Control-Based Continuation for self-oscillating systems: Application to flow induced vibrations

An enhanced version of Control-Based Continuation (CBC) is proposed to carry out experimental continuation on self-sustained systems, whose working frequency is not known a priori. Our approach combines three main stages: an online frequency tracking algorithm using an embedded phase-locked loop, an online noninvasive CBC stabilization loop using adaptive filters, and a derivative free arc continuation algorithm. As a proof of concept, it is implemented to study an elementary aero-vibro-acoustical model of buzzing lips that exhibits self-sustained oscillations with a wide range of fundamental frequency. The model relies on interactions between an acoustical resonator (the air column) and an oscillating valve (the lips) through a nonlinear flow. The Control-Based Continuation is implemented without taking advantage of the modelling equations, mimicking a real experiment. This results in a pseudo-experimental bifurcation diagram, showing strong accordance with virtual open-loop testing and numerical continuation, which proves robustness of our method.