Derivative-Less Arclength Control-Based Continuation for the Experimental Identification of Nonlinear Frequency Responses

This study focuses on the continuation process that is inherent to control-based continuation. Existing continuation procedures can be separated in two families. Similarly to numerical continuation, derivative-based methods find the solution of an objective function, the derivatives of which are estimated using finite differences. In mapping-based methods, the input parameter space is exhaustively or partially explored during the experiment. The features of interest can then be extracted during a post-processing phase or in parallel to the experiment. A novel arclength continuation procedure is developed in this paper. It requires neither the estimation of derivatives nor the identification of responses outside the features of interest, thus simplifying and accelerating the continuation process. The method is demonstrated numerically using a Duffing oscillator.