Application of control-based continuation to a nonlinear structure with harmonically coupled modes

Ludovic Renson*, Alexander D Shaw, David Barton, Simon Neild

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

43 Citations (Scopus)
210 Downloads (Pure)


This paper presents a systematic method for exploring the nonlinear dynamics of multi-degree-of-freedom (MDOF) physical experiments. To illustrate the power of this method, known as control-based continuation (CBC), it is applied to a nonlinear beam structure that exhibits a strong 3:1 modal coupling between its first two bending modes. CBC is able to extract a range of dynamical features, including an isola, directly from the experiment without recourse to model fitting or other indirect data-processing methods.

Previously, CBC has only been applied to (essentially) single-degree-of-freedom experiments; in this paper we show that the required feedback-control methods and path-following techniques can equally be applied to MDOF systems. A low-level broadband excitation is initially applied to the experiment to obtain the requisite information for controller design and, subsequently, the physical experiment is treated as a `black box' that is probed using CBC. The invasiveness of the controller used is analysed and experimental results are validated with open-loop measurements. Good agreement between open- and closed-loop results is achieved, though it is found that care needs to be taken in dealing with the presence of higher-harmonics in the force applied to the structure.
Original languageEnglish
Pages (from-to)449-464
Number of pages16
JournalMechanical Systems and Signal Processing
Early online date1 Nov 2018
Publication statusPublished - 1 Apr 2019

Structured keywords

  • Engineering Mathematics Research Group


  • nonlinear dynamics
  • experiment
  • control-based continuation
  • multi-degree-of-freedom
  • modal interaction
  • isola


Dive into the research topics of 'Application of control-based continuation to a nonlinear structure with harmonically coupled modes'. Together they form a unique fingerprint.

Cite this