Exponentially stabilizing boundary control of string-mass systems

Catalin F. Baicu, Christopher D. Rahn, Darren M. Dawson

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Exponentially stabilizing controllers are derived for the transverse vibration of a string-mass system modeled by the one-dimensional wave equation with a pinned and a controlled boundary condition. Lyapunov's theory for distributed parameter systems, the Meyer-Kalman-Yakubovitch Lemma, and integral inequalities prove that a class of boundary controllers provide strong exponential stability. These controllers are designed so that the transfer function between boundary slope and velocity satisfies a restricted strictly positive real condition. An example controller, consisting of boundary position, velocity, slope, slope rate, and integrated slope feedback, is implemented on a laboratory test stand. In experimental impulse response tests, the controlled response decays six times faster than the open-loop response and has half the response amplitude.

Original languageEnglish (US)
Pages (from-to)491-502
Number of pages12
JournalJVC/Journal of Vibration and Control
Volume5
Issue number3
DOIs
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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