Control-based methods for the identification of nonlinear structures

One of the key roles of structural engineering is to describe how a structure vibrates, or "responds", when a dynamic load, or "excitation", is applied to it. Often, the assumption of linear behavior is adopted, meaning that the response to a combination of excitation signals is the combination of the responses to the signals taken individually. When this assumption does not hold, complex dynamical phenomena can arise, including the coexistence of multiple responses for the same excitation, the sudden transition from one such response to another, or responses that are not stable. They render the experimental interrogation of engineering structures particularly challenging. An emerging family of testing methods, termed control-based methods, uses feedback loops and controllers to make the interrogation exhaustive and predictable. In this context, this thesis investigates carefully two recently-introduced methods, namely control-based continuation during which the excitation is corrected or generated by a controller, and phase-locked loop testing which imposes the phase lag between the response and the excitation using feedback control. In the first part of the thesis, we aim to deepen the understanding of control-based methods with the objective to design and tune experiments more systematically, reducing the need for trial and error. In the second part of the thesis, new developments exploiting adaptive filtering are carried out to expand the capabilities of both control-based continuation and phase-locked loop testing, but also to tackle dynamical features that were never identified experimentally before. Finally, this thesis opens the way towards more robust control-based methods and, eventually, to their industrial application.