We demonstrate a method for tracking oscillations and their stability boundaries (bifurcations) in nonlinear systems. Our method does not require an underlying model of the dynamical system but instead relies on feedback stabilizability. Our method allows one to determine bifurcations of the dynamical system without the need to observe the transient oscillations for a long time to determine their decay or growth. Moreover, in the context of hybrid experiments, which couple experiments and computer simulations bidirectionally and in real-time, our method is able to overcome the presence of coupling delays (or, more generally, unknown actuator dynamics), which is a fundamental problem that is currently limiting the use of hybrid testing. We illustrate the basic ideas with a computer simulation (including coupling delays and noise) of a prototype nonlinear hybrid experiment: a real pendulum coupled at its pivot to a computer simulation of a vertically excited mass-spring-damper system.
|Publication status||Accepted/In press - Apr 2008|
Bibliographical noteAdditional information: Preprint of a conference paper to be given at the 7th European Conference on Structural Dynamics, 7-9 July 2008, Southampton, UK, organised by the European Association for Structural Dynamics (EASD).
- bifurcation analysis
- coupling delay
- hybrid testing
- numerical continuation