Parametric Identification of a Base-Excited Single Pendulum

A harmonic balance based identification algorithm was applied to the simulated single pendulum with horizontal base-excitation. The purpose of this simulation was to examine the applicability of the algorithm on parametrically excited, whirling chaotic systems. Modifications were adopted to adapt to the whirling systems. The system was supposed to be unknown except only the excitation frequency. Linear interpolation functions and the Fourier series functions were tested to approximate unknown nonlinear functions in the governing differential equation. After extracting unstable periodic orbits, all of the parameters were simultaneously identified. By direct comparison, Poincaré section plots and reconstructed phase portrait techniques, it was shown that the identified system had similar dynamical characteristics to the original simulated pendulum, which implies the effectiveness of the examined algorithm.