Nonlinear Dynamics

, Volume 51, Issue 3, pp 365–377 | Cite as

Control based bifurcation analysis for experiments

Original Paper

Abstract

We introduce a method for tracking nonlinear oscillations and their bifurcations in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system nor the ability to set its initial conditions. Instead it relies on feedback stabilizability, which makes the approach applicable in an experiment. This is demonstrated with a proof-of-concept computer experiment of the classical autonomous dry-friction oscillator, where we use a fixed time step simulation and include noise to mimic experimental limitations. For this system we track in one parameter a family of unstable nonlinear oscillations that forms the boundary between the basins of attraction of a stable equilibrium and a stable stick-slip oscillation. Furthermore, we track in two parameters the curves of Hopf bifurcation and grazing-sliding bifurcation that form the boundary of the bistability region.

Keywords

Bifurcation analysis Numerical continuation Hybrid experiments Hardware-in-the-loop 

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Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of EngineeringKing’s College, University of AberdeenAberdeenUK
  2. 2.Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering MathematicsQueen’s Building, University of BristolBristolUK

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