Dynamics of the fractional‐order chaotic PMSG, its stabilisation using predictive control and circuit validation

Borah, Manashita; Roy, Binoy Krishna

doi:10.1049/iet-epa.2016.0506

Cited by 36 publications

(8 citation statements)

References 36 publications

(58 reference statements)

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“…Then, according to Theorem 5 the product p • q should always be negative. In our case, however, for (κ, μ) given in (19), we obtain the following equality…”

Section: Proof Of Theoremmentioning

confidence: 60%

“…Therefore, for the last five decades researchers have made a great effort for constructing new chaotic models for chaos-needed applications. Among others, let us mention classical ones: the logistic and the Hénon maps [2,3], Chua's circuits [4], the Lorenz-like systems introduced by Chen and Lü in [5,6], and more recent systems, studied by Qi and Li in [7][8][9], the 4D chaotic Duffing system [10], the Chameleon model [11], and many more [12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Integrability analysis of chaotic and hyperchaotic finance systems

Szumiński

2018

Nonlinear Dyn

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In this paper, we consider two chaotic finance models recently studied in the literature. The first one, introduced by Huang and Li, has a form of three first-order nonlinear differential equationṡ x = z + (y − a)x,ẏ = 1 − by − x 2 ,ż = − x − cz. The second system, called a hyperchaotic finance model, is defined bẏ x = z + (y − a)x + u, z = − x − cz,ẏ = 1 − by − x 2 , u = − dx y − ku. In both models, (a, b, c, d, k) are real positive parameters. In order to present the complexity of these systems Poincaré cross sections, bifurcation diagrams, Lyapunov exponents spectrum and the Kaplan-Yorke dimension have been calculated. Moreover, we show that the Huang-Li system is not integrable in a class of functions meromorphic in variables (x, y, z), for all real values of parameters (a, b, c), while the hyperchaotic system is not integrable in the case when k = c and := 1 + d(a + d − c) > 0. We give analytic proofs of these facts analyzing properties of the differential Galois groups of variational equations along cer-The research has been supported by the National Science Centre of Poland under Grants DEC

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“…Then, according to Theorem 5 the product p • q should always be negative. In our case, however, for (κ, μ) given in (19), we obtain the following equality…”

Section: Proof Of Theoremmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Integrability analysis of chaotic and hyperchaotic finance systems

Szumiński

2018

Nonlinear Dyn

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“…Here, D q represents the Caputo derivative with fractional order q. Inspired from [33] and the ESERS in Eq. (1), the dynamic model of the FOESERS can be formulated as follows, In the second formula in Eq.…”

Section: Property 1 ([35])mentioning

confidence: 99%

“…Thus, the fractional calculus can extend the integer-order calculus models to the non-integer order models [24], and is proven to be a very suitable and flexible tool to characterize the genetic memory properties in various chaotic evolutionary processes [23][24][25][26][27][28]. So far, many practical nonlinear systems in electrical energy fields [27][28][29][30][31][32][33][34], such as the energy supply-demand system [27], hydro-turbine governing system [29], and wind turbine [31], have been modelled using fractional differential equations. This paper aims to investigate the modeling and control of the fractionalorder energy-saving and emission-reduction system (FOESERS) to coordinate the dynamic performance of energy conservation, economic growth, carbon emissions, and renewable energy development.…”

Section: Introductionmentioning

confidence: 99%

Fractional-order modeling and sliding mode control of energy-saving and emission-reduction dynamic evolution system

Huang

Zhou

et al. 2018

International Journal of Electrical Power & Energy Systems

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A B S T R A C TThis paper proposes the fractional-order modeling for sliding mode control of a complex four-dimensional energy-saving and emission-reduction system (ESERS). In the proposed methodology, the fractional calculus techniques are employed to accurately model the dynamics of the ESERS, and the fractional-order model of the energy-saving and emission-reduction system (FOESERS) is formulated. With the proposed FOESERS, all of the equilibrium points and the corresponding eigenvalues are obtained, and the instability region and the state trajectories of FOESERS are also given. The FOESERS can represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust control theory, a sliding-mode controller is designed to control the FOESERS with model uncertainties and external disturbances to the equilibrium point in the finite time. Finally, simulation results confirm the effectiveness and robustness of the proposed scheme.

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“…This paper aims to study the modeling and stability of the fractional‐order energy‐saving and emission‐reduction system to coordinate the link among energy‐saving and emission‐reduction, economic growth, and carbon emissions. Therefore, inspired from Borah and Roy () and the energy‐saving and emission‐reduction system in (1.1), the dynamic model of the fractional‐order energy‐saving and emission‐reduction system can be formulated as follows:

\begin{matrix} right \frac{{italicd}^{α} x}{d t^{α}} & center = & left a_{1} x true(\frac{y}{M} - 1 true) - a_{2} y + a_{3} z - a_{4} x, \\ right \frac{{italicd}^{α} y}{d t^{α}} & center = & left - b_{1} x + b_{2} y true(1 - \frac{y}{C} true) + b_{3} z true(1 - \frac{z}{E} true) - b_{4} y, \\ right \frac{{italicd}^{α} z}{d t^{α}} & center = & left c_{1} x true(\frac{x}{N} - 1 true) - c_{2} y - c_{3} z - c_{4} z, \end{matrix}

in which

α

is subject to

0 < α \leq 1

. Moreover, based on the normalization of the energy‐saving and energy‐reduction system from the statistical data in China (National Bureau of Statistics of China, ), the impact factors of the system can be obtained by the parameter identification using artificial neural network in Fang et al () and National Bureau of Statistics of China ().…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

Chen

Liu

2018

Natural Resource Modeling

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This paper attempts to explore dynamical behavior and mathematical properties of the three‐dimensional fractional‐order energy‐saving and emission‐reduction system. Theoretically, the conditions of local stability of fractional‐order system's equilibrium points are obtained. Numerical investigations on the dynamics of this system are carried out, and the existence of the asymptotically stable attractor is found. Combined with the fractional‐order subsystem, we discuss the relationship between energy‐saving and emission‐reduction and economic growth, and carbon emissions and economic growth. Furthermore, we discretize the fractional‐order system and give necessary and sufficient conditions of its stabilization. It is shown that the stability of the discretization system is impacted by the system's fractional parameter. Numerical simulations show the richer dynamical behavior of the fractional‐order system and verify the theoretical results. Recommendations for Resource Managers The impact of carbon emissions on economic growth is one of the main reasons for energy‐saving and emission‐reduction. Control measures on people's low‐carbon life through government intervention are required to protect the natural environment. New energy‐saving and emission‐reduction technologies should be implemented to achieve sustainable social and economic development.

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Dynamics of the fractional‐order chaotic PMSG, its stabilisation using predictive control and circuit validation

Cited by 36 publications

References 36 publications

Integrability analysis of chaotic and hyperchaotic finance systems

Integrability analysis of chaotic and hyperchaotic finance systems

Fractional-order modeling and sliding mode control of energy-saving and emission-reduction dynamic evolution system

Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

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