Arbitrary Decay Rate for Euler-Bernoulli Beam by Backstepping Boundary Feedback

We consider a problem of stabilization of the Euler-Bernoulli beam. The beam is controlled at one end (using position and moment actuators) and has the ldquoslidingrdquo boundary condition at the opposite end. We design the controllers that achieve any prescribed decay rate of the closed loop system...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2009-05, Vol.54 (5), p.1134-1140
Main Authors: Smyshlyaev, A., Bao-Zhu Guo, Krstic, M.
Format: Article
Language:English
Subjects:
Actuators
Applied sciences
Backstepping
Beams (structural)
Boundary conditions
boundary control
Computer science
control theory
systems
Control design
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Controllers
Decay rate
Design engineering
distributed parameter systems
Eigenvalues and eigenfunctions
Euler-Bernoulli beam
Euler-Bernoulli beams
Exact sciences and technology
Feedback
Integral equations
Open loop systems
Riesz basis
Schrodinger equation
Schroedinger equation
Transformations
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Description
Summary:We consider a problem of stabilization of the Euler-Bernoulli beam. The beam is controlled at one end (using position and moment actuators) and has the ldquoslidingrdquo boundary condition at the opposite end. We design the controllers that achieve any prescribed decay rate of the closed loop system, removing a long-standing limitation of classical ldquoboundary damperrdquo controllers. The idea of the control design is to use the well-known representation of the Euler-Bernoulli beam model through the Schrodinger equation, and then adapt recently developed backstepping designs for the latter in order to stabilize the beam. We derive the explicit integral transformation (and its inverse) of the closed-loop system into an exponentially stable target system. The transformation is of a novel Volterra/Fredholm type. The design is illustrated with simulations.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2013038