Diffusive wave-absorbing control: example of the boundary stabilization of a thin flexible beam

Montseny, G.

doi:10.1177/1077546311419933

Cited by 6 publications

(9 citation statements)

References 28 publications

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“…The analysis and the numerical simulation of the system are considerably simplified using diffusive input/output realization of this fractional operator, which allows the diffusive closed-loop system to be represented under the traditional form dX/dt = AX, with A representing the infinitesimal generator of a semigroup on a convenient Hilbert space including a diffusive variable. Such diffusive realizations of complex non-rational operators have revealed themselves as judicious in various problems in modeling (Laudebat et al, 2004), identification (Casenave, 2011), control (Montseny, 2011), and other research thematic.…”

Section: Introductionmentioning

confidence: 99%

Passive optimal feedback control of an articulated flexible arm

Tebbikh

Kechida

2020

Journal of Vibration and Control

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This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

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Section: Introductionmentioning

confidence: 99%

Passive optimal feedback control of an articulated flexible arm

Tebbikh

Kechida

2020

Journal of Vibration and Control

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“…However, the use of fractional operators leads to some di¢ culties and problems, which come mainly from the fact that these operators are hereditary with singular kernels, and hence the numerical approximation becomes very di¢ cult and requires large memory storage capacities. To remedy these problems, the fractional control will be achieved by DIFFUSIVE REPRESENTATION OF A FRACTIONAL CONTROL 169 using the di¤usive representation [9]. This representation allows the realization of the fractional operators in non-hereditary way using linear dynamical systems of di¤usive nature.…”

Section: Introductionmentioning

confidence: 99%

“…This representation allows the realization of the fractional operators in non-hereditary way using linear dynamical systems of di¤usive nature. [9] We apply this concept to the control of a DC motor of which the transfer function is uncertain. The uncertainty is carried at the mechanical load and the current loop constant time.…”

Section: Introductionmentioning

confidence: 99%

Diffusive representation of a fractional control using adaptive partitioning algorithm

BOUDJEHEM

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Abstract. This article presents optimal fractional control. This control is based on the property of the invariance of a fractional order di¤erential equation. The problem formulation of the used control is expressed by di¤usive representation. The fractional control problem is described in a minimization form, where the global optimum represents the di¤usive realization of the controller. To determine the optimal fractional di¤usive control, an adaptive partitioning algorithm is used. As an application, we have chosen the control of a DC motor with uncertain parameters.

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“…Thereafter, the proposed control scheme is applied to the moving Euler–Bernoulli beam under axial load, for which, to the authors’ best knowledge, alternative absorbing boundary conditions have not yet been devised. In comparison, alternative absorbing boundary conditions for the simplified nonmoving Euler–Bernoulli beam without axial load, such as the classic PML approach derived by Arbabi and Farzanian (2014) or the procedure proposed by Montseny (2011), become highly problem-specific and several auxiliary partial differential equations or additional dynamic state variables are introduced.…”

Section: Introductionmentioning

confidence: 99%

Absorbing boundary layer control for linear one-dimensional wave propagation problems

Ritzberger

Schirrer

Jakubek

2016

Journal of Vibration and Control

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In this work, a boundary layer control scheme for one-dimensional wave propagation problems is presented that provides reflection-less absorption of incident waves in numerical simulations. The desired absorption properties are formulated as an optimization problem. By using the dispersion relation to predict the unbounded wave propagation as a reference trajectory, a constant-gain state-feedback boundary layer controller is found. Since no additional auxiliary variables are introduced, this approach is highly computationally efficient, making it suitable for simulations under real-time requirements. The performance of the boundary layer controller is first evaluated and demonstrated on the scalar wave equation (vibrating string), for which reference absorbing boundary conditions are well established. Afterward, the moving Euler–Bernoulli beam under axial tension is considered, for which a good absorbing performance is achieved.

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Diffusive wave-absorbing control: example of the boundary stabilization of a thin flexible beam

Cited by 6 publications

References 28 publications

Passive optimal feedback control of an articulated flexible arm

Passive optimal feedback control of an articulated flexible arm

Diffusive representation of a fractional control using adaptive partitioning algorithm

Absorbing boundary layer control for linear one-dimensional wave propagation problems

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