Passivity Analysis of Nonlinear Euler-Bernoulli Beams

Fard, Mehrdad P.

doi:10.4173/mic.2002.4.1

Cited by 4 publications

(5 citation statements)

References 3 publications

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“…From the coordinate transformation, equation (15) and together with the BC, equation (18), give the controller which will be applied at the boundary x = 1. The controller is in the following form 9 u(1, t) =…”

Section: Boundary Controller Designmentioning

confidence: 99%

“…One can find the gain kernel by substituting equation (15) into equation (16) and with the help of the Leibniz integral rule and integration by parts, to get the following hyperbolic PDE of the gain kernel k xx (x, j) À k jj (x, j) = lk(x, j) ð19Þ…”

Section: Boundary Controller Designmentioning

confidence: 99%

“…The passivity property of nonlinear Euler-Bernoulli beams has been studied in Fard. 15 The method guarantees finite gain L 2 stability and passivity of closed-loop systems. Krstic et al 16 presented backstepping boundary controller and observer for undamped shear beams with an anticollocated setup.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Backstepping boundary control: An application to rod temperature control with Neumann boundary condition

Boonkumkrong

Kuntanapreeda

2014

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article presents a backstepping boundary control technique to stabilize the temperature of a rod. The rod is modeled by a parabolic partial differential equation with a Neumann boundary condition at one end of rod and a Dirichlet boundary condition at the other end. The rod also includes an internal heat generator to emulate an unstable behavior. Based on backstepping boundary control, a partial differential equation gain kernel of the system is determined. It is calculated numerically by using a finite difference method and then used in a control law. Since the control law requires temperatures along the rod for feedback, a Luenberger-like observer is used to estimate the temperatures. A copper rod with a heater installed inside the rod is used as an experimental plant. The control setup is anticollocation. The temperature signal at one end is sent to the observer for estimation of the temperatures along the rod. The estimated values are then fed to the controller. Simulation results using a finite difference method and experimental results are compared and used to confirm the effectiveness of the control method.

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Section: Boundary Controller Designmentioning

confidence: 99%

Section: Boundary Controller Designmentioning

confidence: 99%

See 1 more Smart Citation

Backstepping boundary control: An application to rod temperature control with Neumann boundary condition

Boonkumkrong

Kuntanapreeda

2014

Proceedings of the Institution of Mechanical Engineers, Part I:

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“…The passivity-based control problem of the flexible beam was examined by Fard [ 17 ]. The controller was applied at the beam end.…”

Section: Introductionmentioning

confidence: 99%

Passivity-based boundary control with the backstepping observer for the vibration suppression of the flexible beam

Boonkumkrong

Chinvorarat

Asadamongkon

2023

Heliyon

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“…Fard 17 investigated the boundary control of the Euler-Bernoulli beam. The control scheme was designed with the defined Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

Passivity-based boundary control for vibration suppression of the shear beam

Boonkumkrong

Chinvorarat

Asadamongkon

2022

Advances in Mechanical Engineering

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In this paper, the passivity-based boundary controller for the vibration suppression of the flexible beam is studied. The undamped shear beam model is used as a beam model. The beam is a parameter-distributed system represented by partial differential equations (PDEs). This technique uses the energy principle for control design by exploiting the passivity property of the beam. The storage or energy function of the beam is first introduced and then used to determine the passivity-based controller. The passivity of the system is proven using direct integration. The feedback system is proven in the sense of finite-gain [Formula: see text] stability. The proposed controller consists of the damping and elastic components applied at the beam end so that the domain (body) of the beam is not disturbed. The beam PDEs are treated directly without model reduction or truncation, so the control spillover problem is avoidable. The beam model PDEs are solved numerically by using the finite difference method. Numerical simulation results of the beam under control are presented to verify the performance of the control scheme.

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Passivity Analysis of Nonlinear Euler-Bernoulli Beams

Cited by 4 publications

References 3 publications

Backstepping boundary control: An application to rod temperature control with Neumann boundary condition

Backstepping boundary control: An application to rod temperature control with Neumann boundary condition

Passivity-based boundary control with the backstepping observer for the vibration suppression of the flexible beam

Passivity-based boundary control for vibration suppression of the shear beam

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