  Phase-locked loops are commonly used for shaker-based backbone tracking of
nonlinear structures. The state of the art is to tune the control parameters by
trial and error. In the present work, an approach is proposed to make backbone
tracking much more robust and faster. A simple PI controller is proposed, and
closed-form expressions for the gains are provided that lead to an optimal
settling of the phase transient. The required input parameters are obtained
from a conventional shaker-based linear modal test, and an open-loop sine test
at a single frequency and level. For phase detection, an adaptive filter based
on the LMS algorithm is used, which is shown to be superior to the synchronous
demodulation commonly used. Once the phase has locked, one can directly take
the next step along the backbone, eliminating the hold times. The latter are
currently used for recording the steady state, and to estimate Fourier
coefficients in the post-process, which becomes unnecessary since the adaptive
filter yields a highly accurate estimation at runtime.The excellent performance
of the proposed approach is demonstrated for a doubly clamped beam undergoing
bending-stretching coupling leading to a 20 percent shift of the lowest modal
frequency. Even for fixed control parameters, designed for the linear regime,
only about 100 periods are needed per backbone point, also in the nonlinear
regime. This is much faster than what has been reported in the literature so
far.
