Principal resonance and singularity of a hysteretic nonlinear control system with a PID controller

A hysteretic closed-loop nonlinear control system with a PID controller was studied. A model based on Backlash neutral network was adopted to approach the hysteretic nonlinear part of the system, the dynamic model of the system was established. The principal resonance of the system under a simple harmonic excitation was studied. The bifurcation equation of the system was obtained with the averaging method, and then the system's singularity was analyzed completely, the transition sets and bifurcation plots were gained. The effects of the system's parameters on its unfolding and bifurcation parameters were discussed. The results provided a theoretical guidance for selecting the system's parameters.