  One unique feature of nonlinear dynamical systems is the existence of
superharmonic and subharmonic resonances in addition to primary resonances. In
this study, an effective vibration testing methodology is introduced for the
experimental identification of these secondary resonances. The proposed method
relies on phase-locked loop control combined with adaptive filters for online
Fourier decomposition. To this end, the concept of a resonant phase lag is
exploited to define the target phase lag to be followed during the experimental
continuation process. The method is demonstrated using two systems featuring
cubic nonlinearities, namely a numerical Duffing oscillator and a physical
experiment comprising a clamped-clamped thin beam. The obtained results
highlight that the control scheme can accurately characterize secondary
resonances as well as track their backbone curves. A particularly salient
feature of the developed algorithm is that, starting from the rest position, it
facilitates an automatic and smooth dynamic state transfer toward one point of
a subharmonic isolated branch, hence, inducing branch switching.
