An Optimal Control of Transverse Vibrations of anEuler-Bernoulli Beam-String Complex System


KÜÇÜK İ. , ÇINAR M.

The International conference of Applied and Engineering Mathematics, Londrina, Brazil, 5 - 07 July 2017

  • Publication Type: Conference Paper / Full Text
  • City: Londrina
  • Country: Brazil

Abstract

In this paper, an optimal control of transverse
vibrations of an Euler-Bernoulli beam and string complex
system is studied. The dynamic response of the system is
measured by a performance index that consists of a modified
energy functional of two coupled structures at the terminal time
and the expenditure of the control forces as a penalty term.
The minimization of the performance index over these forces
is subject to the equation of motion governing the structural
vibrations, the imposed initial condition as well as the boundary
conditions. The optimal control of distributed parameter
systems is transformed into the optimal control of a linear time-invariant
lumped-parameter systems by employing Galerkin
method in space. Fourier series approximation with unknown
Fourier coefficients and frequencies is used to parameterize
the control function. The applicability and effectiveness of the
proposed method is demonstrated by a numerical example.