Numerical Continuation in a Physical Experiment: Investigation of a Nonlinear Energy Harvester

Abstract

In this paper, we demonstrate the use of control-based continuation within a physical experiment: a nonlinear energy harvester, which is used to convert vibrational energy into usable electrical energy. By employing the methodology of Sieber et al. (2008, “Experimental Continuation of Periodic Orbits Through a Fold,” Phys. Rev. Lett., 100(24), p. 244101), a branch of periodic orbits is continued through a saddle-node bifurcation and along the associated branch of unstable periodic orbits using a modified time-delay controller. At each step in the continuation, the pseudo-arclength equation is appended to a set of equations that ensure that the controller is noninvasive. The resulting nonlinear system is solved using a quasi-Newton iteration, where each evaluation of the nonlinear system requires changing the excitation parameters of the experiment and measuring the response. We present the continuation results for the energy harvester in a number of different configurations.