Constant-gain linear feedback control of piecewise linear structural systems via nonlinear normal modes

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4 Scopus citations


We present a technique for using constant-gain linear position feedback control to implement eigen-structure assignment of n-degrees-of-freedom conservative structural systems with piecewise linear nonlinearities. We employ three distinct control strategies which utilize methods for approximating the nonlinear normal mode (NNM) frequencies and mode shapes. First, the piecewise modal method (PMM) for approximating NNM frequencies is used to determine n constant actuator gains for eigenvalue (pole) placement. Secondly, eigenvalue placement is accomplished by finding an approximate single-degree-of-freedom reduced model with one actuator gain for the mode to be controlled. The third strategy allows the frequencies and mode shapes (eigenstructure) to be placed by using a full n × n matrix of actuator gains and employing the local equivalent linear stiffness method (LELSM) for approximating NNM frequencies and mode shapes. The techniques are applied to a two-degrees-of-freedom system with two distinct types of nonlinearities: a bilinear clearance nonlinearity and a symmetric deadzone nonlinearity.

Original languageEnglish (US)
Pages (from-to)1535-1558
Number of pages24
JournalJVC/Journal of Vibration and Control
Issue number10
StatePublished - Oct 2004


  • Eigenstructure assignment
  • Nonlinear normal modes
  • Piecewise linear nonlinearities

ASJC Scopus subject areas

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


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