Online Control-Based Continuation of Nonlinear Structures Using Adaptive Filtering

Control-Based Continuation uses feedback control to follow stable and unstable branches of periodic orbits of a nonlinear system without the need for advanced post-processing of experimental data. CBC relies on an iterative scheme to modify the harmonic content of the control target and obtain a non-invasive control signal. This scheme currently requires to wait for the experiment to settle down to steady-state and hence runs offline (i.e. at a much lower frequency than the feedback controller). This paper proposes to replace this conventional iterative scheme by adaptive filters. Adaptive filters can directly synthesize the control target adequately and can operate online (i.e. at the same frequency as the feedback controller). This novel approach is found to significantly accelerate convergence to non-invasive steady-state responses to the extent that the structure response can be characterized in a continuous amplitude sweep. Importantly, the stabilizing effect of the controller is not affected.