A freely damped oscillating fractional dynamic system modeled by fractional Euler–Lagrange equations

Agila, Adel; Băleanu, Dumitru; Eid, R.; Irfanoglu, Bulent

doi:10.1177/1077546316685228

Cited by 13 publications

(6 citation statements)

References 45 publications

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“…The mathematical model of fractional-order calculus can be applied to many aspects, making the dynamic response of the system more accurate, and improving the ability of dynamic system design, characterization and control [21]. At present, fractional-order has provided a new theoretical basis for the development of many fields, and has gradually been widely used in engineering [22][23][24][25][26]. In [24], the fractional-order PID control method is used in the hydraulic servo system of hydraulic turbine regulation, and the genetic algorithm of chaotic sequencing is adopted, so that the problem of system control parameter tuning is transformed into the problem of multiobjective optimization, and finally the overall accuracy of parameters is improved.…”

Section: Introductionmentioning

confidence: 99%

Research on Fractional-Order Global Fast Terminal Sliding Mode Control of MDF Continuous Hot-Pressing Position Servo System Based on Adaptive RBF Neural Network

et al. 2022

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In this paper, a novel fractional-order global fast terminal sliding mode control (FGFTSMC) strategy based on an adaptive radial basis function (RBF) neural network is proposed to improve the performance of a medium density fiberboard (MDF) continuous hot-pressing position servo system with parameter perturbation and external load disturbance. Primarily, the mathematical model of the MDF continuous hot-pressing position servo system is constructed based on the dynamic equation of the hydraulic system. Then, a FGFTSMC is designed to speed up the convergence rate of the system, in which an adaptive law is used to estimate the upper bound of the unknown parameters to overcome the existing parameter perturbation of the system. In addition, an RBF neural network is introduced to approximate the external load disturbance of the system. The stability of MDF continuous hot-pressing position servo system based on the control scheme developed in this paper is proven using the Lyapunov theory. Finally, the simulation results show that the presented control scheme can effectively ensure the tracking accuracy of the system and enhance the robustness of the system.

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Section: Introductionmentioning

confidence: 99%

Research on Fractional-Order Global Fast Terminal Sliding Mode Control of MDF Continuous Hot-Pressing Position Servo System Based on Adaptive RBF Neural Network

et al. 2022

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“…Agila [12] proposed applying fractional Euler-Lagrange equations for solving the problem of free damped oscillations. He et al [13] analyzed the dynamic response of viscosimeters based on fractional-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

Improvement of Mathematical Model for Sedimentation Process

Pavlenko

Ochowiak

Agarwal³

et al. 2021

Energies

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In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers the Basset force’s fractional origin and contains the Riemann–Liouville fractional integral rewritten as a Grunwald–Letnikov derivative. As a result, the general solution of the proposed fractional-order differential equation was found analytically. The belonging of this solution to the real range of values was strictly theoretically proven. The obtained solution was validated on a particular analytical case study. In addition, it was proven numerically with the approach based on the S-approximation method using the block-pulse operational matrix. The proposed mathematical model can be applied for modeling the processes of fine particles sedimentation in liquids, aerosol deposition in gas flows, and particle deposition in gas-dispersed systems.

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“…Recently, some researchers investigated the related dynamical system of fractional differential equations appeared in the model of mass-spring-dampers and freely damped oscillating dynamic systems (Sahoo et al, 2017; Singh et al, 2011; Zahra and Hikal, 2017; Agila et al, 2018; Muresan et al, 2013). In Sahoo et al (2017), a simple single degree of freedom system of fractional differential equations was solved analytically by the iterative method.…”

Section: Introductionmentioning

confidence: 99%

Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models

Khiabani

Ghaffarzadeh

Shiri

et al. 2020

Journal of Vibration and Control

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The visco-elastic dampers can be economically designed for response reduction of dynamical systems. Recent developments in fractional calculus have affected the modeling of visco-elastic materials. The fractional models for visco-elastic dampers, which are parsimonious, require fewer parameters in comparison with other models. In this paper, we use the visco-elastic dampers for control of structural responses. The visco-elastic damper utilizes three important parameters including damping coefficient, stiffness, and fractional order. The dynamic model of the building with visco-elastic dampers can be acquired by a system of fractional differential equations, which includes both fractional and ordinary derivatives. We apply spline collocation methods for obtaining the numerical solution of this complex system. The collocation method is implemented in a graded mesh. The discrete data of earthquake are smoothed by spline interpolation of higher degree. The introduced method is used to simulate the response of a structure with active and passive controllers. A comparison of using different dampers is considered. Also, [Formula: see text] norm of the transform function is used for response analysis. The results of simulations for four-story and 10-story buildings show significant reductions in structural responses. Moreover, our analysis presents that the large variety of values can be used for parameters of the visco-elastic damper to provide flexibility in designing appropriate visco-elastic-dampers.

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A freely damped oscillating fractional dynamic system modeled by fractional Euler–Lagrange equations

Cited by 13 publications

References 45 publications

Research on Fractional-Order Global Fast Terminal Sliding Mode Control of MDF Continuous Hot-Pressing Position Servo System Based on Adaptive RBF Neural Network

Research on Fractional-Order Global Fast Terminal Sliding Mode Control of MDF Continuous Hot-Pressing Position Servo System Based on Adaptive RBF Neural Network

Improvement of Mathematical Model for Sedimentation Process

Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models

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