An Optimal Regulator Design of Fractional Differential Systems

Ikeda, Fujio; Kawata, Seiichi; Watanabe, Atsushi

doi:10.9746/sicetr1965.37.856

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…However, it has been clarified that the feedback-gain matrix F cannot be obtained based on the above-mentioned method reported in a previous study [29]. This is because the equation resulting from differentiation directly with respect to F becomes too complicated to be appropriate for obtaining the optimal feedback-gain matrix F opt .…”

Section: Fractional-order Vibratory System With Viscoelasticitymentioning

confidence: 97%

“…The operator D 1 2 is applied to both sides of Equation ( 18) once, and then the following equation is obtained [29]:…”

Section: Fractional-order Vibratory System With Viscoelasticitymentioning

confidence: 99%

“…Therefore, the undetermined multipliers are arranged in the form of K(n × n) = k ij . As a result, the Lagrangian function can be expressed as follows [29]:…”

Section: Fractional-order Vibratory System With Viscoelasticitymentioning

confidence: 99%

“…Next, the solution obtained by the above-mentioned numerical calculation method is compared with the exact solution. The exact solution of Equation ( 15) can be given as follows using the Mittag-Leffler function E a 1 , a 2 [29,37]:…”

Section: Comparison Between Numerical and Exact Solutionsmentioning

confidence: 99%

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Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System

et al. 2021

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The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second, a fractional-order LQR is designed for a system in which fractional-order differential terms are contained in the equation of motion. An iteration-based method for solving the algebraic Riccati equation is proposed in order to obtain the feedback gains for the fractional-order LQR. Third, a fractional-order state observer is constructed in order to estimate the states originating from the fractional-order derivative term. Fourth, numerical simulations are presented using a numerical calculation method corresponding to a fractional-order state equation. Finally, the numerical simulation results demonstrate that the fractional-order LQR control can suppress vibrations occurring in the vibratory system with viscoelastic damping.

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Section: Fractional-order Vibratory System With Viscoelasticitymentioning

confidence: 97%

“…The operator D 1 2 is applied to both sides of Equation ( 18) once, and then the following equation is obtained [29]:…”

Section: Fractional-order Vibratory System With Viscoelasticitymentioning

confidence: 99%

“…Therefore, the undetermined multipliers are arranged in the form of K(n × n) = k ij . As a result, the Lagrangian function can be expressed as follows [29]:…”

Section: Fractional-order Vibratory System With Viscoelasticitymentioning

confidence: 99%

Section: Comparison Between Numerical and Exact Solutionsmentioning

confidence: 99%

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Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System

et al. 2021

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“…Reference [17] discusses the problem of complete tracking for a class of fractional-order systems in a finite-time interval, and gives fractional-order iterative learning control laws involving a local average operator associated with probability. In addition, the fractional-order system has been successfully applied to the design of the fractional-order damper, antilock braking systems, and other practical engineering problems [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Preview tracking control for a class of fractional-order linear systems

Liao

Xie

2019

Adv Differ Equ

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This paper studies the preview tracking control of a class of fractional-order linear systems. Firstly, we use the fractional derivative property to take the fractional derivative of both sides of the state equation several times, and we obtain a formal ordinary linear system. An augmented error system is constructed for the transformed ordinary linear system, the appropriate performance index function is introduced and relevant results of the optimal preview control are applied to design the optimal preview controller for the augmented error system when the reference signal is previewable. Based on the relationship between the original system and the augmented error system, the preview tracking controller of the original system can be obtained. It can guarantee the asymptotic tracking of the output of the original closed-loop system to the reference signal. The validity of the theoretical results is verified by numerical simulation.

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New pure multi-order fractional optimal control problems with constraints: QP and LP methods

Malmir

2024

ISA Transactions

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An Optimal Regulator Design of Fractional Differential Systems

Cited by 4 publications

References 10 publications

Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System

Fractional-Order LQR and State Observer for a Fractional-Order Vibratory System

Preview tracking control for a class of fractional-order linear systems

New pure multi-order fractional optimal control problems with constraints: QP and LP methods

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