Hamiltonian-Based Energy Analysis for Brushless DC Motor Chaotic System

Faradja, Philippe; Qi, Guoyuan

doi:10.1142/s0218127420501126

Cited by 6 publications

(4 citation statements)

References 32 publications

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“…By analyzing Hamilton energy, it is possible to reveal the mechanism of transition between the active and resting states of neurons. Helmholtz's theorem states that any vector field can be decomposed into a conservative field, a dissipative field and an external stimulus field in a nonlinear system [55,56], that is Thus, for the LAMHR neuron model given in equation ( 5), we have…”

Section: Energy Conversion Analysismentioning

confidence: 99%

Multiple firing patterns, energy conversion and hardware implementation within Hindmarsh-Rose-improved neuron model

Yan,

Jiang,

Zhang

et al. 2024

Phys. Scr.

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The transmission of information between neurons is accomplished in living organisms through synapses. The memristor is an electronic component that simulates the tunability of the strength of biological synaptic connections in artificial neural networks. This article constructs a novel type of locally active memristor and verifies by nonlinear theoretical analysis, locally active analysis and circuit simulation. The designed memristor is simulated as a biological autapse of Hindmarsh-Rose(HR) neuron to obtain the improved HR neuron model of memristive autapse, and the Hamilton energy is obtained according to Helmholtz theorem. By varying the external forcing current and the memristive autapse strength, this article analyses the changes of the Hamilton energy and explores its self-excited and hidden firing behavior. The analog circuit simulation and digital circuit implementation of the HR model confirm the consistency between the mathematical model and the actual behavior, which can advance the field of neuroscience and artificial intelligence.

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Section: Energy Conversion Analysismentioning

confidence: 99%

Multiple firing patterns, energy conversion and hardware implementation within Hindmarsh-Rose-improved neuron model

Yan,

Jiang,

Zhang

et al. 2024

Phys. Scr.

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“…Now, we test whether the Hamiltonian energy is still conservative. The generalized Hamiltonian form was used [ 33 ]. We consider the input of the fifth term as a non-conservative force, and get

where

with new Hamiltonian

and

…”

Section: Modeling Of Conservative Chaotic System Based On Three-tementioning

confidence: 99%

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

Wang

2021

Entropy

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In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.

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“…The non-salient-pole (or smooth air gap) BLDCM model in the rotating frame (d-q) obtained after a Park transformation comprises differential equations for three state variables [9] is expressed as follows: Using Hamiltonian function [25] Dynamics with singular parameter Electromechanical parameter: motor torque constant [26] Electrical input: Direct axis voltage [27] Mechanical design parameter: damping coefficient…”

Section: Model Description Of Bldcmmentioning

confidence: 99%

“…Besides traditional bifurcation techniques, other mechanisms to explain dynamics in the BLDCM were investigated, like energy-based methods using Casimir functions and Kolmogorov systems [24], using generalized Hamiltonian functions explained the onset of different dynamical behaviors such as sink, limit cycle, chaos [25].…”

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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Hamiltonian-Based Energy Analysis for Brushless DC Motor Chaotic System

Cited by 6 publications

References 32 publications

Multiple firing patterns, energy conversion and hardware implementation within Hindmarsh-Rose-improved neuron model

Multiple firing patterns, energy conversion and hardware implementation within Hindmarsh-Rose-improved neuron model

Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

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

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