Analysis of multistability, hidden chaos and transient chaos in brushless DC motor

Faradja, Philippe; Qi, Guoyuan

doi:10.1016/j.chaos.2020.109606

Cited by 48 publications

(17 citation statements)

References 34 publications

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“…2069 various fields such as in secure communication, neural networks, laser, nonlinear circuits, mobile robots, oscillators, artificial neural networks, chemical reactors, finance systems, circuits and others [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…In classical chaotic theory, the excitation of strange attractors of chaotic systems comes from their unstable equilibria, so they are referred to as self-excited chaotic systems [8,9]. More recently, another type of chaotic systems has been appeared, where no equilibria or just a stable equilibrium points system with chaotic behavior [20,21].…”

Section: Introductionmentioning

confidence: 99%

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A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

Jasim

Hassan

Omran

2021

IJECE

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In this paper, a simple 4-dimensional hyperchaotic system is introduced. The proposed system has no equilibria points, so it admits hidden attractor which is an interesting feature of chaotic systems. Another interesting feature of the proposed system is the coexisting of attractors where it shows periodic and chaotic coexisting attractors. After introducing the system, the system is analyzed dynamically using numerical and theoretical techniques. In this analysis, Lyapunov exponents and bifurcation diagrams have been used to investigate chaotic and hyperchaotic nature, the ranges of system parameters for different behaviors and the route for chaos and coexisting attractors regions. In the next part of our work, a synchronization control system for two identical systems is designed. The design procedure uses a combination of simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Microcontroller (MCU) based hardware implementation system is proposed and tested by using MATLAB as a display side. As an application, the designed synchronization system is used as a secure analog communication system. The designed MCU system with MATLAB Simulation is used to validate the designed synchronization and secure communication systems and excellent results have been obtained.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

Jasim

Hassan

Omran

2021

IJECE

View full text Add to dashboard Cite

show abstract

“…Hyperchaotic systems show more dynamical complexity comparing with that systems which have one Lyapunov exponent or simply ordinary chaotic systems [6]. Chaotic systems get great attention in last decades due to their theoretical and practical applications and in various fields such as in secure communication, neural networks, laser, nonlinear circuits, mobile robots, oscillators, artificial neural networks, chemical reactors, finance systems, circuits and others [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel 4 dimensional hyperchaotic system with its control, Synchronization and Implementation

Jasim

Mjily

AL-Aaragee

2021

IJECE

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This paper presents a new hyperchaotic system which shows some interesting features, the system is 4-dimensional with 4 nonlinearities. An extensive numerical analysis has showed that the system has some interesting features and strange behaviors. The numerical analysis includes studying the effect of system parameters and initial conditions. Some of the important properties of the system with parameter set, in which the system is hyperchaotic, such as Lyapunov exponents and Lyapunov dimension, dissipation and symmetry are found and discussed. In the next part of our work, a tracking controller for the proposed system is designed and then a synchronization control system for two identical systems is designed. The design procedure uses combination of a simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Hardware implementation based on microcontroller unit (MCU) board is proposed and tested and used to experimentally validate the designed control and synchronization systems. As an application, the designed synchronization system is used as a secure analogue communication system. Using MATLAB, Simulation study for the control and synchronization systems is presented. The simulation and experimental study have been showed excellent results.

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“…Besides the self-excited chaos, the hidden chaos was investigated. The hidden chaos was first reported in the original BLDCM [20,21] and then in the modified model of PMSM.…”

Section: Introductionmentioning

confidence: 99%

Local bifurcation of brushless DC motor through a mechanical parameter: the viscous damping coefficient

Faradja¹,

Kabonzo

2021

Int. J. Dynam. Control

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The dynamics of brushless DC motor (BLDCM) is studied in detail from the viscous damping coefficient, a mechanical parameter. While this parameter intervenes in determining the dissipativity of the system; it shows the high complexity of the brushless DC motor. The pitchfork bifurcation is revealed. The Hopf bifurcation is identified twice in the road towards and from chaotic dynamics regions. Rigorous methods such as the center manifold theorem and the normal form theory confirm Hopf bifurcation. The different theoretical scenarios and motor parameters are also illustrated. Real positive parameters of the coefficient are only considered to keep the physical meaning from the analysis. With some special conditions around Hopf bifurcation, the transient chaotic behaviors of the BLDCM are detected. Bifurcation diagrams and Lyapunov exponents are used to support the theoretical findings.

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Analysis of multistability, hidden chaos and transient chaos in brushless DC motor

Cited by 48 publications

References 34 publications

A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

A new 4-D hyperchaotic hidden attractor system: Its dynamics, coexisting attractors, synchronization and microcontroller implementation

A novel 4 dimensional hyperchaotic system with its control, Synchronization and Implementation

Local bifurcation of brushless DC motor through a mechanical parameter: the viscous damping coefficient

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