DELAYED CHAOTIC CIRCUIT WITH THRESHOLD CONTROLLER

2011 ◽  
Vol 21 (03) ◽  
pp. 725-735 ◽  
Author(s):  
K. SRINIVASAN ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
M. LAKSHMANAN ◽  
SUDESHNA SINHA
Keyword(s):  
Numerical Simulations ◽  
Linear Function ◽  
Piecewise Linear ◽  
Piecewise Linear Function ◽  
Operational Amplifiers ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Threshold Values ◽  
Chaotic Circuit

A novel time delayed chaotic oscillator exhibiting mono- and double scroll complex chaotic attractors is designed. This circuit consists of only a few operational amplifiers and diodes and employs a threshold controller for flexibility. It efficiently implements a piecewise linear function. The control of piecewise linear function facilitates controlling the shape of the attractors. This is demonstrated by constructing the phase portraits of the attractors through numerical simulations and hardware experiments. Based on these studies, we find that this circuit can produce multi-scroll chaotic attractors by just introducing more number of threshold values.

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