Exponential Stabilization of a Transversely Vibrating Beam by Boundary Control Via Lyapunov’s Direct Method

Fard, Mehrdad P.; Sagatun, Svein I.

doi:10.1115/1.1369111

Cited by 45 publications

(13 citation statements)

References 11 publications

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“…For example, there are several contributions on control problems with fixed spatial domain for linear PDEs, 16,17,19 nonlinear PDEs, [20][21][22] problems with spatially distributed actuation, 17,19,23 and boundary control problems. 20,21,24 Despite distributed parameter control strategies, state estimation algorithms for parabolic PDEs are less developed and are of interest in the context of temperature estimation in the crystal growth process. In particular, Xu et al 25 provide a simple observer for dissipative bilinear systems with weak error convergence to zero.…”

Section: Introductionmentioning

confidence: 99%

Temperature distribution reconstruction in Czochralski crystal growth process

2014

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A mechanical geometric crystal growth model is developed to describe the crystal length and radius evolution. The crystal radius regulation is achieved by feedback linearization and accounts for parametric uncertainty in the crystal growth rate. The associated parabolic partial differential equation (PDE) model of heat conduction is considered over the timevarying crystal domain and coupled with crystal growth dynamics. An appropriately defined infinite-dimensional representation of the thermal evolution is derived considering slow time-varying process effects. The computational framework of the Galerkin's method is used for parabolic PDE order reduction and observer synthesis for temperature distribution reconstruction over the entire crystal domain. It is shown that the proposed observer can be utilized to reconstruct temperature distribution from boundary temperature measurements. The developed observer is implemented on the finite-element model of the process and demonstrates that despite parametric and geometric uncertainties present in the model, the temperature distribution is reconstructed with the high accuracy.

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Section: Introductionmentioning

confidence: 99%

Temperature distribution reconstruction in Czochralski crystal growth process

2014

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“…The controllers may also be difficult to implement from the engineering point of view since full states measurements or observers are often required. To avoid the problems associated with the truncated-model-based design, control methodologies such as variable structure control [6] and boundary control [7] can be used. In this paper, we design the boundary control based on the PDE directly to avoid the above mentioned problems.…”

Section: Introductionmentioning

confidence: 99%

“…Boundary control has been applied to beams in [8,9] where boundary feedback was used to stabilize the wave equations and design active constrained layer damping. In [7], the coupled model for longitudinal and transverse beam was derived, and the exponential stabilization of a beam in free transverse vibration, via boundary control was shown.…”

Section: Introductionmentioning

confidence: 99%

Top angle control and vibration reduction of flexible marine risers

How

Choo

2008

2008 SICE Annual Conference

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In this article, control of the flexible marine riser top angle and the reduction of forced vibration under a timevarying distributed load are considered using boundary control approach. A torque actuator is introduced in the upper riser package and a boundary control law is designed for riser angle control and vibration reduction with guaranteed closed-loop stability. The proposed controller is independent of system parameters, thus possesses stability robustness to variations in parameters. Numerical simulations with a worst case excitation are provided to verify the effectiveness of the approach presented.

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“…There are several controller designs in the literature for stabilizing and controlling beam bending (see, for example, [32,88,101,27,40]). We design a perturbation observer-based controller to facilitate a motion planning-based tracking controller for bending.…”

Section: Controlmentioning

confidence: 99%

Bio-Inspired Integrated Sensing and Control Flapping Flight for Micro Aerial Vehicles

Chung¹

2012

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Exponential Stabilization of a Transversely Vibrating Beam by Boundary Control Via Lyapunov’s Direct Method

Cited by 45 publications

References 11 publications

Temperature distribution reconstruction in Czochralski crystal growth process

Temperature distribution reconstruction in Czochralski crystal growth process

Top angle control and vibration reduction of flexible marine risers

Bio-Inspired Integrated Sensing and Control Flapping Flight for Micro Aerial Vehicles

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