Phase resonance method for nonlinear mechanical structures with phase locked loop control

Abstract

The identification of nonlinear mechanical structures is still a field of active research. Several researchers applied the concept of nonlinear normal modes for numerical nonlinear modal analysis of mechanical structures. This method can also be used for experimental identification of mechanical structures; however, successful demonstration on highly nonlinear structures with multiple degrees of freedom for input and output are not state of the art. Phase locked loop control is one method for identifying nonlinear normal modes, but the theoretical foundation of this control is limited to single degree of freedom systems and phase estimation fails if the response of higher harmonics due to nonlinear behavior is significant. Hence, an input-output blending with a modal approach is used in order to extend the single-input, single-output into a multiple-input, multiple-output controller. Furthermore, phase estimation is improved with an adaptive least-squares sine fit. The proposed method has been implemented and tested on a laboratory structure, where a mode with highly nonlinear behavior has been extracted.