Exponential Stabilization of a Transversely Vibrating Beam via Boundary Control

Fard, Mehrdad P.; Sagatun, Svein I.

doi:10.1006/jsvi.2000.3252

Cited by 44 publications

(22 citation statements)

References 10 publications

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“…Applications are in fluid dynamics (Aamo 2003;Schuster et al 2008), in mechanical systems applied to beams (Fard and Sagatun 2001) and strings (Morgül 1994), and in thermodynamic systems (Boskovic et al 2001;Liu 2003). Boundary control applied to chemical systems is found in Boskovic and Krstic (2002), Smyshlyaev and Krstic (2007), and Meurer and Kugi (2009), and an application to stabilize an unstable wave equation is described in Krstic et al (2008).…”

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confidence: 99%

Boundary Control of a Horizontal Oil Reservoir

Sagatun

2010

SPE Journal

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This article presents a model-based boundary-control strategy for the drainage of a horizontal oil reservoir with a gas cap. The control objective is to maximize the net present value (NPV) of the produced oil from a well before gas is coned into the well. A nonlinear partial-differential equation (PDE) representing the reservoir dynamics has been derived. The linearized model is a parabolic PDE with mixed boundary conditions. The linearized model is used together with an output-feedback boundary-control law. Performance guarantee in the linear case is proved.

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confidence: 99%

Boundary Control of a Horizontal Oil Reservoir

Sagatun

2010

SPE Journal

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“…Zhang et al (2000) introduced boundary controllers for a general class of non-linear string-actuator systems. Fard and Sagatun (2001) designed a boundary control law consisting only of feedback from the slope and velocity of the beam at the boundary to stabilize the transversal vibration of a beam exponentially and shown that exponential stability can be achieved via boundary control without resorting to truncation of model. Guo and Guo (2005) constructed a high-gain adaptive control and regulator to guarantee asymptotic stability of an Euler-Bernoulli beam with control and uncertain amplitude of harmonic disturbance at free end.…”

Section: Introductionmentioning

confidence: 99%

Active control of axial dynamic response of deepwater risers with Linear Quadratic Gaussian controllers

Zhang

2015

Ocean Engineering

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“…In [18], a P-type steady-state iterative learning control scheme is applied to the boundary control of a class of nonlinear processes, which are described by PDEs. In [22] and [23], boundary control is designed to stabilize string and beam systems, respectively. In [22] and [23], boundary control is designed to stabilize string and beam systems, respectively.…”

Section: Introductionmentioning

confidence: 99%

Boundary and Distributed Control for a Nonlinear Three‐Dimensional Euler‐Bernoulli Beam Based On Infinite Dimensional Disturbance Observer

Jiang

Liu

2016

Asian Journal of Control

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Control problems in spatially distributed systems are challenging because the disturbance is of infinite dimensions. To this end, this paper discusses an infinite dimensional disturbance observer design, which is illustrated based on a partial differential equation (PDE) model of a nonlinear three-dimensional Euler-Bernoulli beam. The basic idea of the observer design is to modify the estimations based on the difference between the estimated output and actual output. Moreover, an auxiliary parameter system is established to help with the analysis. Then a Lyapunov function candidate consisting of the energy of the system, the observer error and an auxiliary term is given. After a series of analyses of the function, distributed controllers and boundary controllers based on the proposed observer are given to restrain vibration. Finally, by numerical simulations, the convergence of the observer is demonstrated, and the efficacy of control performance is also shown.

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Exponential Stabilization of a Transversely Vibrating Beam via Boundary Control

Cited by 44 publications

References 10 publications

Boundary Control of a Horizontal Oil Reservoir

Boundary Control of a Horizontal Oil Reservoir

Active control of axial dynamic response of deepwater risers with Linear Quadratic Gaussian controllers

Boundary and Distributed Control for a Nonlinear Three‐Dimensional Euler‐Bernoulli Beam Based On Infinite Dimensional Disturbance Observer

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