Bifurcation surfaces and multi-stability analysis of state feedback control of PMSM

Souhail, Wahid; Khammari, Hédi; Mimouni, Mohamed Faouzi

doi:10.1007/s40435-018-0443-x

Cited by 7 publications

(3 citation statements)

References 28 publications

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“…First, we will discuss the Lyapunov exponent (LE). Recently, many scholars have addressed this type of behavior in different models (see [51], [52], and [53]). We choose the step size h = 0 : 01.…”

Section: Two Parameters Lyapunov Exponent and Basin Of Attractionsmentioning

confidence: 99%

A Predator-Prey model with Prey Refuse: under a stochastic and deterministic environment

Chatterjee,

Abbasi,

Venturino

et al. 2024

Preprint

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This study aims to thoroughly investigate the dynamics of a predator-prey model with a Beddington-De Angelis functional response. We assume that the prey refuge is proportional to both species. We establish the standard properties of boundedness, permanence, and local stability. We show that under certain parameter conditions, transcritical bifurcation and Hopf bifurcation occur. To understand the nature of the limit cycle, we determine the direction of the Hopf bifurcation. We focus on the significant ranges of the predators' Prey capturing rate and examine how the level of prey fear and the predator's mutual interference affect the system's stability. Through numerical analysis, we study the behavior of the Lyapunov exponent and observe multiple self-repeating shrimp-shaped patterns that indicate periodic attractors in discrete-time predator-prey system. These structures appear across a broad region associated with chaotic dynamics. Additionally, if the intensity of white noise is kept below a specific threshold, the deterministic control approach is equally effective in environmental fluctuation. Numerical simulations support these findings..

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Section: Two Parameters Lyapunov Exponent and Basin Of Attractionsmentioning

confidence: 99%

A Predator-Prey model with Prey Refuse: under a stochastic and deterministic environment

Chatterjee,

Abbasi,

Venturino

et al. 2024

Preprint

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“…Theory of piecewise-smooth maps has attracted the interest of many researchers lately to analyze the non-linear dynamics of various types of systems. These systems are from different fields like power electronics and drives [1][2][3][4][5] bio sciences [6][7][8][9] finance [10][11][12], analysis of relaxation oscillators in planar fast-slow systems [13] to name the few. Analysis of 1-D linear piecewisesmooth discontinuous (LPSD) map has been the focus point and given special attention by the researchers in recent years due to the inherent rich dynamics in it even though the underlying map equation is very simple [14].…”

Section: Introductionmentioning

confidence: 99%

Analysis of atypical orbits in one dimensional linear piecewise-smooth discontinuous map

Metri

Rajpathak

Pillai

2022

Preprint

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In this paper, boundary regions of 1-D linear piecewise-smooth discontinuous map are examined analytically. It is shown that, under certain parameter conditions, the map exhibits atypical orbits like a continuum of periodic orbits and quasi-periodic orbits. Further, we have derived the conditions under which such phenomena occurs. The paper also illustrate that there exists a specific parameter region in which as parameter is varied, there is a smooth transition from stable to unstable periodic orbits. Moreover, we have derived the expression for the value of parameter at which this transition from stable to unstable periodic orbits occurs. Additionally, the dynamics that exist at this value of parameter is also found out.Mathematics Subject Classification (2020) 39A23 · 39A28 · 39A33

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“…From then on, there have been numerous efforts at the detection and control of chaos in electrical machines operations (Ge & Huang, 2005, september;Harb, 2004;Li et al, 2002;Luo et al, 2007;Ren et al, 2003;Ren & Liu, 2006;Zribi et al, 2009). The chaos in PMSMs is associated with adverse outcomes such as instability and failure of the entire system (Souhail et al, 2019;Yu et al, 2016). Thus, chaos should be avoided in PMSMs using effective control schemes.…”

Section: Introductionmentioning

confidence: 99%

Control of PMSM chaos using backstepping-based adaptive fuzzy method in the presence of uncertainty and disturbance

Zhang

Sun

et al. 2021

Systems Science & Control Engineering

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This paper presents a novel nonlinear control strategy based on a backstepping fuzzy adaptive approach to avoid chaos in a synchronous motor. In the controller design and stability proof, the parameter uncertainty and the system disturbance are taken into account. The matching condition is not satisfied in this model, and disturbances with an unknown upper bound are also exerted on the system. The disturbance and uncertainty are considered in one manifold with an unspecified upper bound. The system stability is verified using the Lyapunov method. The cuckoo optimization algorithm is employed to optimize the adaptive and backstepping control coefficients.

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Bifurcation surfaces and multi-stability analysis of state feedback control of PMSM

Cited by 7 publications

References 28 publications

A Predator-Prey model with Prey Refuse: under a stochastic and deterministic environment

A Predator-Prey model with Prey Refuse: under a stochastic and deterministic environment

Analysis of atypical orbits in one dimensional linear piecewise-smooth discontinuous map

Control of PMSM chaos using backstepping-based adaptive fuzzy method in the presence of uncertainty and disturbance

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