scholarly journals Stability Analysis and Chaos Control of Electronic Throttle Dynamical System

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Shun-Chang Chang
Keyword(s):  
Control Strategy ◽  
Chaos Control ◽  
Period Doubling ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Electronic Throttle ◽  
Controlling Chaos ◽  
Analysis Techniques ◽  
Continuous Feedback

This study addresses bifurcation analysis and controlling chaos in a vehicular electronic throttle. Using analysis techniques from nonlinear dynamics of an electronic throttle system based on bifurcation diagrams, we establish the existence of period-doubling and intermittency routes to chaos. The largest Lyapunov exponent is estimated from the synchronization to identify periodic and chaotic motions. Finally, the proposed continuous feedback control is employed to control chaos. To verify the effectiveness of the raised control strategy, we present a number of numerical simulations.

SYNCHRONIZATION TRANSITION INDUCED BY SYNAPTIC DELAY IN COUPLED FAST-SPIKING NEURONS

2008 ◽  
Vol 18 (04) ◽  
pp. 1189-1198 ◽  
Author(s):  
QINGYUN WANG ◽  
QISHAO LU ◽  
GUANRONG CHEN
Keyword(s):  
Spiking Neurons ◽  
Synaptic Delay ◽  
Largest Lyapunov Exponent ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Collective Behaviors ◽  
Phase Errors ◽  
Different Types ◽  
Fast Spiking ◽  
Chemical Synapses

Synchronization of coupled fast-spiking neurons with chemical synapses is studied in this paper. It is shown that by varying some key parameters such as the coupling strength and the decay rate of synapses, two coupled fast-spiking neurons can exhibit various firing synchronizations including periodic and chaotic motions. Different types of firing synchronizations are diagnosed by means of bifurcation diagrams and the largest Lyapunov exponent of the error dynamical system. However, with the synaptic delay considered, two coupled neurons can show different types of transitions of in-phase and anti-phase synchronizations and these transitions can be identified from the bifurcation diagrams and the variations of the phase errors of the coupled neurons. The revealed complicated synchronization modes effectively provide important guidelines to understanding collective behaviors of coupled neurons.

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.

Chaos in Robot Control Equations

1997 ◽  
Vol 07 (03) ◽  
pp. 707-720 ◽  
Author(s):  
Shrinivas Lankalapalli ◽  
Ashitava Ghosal
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
System Of Nonlinear Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Bifurcation Diagrams ◽  
Chaotic Motions ◽  
Repetitive Motion ◽  
Route To Chaos

The motion of a feedback controlled robot can be described by a set of nonlinear ordinary differential equations. In this paper, we examine the system of two second-order, nonlinear ordinary differential equations which model a simple two-degree-of-freedom planar robot, undergoing repetitive motion in a plane in the absence of gravity, and under two well-known robot controllers, namely a proportional and derivative controller and a model-based controller. We show that these differential equations exhibit chaotic behavior for certain ranges of the proportional and derivative gains of the controller and for certain values of a parameter which quantifies the mismatch between the model and the actual robot. The system of nonlinear equations are non-autonomous and the phase space is four-dimensional. Hence, it is difficult to obtain significant analytical results. In this paper, we use the Lyapunov exponent to test for chaos and present numerically obtained chaos maps giving ranges of gains and mismatch parameters which result in chaotic motions. We also present plots of the chaotic attractor and bifurcation diagrams for certain values of the gains and mismatch parameters. From the bifurcation diagrams, it appears that the route to chaos is through period doubling.

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

Dynamic Analysis and Adaptive Sliding Mode Controller for a Chaotic Fractional Incommensurate Order Financial System

2017 ◽  
Vol 27 (13) ◽  
pp. 1750198 ◽  
Author(s):  
Ahmad Hajipour ◽  
Hamidreza Tavakoli
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Financial System ◽  
Period Doubling ◽  
Largest Lyapunov Exponent ◽  
Sliding Mode Controller ◽  
Adaptive Sliding Mode Controller ◽  
Uncertain Dynamics ◽  
Route To Chaos ◽  
Doubling Sequence

In this study, the dynamic behavior and chaos control of a chaotic fractional incommensurate-order financial system are investigated. Using well-known tools of nonlinear theory, i.e. Lyapunov exponents, phase diagrams and bifurcation diagrams, we observe some interesting phenomena, e.g. antimonotonicity, crisis phenomena and route to chaos through a period doubling sequence. Adopting largest Lyapunov exponent criteria, we find that the system yields chaos at the lowest order of [Formula: see text]. Next, in order to globally stabilize the chaotic fractional incommensurate order financial system with uncertain dynamics, an adaptive fractional sliding mode controller is designed. Numerical simulations are used to demonstrate the effectiveness of the proposed control method.

Nonlinear Dynamic Analysis on Planetary Gears-Rotor System in Geared Turbofan Engines

2019 ◽  
Vol 29 (06) ◽  
pp. 1950076 ◽  
Author(s):  
Lanlan Hou ◽  
Shuqian Cao
Keyword(s):  
Nonlinear Dynamic Analysis ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Rotor System ◽  
Chaotic Motions ◽  
Planetary Gears ◽  
Gear Noise ◽  
Turbofan Engines ◽  
Vibration Responses ◽  
Nonlinear Analytical Model

Rotor fatigue and gear noise triggered by nonlinear vibration are the key concerns in Geared Turbofan (GTF) engine which features a new configuration by introducing planetary gears into low-pressure compressor. A nonlinear analytical model of the GTF planetary gears-rotor system is developed, where the torsional effect of rotor and pivotal parameters from gears are incorporated. The nonlinear behavior of the model can be obtained by focusing on the relative torsional vibration responses between gear and rotor. The torsional nonlinear responses are illustrated with bifurcation diagrams, the largest Lyapunov exponents (LLE), Poincaré maps, phase diagrams and spectrum waterfall. Numerical results reveal that the gears-rotor system exhibits abundant torsional nonlinear behaviors, including multiperiodic, quasi-periodic, and chaotic motions. Furthermore, the roads to chaos via quasi-periodicity, period-doubling scenario, mutation and intermittence are demonstrated. The ring gear stiffness at a low value can propel the system into chaos. The damping may complicate the motion, i.e. the system may enter chaos with increasing damping. These results provide an understanding of undesirable torsional dynamic motion for the GTF engine rotor system and therefore serve as a useful reference for engineers in designing and controlling such system.

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