Dynamical behaviors of the chaotic Brushless <scp>DC</scp> motors model

Zhang, Fuchen; Lin, Da; Xiao, Min; Li, Huanrong

doi:10.1002/cplx.21622

Cited by 16 publications

(12 citation statements)

References 38 publications

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“…Zhang et al [8] used Lyapunov stability theory to analyze a 3D autonomous system model of the BLDCM; these authors verified that the chaotic motion of the system is bounded; they also calculated the switching rate of the system phase trajectory among different attractors. Farzaneh et al [12] studied the chaos of the BLDCM model with a single time-scale transformation.…”

Section: State Of the Artmentioning

confidence: 99%

“…Therefore, exploring the mechanism of chaos caused by load disturbance and analyzing the conditions of chaos formation are theoretical innovations of the present study. At present, research on non-linear behavior of a BLDCM is mainly based on the theory analysis and simulation of a mathematical model; moreover, experimental verification is rarely applied [8][9], because the actual chaotic state is difficult to maintain and observe; furthermore, the conditions for entering the chaotic state are special.…”

Section: Introductionmentioning

confidence: 99%

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Chaotic Characteristic Analysis of Brushless DC Motor with Vibration Load Disturbance

Li¹,

Wang²,

Shi³

2018

JESTR

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A brushless DC motor (BLDCM) is a kind of nonlinear system with multivariable coupling. Under certain conditions, chaos and other non-linear dynamic phenomena will occur and bring adverse effects to the motor itself and the drive system. However, in existing research on chaotic mechanism of BLDCM, the chaotic phenomena caused by the disturbance of load torques are seldom involved. However, in practical engineering applications, the disturbance in the load of the motor is extensive. To analyze the non-linear characteristics of the BLDCM caused by this disturbance, a disturbance variable was added to the d-q axis mathematical model of the BLDCM. Then, a non-autonomous system model of 5-D BLDCM was constructed by using time scale and linear affine transformations. First, the non-linear dynamic characteristics of the system caused by the torque disturbance were analyzed by calculating the dissipation and equilibrium points of the system. Second, the chaotic dynamic behavior of the system under load disturbance was discussed through Lyapunov exponent and bifurcation graph. Finally, the accuracy of the model and analysis was verified through experiments. Results show that when the frequency of the disturbance component of the load increases from 0 Hz to 100 Hz, the system experiences various motions, such as stable, period doubling, paroxysmal chaos, and periodic. This study provides a theoretical reference for further exploring the engineering physical characteristics of the BLDCM under load disturbance and searching for an improved control method.

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Section: State Of the Artmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chaotic Characteristic Analysis of Brushless DC Motor with Vibration Load Disturbance

Li¹,

Wang²,

Shi³

2018

JESTR

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“…In the past few decades, the study of fractional calculus has attracted substantial attention. Fractional calculus is a powerful mathematical tool for modeling systems in the elds of secure communication, biological science, chemical reactors, laser systems, and so on [1][2][3][4][5]. Recently, tempered fractional derivatives have drawn the wide interests of researchers.…”

Section: Introductionmentioning

confidence: 99%

Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach

Deng

2019

Complexity

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In the famous continuous time random walk (CTRW) model, because of the finite lifetime of biological particles, it is sometimes necessary to temper the power law measure such that the waiting time measure has a convergent first moment. The CTRW model with tempered waiting time measure is the so-called tempered fractional derivative. In this article, we introduce the tempered fractional derivative into complex networks to describe the finite life span or bounded physical space of nodes. Some properties of the tempered fractional derivative and tempered fractional systems are discussed. Generalized synchronization in two-layer tempered fractional complex networks via pinning control is addressed based on the auxiliary system approach. The results of the proposed theory are used to derive a sufficient condition for achieving generalized synchronization of tempered fractional networks. Numerical simulations are presented to illustrate the effectiveness of the methods.

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“…The chaotic dynamics of deterministic systems have been studied extensively in the various subfields of science and engineering including physics, biology, electronic circuits, chemistry, chaotic synchronization, secure communication, neural networks, and mechanical engineering . The well‐known systems of Lorenz, Rössler, Chua's circuit, Chen, Lu, and other chaotic dynamical systems all of which exhibit interesting chaotic and random behavior have served as important models in the development of chaos theory . Due to great potential applications in electrical engineering, information processing, and so on, it is important to analyze the dynamical behaviors and properties of the new chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Ultimate boundedness of the Lorenz system has been investigated by Leonov in a series of articles . Since then other studies have developed solution bounds of similar chaotic systems, such as the complex Lorenz chaotic system , the synchronous motor system , the Lü system , the brushless DC motor system , the monetary chaotic system , and the family of Lorenz‐like chaotic systems . Although the results of these studies are very useful for chaos control and synchronization, the approach taken in each paper is only suitable for that particular chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Qualitative behavior of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres

2016

Self Cite

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In this article, the bounds of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres have been studied. Based on Lagrange multiplier method, the function extremum theory and the generalized positive definite and radially unbound Lyapunov functions with respect to the parameters of the system, we derive the ultimate bound and the globally exponentially attractive set for this system. The results that obtained in this article provides theory basis for chaotic synchronization, chaotic control, Hausdorff dimension and the Lyapunov dimension of chaotic attractors. © 2016 Wiley Periodicals, Inc. Complexity 21: 67–72, 2016

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Dynamical behaviors of the chaotic Brushless DC motors model

Cited by 16 publications

References 38 publications

Chaotic Characteristic Analysis of Brushless DC Motor with Vibration Load Disturbance

Chaotic Characteristic Analysis of Brushless DC Motor with Vibration Load Disturbance

Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach

Qualitative behavior of the Lorenz‐like chaotic system describing the flow between two concentric rotating spheres

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