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Takagi-Sugeno Fuzzy Regulator Design for Nonlinear and Unstable Systems Using Negative Absolute eigenvalue approach

IEEE/CAA Journal of Automatica Sinica 2020年第2期7卷 482-493页

作者： Ravi V.Gandhi Dipak M.Adhyaru Department of Electrical Engineering Indian Institute of Technology(IIT)GandhinagarGandhinagar 382355India Department of Instrumentation&Control Engineering Institute of TechnologyNirma UniversityAhmedabad-382481India

This paper introduces a Takagi-Sugeno(T-S)fuzzy regulator design using the negative absolute eigenvalue(NAE)approach for a class of nonlinear and unstable *** open-loop system is initially embodied by the traditional T-S fuzzy model and then,all closed-loop subsystems are combined using the proposed Max-Min operator in place of traditional weighted average operator from the controller side to lessen the coupling virtually and simplify the proposed regulator *** each virtually decoupled closed-loop subsystem,the composite regulators(i.e.,primary and secondary regulators)are designed by the NAE approach based on the enhanced eigenvalue *** Lyapunov function is utilized to guarantee the asymptotic stability of the overall T-S fuzzy control *** most popular and widely used nonlinear and unstable systems like the electromagnetic levitation system(EMLS)and the inverted cart pendulum(ICP)are simulated for the wide range of the initial conditions and the enormous variation in the *** transient and steady-state performance of the considered systems using the proposed design are analyzed in terms of the decay rate,settling time and integral errors as IAE,ISE,ITAE,and ITSE to validate the effectiveness of the proposed approach compared to the most popular and traditional parallel distributed compensation(PDC)approach.

关键词： eigenvalue approach nonlinear and unstable systems stability analysis Takagi-Sugeno(T-S)fuzzy regulator

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Novel model of thermo-magneto-viscoelastic medium with variable thermal conductivity under effect of gravity

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Applied Mathematics and Mechanics(English Edition) 2020年第5期41卷 819-832页

作者： S.M.SAID Department of Mathematics Faculty of ScienceZagazig UniversityZagazig 44519Egypt Department of Mathematics Faculty of Science and ArtsQassim UniversityBuridah 51931Al-mithnabKingdom of Saudi Arabia

The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay(G-L) theory, the coupled(CD) theory, and the Lord-Shulman(L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal *** numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.

关键词： eigenvalue approach variable thermal conductivity thermo-viscoelastic gravity field

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Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux

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Applied Mathematics and Mechanics(English Edition) 2020年第6期41卷 927-938页

作者： T.SAEED I.A.ABBAS Nonlinear Analysis and Applied Mathematics(NAAM)Research Group Department of MathematicsKing Abdulaziz UniversityJeddah 21441Saudi Arabia Department of Mathematics Faculty of ScienceSohag UniversitySohag 82524Egypt

In this article, the generalized model for thermoelastic waves with two relaxation times is utilized to compute the increment of temperature, the displacement components, the stress components, and the changes in the volume fraction field in a two-dimensional porous medium. By using the Fourier-Laplace transform and the eigenvalue method, the considered variables are obtained analytically. The derived approach is estimated with numerical outcomes which are applied to the porous media with a geometrical simplification. The numerical results for the considered variables are performed and presented graphically. Finally, the outcomes are represented graphically to display the difference among the classical dynamical(CD) coupled, the Lord-Shulman(LS), and the Green-Lindsay(GL) models.

关键词： Fourier-Laplace transform thermal relaxation time porous medium eigenvalue approach

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Maximum Interval of Stability and Convergence of Solution of a Forced Mathieu’s Equation

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World Journal of Mechanics 2020年第11期10卷 210-219页

作者： Everestus Obinwanne Eze Uchenna Emmanuel Obasi Rosary Ngozi Ujumadu Grace Ihuoma Kalu Department of Mathematics Michael Okpara University of Agriculture Umuahia Nigeria Department of Mathematics Chukwuemeka Odimegwu Ojukwu University Uli Nigeria

This paper investigates the maximum interval of stability and convergence of solution of a forced Mathieu’s equation, using a combination of Frobenius method and eigenvalue approach. The results indicated that the equilibrium point was found to be unstable and maximum bounds were found on the derivative of the restoring force showing sharp condition for the existence of periodic solution. Furthermore, the solution to Mathieu’s equation converges which extends and improves some results in literature.

关键词： Frobenius Method eigenvalue approach Stability Mathieu’s Equation

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