Exploring the dynamics of nonlinear experiments using control-based continuation Seminar

As mechanical structures are increasingly designed to be lighter and more flexible than historically has been the case, nonlinear behaviour is increasingly being observed during experimental tests. While a significant effort has been, and is, devoted to the mathematical modelling and numerical analysis of nonlinear systems, relatively little research addresses the issue of rigourous experimental testing. In fact, until now, there has been no general, systematic method that can directly measure and characterise nonlinear dynamic behaviours during laboratory tests. Methods commonly used to test nonlinear systems are usually simple extensions of linear techniques (sine sweeps, etc). Time series are collected for a whole range of excitation parameters and one relies on post-processing tools to understand the behaviour of the system. So far, this sort of approach has not allowed quantitative comparisons between experiments and mathematical models; hence it is extremely challenging to incorporate nonlinear features into model development and validation processes.

In this talk, I will present a method, control-based continuation (CBC), which uses sensors and actuators to intelligently probe a physical system. Combining feedback control with numerical continuation algorithms, CBC modifies, on-line, the excitation applied to the system in order to isolate the nonlinear behaviours of interest. In this way, CBC offers the best conditions to analyse these dynamic features in detail, to follow them as inputs and controllable parameters are changed, and to detect and track boundaries between qualitatively different types of behaviours.