Control of chaos in thermal convection loop by state space linearization

Rana, Zainab; Aqeel, Muhammad; Ayub, Javeria; Shaukat, Mansoor

doi:10.1016/j.cjph.2019.01.003

Cited by 5 publications

(5 citation statements)

References 27 publications

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“…Higher harmonics describe deviations of the variables from the linear regime [24]. According to the boundary conditions, we can represent the stream function, the temperature, and the concentration of the magnetic particles and the magnetic potential on the form below in order to obtain the solution of ( 8)- (11):…”

Section: Galerkin Truncated Extensionmentioning

confidence: 99%

“…Calculating the terms of the equations ( 8)- (11) with the Galerkin functions defined from ( 12)-( 15), then multiplying the equations by the orthogonal eigenfunctions, and integrating them in space over the wavelength of a convection cell, 􏽒…”

Section: Galerkin Truncated Extensionmentioning

confidence: 99%

“…Control of chaos in a thermal convection loop by state space linearization has been investigated by Rana et al [11]. A laminar flow has been obtained from a chaotic flow of the thermal convection loop by applying a technique state space linearization converting the nonlinear system into the linear system through a coordinate transformation, based on the concept of Lie brackets.…”

Section: Introductionmentioning

confidence: 99%

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Regular and Chaotic Behavior on the Convection in a Rotating Ferrofluid in Porous Medium under Helical Force

Hounvènou

Monwanou

2022

Complexity

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This article deals with the control of chaos on the convective motion in a ferrofluid filled in a rotating porous medium and under the helical force effect. We performed a truncated expansion of Galerkin and found the Lorenz-type model which described the system. The dynamical system is characterized using appropriate and subsequent criteria. We noticed that the system presents regular and chaotic behaviors according to the parameters at present. A considerable reduction of the chaotic domain is noticed with the increase of the intensity of the helical force and of the Darcy number, thus making it possible to delay the heat transfer in the system. The increase in the viscosity ratio and the Taylor number widen the chaotic domain leading to an acceleration of the heat transfer in the system.

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Section: Galerkin Truncated Extensionmentioning

confidence: 99%

Section: Galerkin Truncated Extensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Regular and Chaotic Behavior on the Convection in a Rotating Ferrofluid in Porous Medium under Helical Force

Hounvènou

Monwanou

2022

Complexity

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“…The specialized literature [13][14][15][16][17] has shown the importance of incorporating control theory in economic and financial analysis, highlighting its potential to enhance policy effectiveness and mitigate economic fluctuations [18,19]. Furthermore, the application of control techniques from different fields [20][21][22][23][24] has a long tradition in macroeconomics [25,26], where models incorporating feedback control [27] have been employed to address issues such as inflation control [28], and monetary policy implementation [29]. Moreover, control techniques have found utility in the study of chaotic financial systems [30,31], and in applications for risk assessment, portfolio optimization, and asset pricing, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model

Perez Avellaneda,

Rosales,

Duffaut Espinosa

2024

PLoS ONE

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The Keen model is designed to represent an economy as a dynamic system governed by the interactions between private debt, wage share, and employment rate. When certain conditions are met, the model can lead to a debt spiral, which accurately mimics the impact of a financial crisis on an economy. This manuscript presents a recipe for breaking this spiral by expressing Keen’s model as an affine nonlinear system that can be modified through policy interventions. We begin by considering critical initial conditions that resemble a financial crisis to achieve this goal. We then locate a desired point within the system’s vector field that leads to a desirable equilibrium and design a path towards it. This path is later followed using one-step-ahead optimal control. We illustrate our approach by presenting simulated control scenarios.

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“…Researchers in different fields have developed various control techniques to address chaos-controlling applications in science and engineering. These techniques include adaptive control strategies (Aghababa, 2019;Tran and Kang, 2015), sliding mode control technique (Fang et al, 2019), state-space linearization method (Rana et al, 2019), sample-data control technique (Liu et al, 2018b), and linear parameter varying controller (Hsu and Bhattacharya, 2020), among others. The adaptive control strategy is an effective control technique that slowly controls time-varying dynamic systems (Pan et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Robust attitude control of the three-dimensional unknown chaotic satellite system

Shafiq

Ahmad

Almatroud

et al. 2021

Transactions of the Institute of Measurement and Control

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This paper proposes a novel continuous-time robust direct adaptive controller for the attitude control of the three-dimensional unknown chaotic spacecraft system. It considers that the plant’s nonlinear terms, exogenous disturbances, and model uncertainties are unknown and bounded; the controller design is independent of the system’s nonlinear terms. These controller attributes flourish the robust performance of the closed-loop and establish smooth state vector convergence to zero. The proposed controller consists of three parts: (1) a linear controller establishes the stability of the closed-loop at the origin, (2) a nonlinear controller component that autonomously adjusts the feedback gain, and (3) a nonlinear adaptive controller compensates for the model uncertainties and external disturbances using the online estimates of bounds and model uncertainties. The output of this part remains within a given upper and lower bound. The feedback controller gain is large when the state variables are away from the origin and become small in the origin’s vicinity. This feature is novel and contributes to the synthesis of smooth control effort that establishes robust fast and oscillation-free convergence of the state variables to zero. The Lyapunov direct stability analysis assures the global asymptotic robust stability of the closed-loop. Computer simulations and comparative analysis are included to verify the theoretical findings.

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Control of chaos in thermal convection loop by state space linearization

Cited by 5 publications

References 27 publications

Regular and Chaotic Behavior on the Convection in a Rotating Ferrofluid in Porous Medium under Helical Force

Regular and Chaotic Behavior on the Convection in a Rotating Ferrofluid in Porous Medium under Helical Force

Feedback dynamic control for exiting a debt-induced spiral in a deterministic Keen model

Robust attitude control of the three-dimensional unknown chaotic satellite system

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