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Abstract
Controlbased continuation is technique for tracking the solutions and bifurcations of nonlinear experiments. The basic idea is to apply the method of numerical continuation to a feedbackcontrolled physical experiment. Since in an experiment it is not (generally) possible to set the state of the system directly, the control target is used as a proxy for the state. The challenge then becomes to determine a control target such that the control is noninvasive, that is, it stabilises a steadystate (or periodic orbit) of the original openloop experiment without altering it otherwise. Once implemented, controlbased continuation enables the systematic investigation of the bifurcation structure of a physical system, much like if it was numerical model. However, stability information (and hence bifurcation detection and classification) is not readily available due to the presence of stabilising feedback control. This paper uses methods from the system identification community to extract stability information in the form of Floquet multipliers from the closedloop experiment, thus enabling the direct detection of bifurcations. In particular, it is shown that a periodic autoregressive model with exogenous inputs (ARX) can be constructed that approximates the timevarying linearisation of the experiment around a particular periodic orbit. This method is demonstrated using a physical nonlinear tuned mass damper.
Original language  English 

Pages (fromto)  54–64 
Number of pages  11 
Journal  Mechanical Systems and Signal Processing 
Volume  84 Part B 
Early online date  20 Jan 2016 
DOIs  
Publication status  Published  1 Feb 2017 
Keywords
 numerical continuation
 bifurcation theory
 system identification
 feedback control
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Dive into the research topics of 'Controlbased continuation: bifurcation and stability analysis for physical experiments'. Together they form a unique fingerprint.Projects
 1 Finished

Systematic experimental exploration of nonlinear structures with controlbased continuation
1/09/13 → 1/09/15
Project: Research
Profiles

Dr David A W Barton
 Department of Engineering Mathematics  Reader in Engineering Maths
 Applied Nonlinear Mathematics
 Systems Centre
Person: Academic , Member