Robust identification of backbone curves using control-based continuation

Control-based continuation is a recently developed approach for testing nonlinear dynamic systems in a controlled manner and exploring their dynamic features as system parameters are varied. In this paper, control-based continuation is adapted to follow the locus where system response and excitation are in quadrature, extracting the backbone curve of the underlying conservative system. The method is applied to a single-degree-of-freedom oscillator under base excitation, and the results are compared with the standard resonant-decay method.