Bifurcations in basic models of delayed force control

Li Zhang, Gabor Stepan

Research output: Contribution to journalArticle


Basic single-degree-of-freedom mechanical models of force control are presented to achieve desired contact forces between actuators and objects. Nonlinear governing equations are constructed for both collocated and non-collocated force sensor configurations. The models take into account large time delays in the feedback loop, which may occur, for example, in case of human or remote force control. The corresponding stability charts are compared for the collocated and non-collocated cases. The bifurcations at the stability boundaries are analyzed in the presence of the relevant nonlinearity that is originated in the saturation of the actuation. The stability properties as well as the nonlinear vibrations for the two sensor locations are compared also from the viewpoint of the achievable maximal proportional gains. The bifurcation calculations are done with the method of multiple scales and normal form calculations. The results on global dynamic properties are supported with numerical simulations, and the two force control strategies are discussed from application viewpoint.

Original languageEnglish
Pages (from-to)99-108
Number of pages10
JournalNonlinear Dynamics
Issue number1
Publication statusPublished - Jan 1 2020


  • Delay
  • Force control
  • Hopf bifurcation
  • Method of multiple scales
  • Period-doubling bifurcation

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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