Vibration Control of Flexible Structures with Fractional Differential Active Mass Dampers.

Ikeda, Fujio; Kawata, Seiichi; Oguchi, Toshiki

doi:10.1299/kikaic.67.2798

Cited by 3 publications

(6 citation statements)

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“…From Equation (38), the poles of the matrix (A − HC) can be moved freely by the state observer gain H, and the convergence characteristics of the estimation error e(t) can be determined freely using the pole assignment method. Moreover, Equations ( 15), ( 34), ( 36), (37), and (39) produce the following relationships:…”

Section: Configuration Of Fractional-order State Observermentioning

confidence: 99%

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: Configuration Of Fractional-order State Observermentioning

confidence: 99%

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

et al. 2021

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“…Let us consider the viscoelastic system, which can be described by the following fractional differential equations [35]…”

Section: Examplementioning

confidence: 99%

Finite-Time Bounded Tracking Control for Fractional-Order Systems

et al. 2021

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This paper solves the finite-time bounded tracking control problem for fractional-order systems. Firstly, by taking the fractional derivative on state equations and error signals, a fractional-order error system is constructed, and the error signal is taken as the output vector of the error system. Secondly, a state feedback controller is introduced into the error system, and the fractional derivative of disturbance signals and desired tracking signals are combined as the disturbance signal of the error system. Thus, the original problem is converted into the input-output finite time stability problem of the closed-loop error systems. Thirdly, based on the linear matrix inequalities (LMIs), the sufficient conditions which ensure the finite-time bounded tracking for the desired tracking signals are derived. Therefore, the finite-time bounded tracking controller of the original system is obtained. Finally, simulation results elucidate the effectiveness of the controller. INDEX TERMS Finite-time bounded tracking, fractional-order systems, error systems, linear matrix inequalities.

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“…Therefore, when the assumptions of this theorem are satisfied, all of the conditions of Theorem 1 are satisfied. The optimal input of System (12) is obtained from Theorem 1 as shown in (19). Further, the first component vector of (19) is taken out and the input of System (6a)-(6b) is obtained.…”

Section: P Is the Unique Semi-positive Definite Solution Of The Riccamentioning

confidence: 99%

“…we substitute them into (19), take the first row on both sides of the equal sign, and get (22), so Theorem 5 can be proved.…”

Section: P Is the Unique Semi-positive Definite Solution Of The Riccamentioning

confidence: 99%

“…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%

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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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Vibration Control of Flexible Structures with Fractional Differential Active Mass Dampers.

Cited by 3 publications

References 0 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

Finite-Time Bounded Tracking Control for Fractional-Order Systems

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

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