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On the Controllability of the Rotation of a Flexible Arm

  • W. Krabs
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)

Abstract

Considered is the rotation of a flexible arm in a horizontal plane about an axis through the arm’s fixed end and driven by a motor whose torque is controlled. The model was derived and investigated computationally by Sakawa for the case that the arm is described as a homogeneous Euler beam. The resulting equation of motion is a partial differential equation of the type of a wave equation which is linear with respect to the state, if the control is fixed, and non-linear with respect to the control.

Considered is the problem of steering the beam, within a given time interval, from the position of rest for the angle zero into the position of rest under a certain given angle.

At first we show that, for every L 2-control which is suitably bounded, there is exactly one (weak) solution of the initial boundary value problem which describes the system without the end condition.

Then we present an iterative method for solving the problem of controllability and discuss its convergence.

1991 Mathematics Subject Classification

93B05 93C10 93C15 

Key words and phrases

Controllability rotation of a flexible arm homogeneous Euler beam 

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References

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    W. Krabs: On Time-Optimal Boundary Control of Vibrating Beams. In: Control Theory for Distributed Parameter Systems and Applications, edited by F. Kappel, K. Kunisch, W. Schappacher. Lecture Notes in Control and Information Sciences No 54, Springer-Verlag: Berlin -Heidelberg -New York -Tokyo 1983, pp. 127 – 137.CrossRefGoogle Scholar
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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • W. Krabs
    • 1
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtWest Germany

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