Method for identifying models of nonlinear systems using linear time periodic approximations

This work presents a new method for identifying models of nonlinear systems from experimental measurements. The system is first forced to oscillate in stable periodic orbit, and then a small impulsive disturbance force is used to perturb the system slightly from that orbit. One then measures the response until the system returns to the periodic orbit. If the nonlinearities in the system are sufficiently smooth and the perturbation from the periodic orbit is sufficiently small, then one can linearize the perturbed response about the periodic orbit and approximate the system as linear time periodic. One of a variety of methods can then be used to extract the time varying modal model of the system from the response. The extracted modes can be used to construct a time periodic state transition matrix and state coefficient matrix, which describe the system's nonlinear dynamics over a range of the states. The resulting model for the nonlinear system encompasses that portion of the state space is traversed by the system during its periodic orbit.