External Synchronization of A Hysteretic System With A Duffing System By Feedback Control Strategy

Two or more dynamical systems can achieve external synchronization motions with an especially designed controller, in which one dynamical system is considered as the master, and the other as the slave. In this paper, a general strategy of feedback control to carry out the external synchronization is firstly introduced. The master system consists of a hysteretic device to account for the friction phenomenon, and the slave system comprises a hardening stiffness component that can generate the third order displacement as a Duffing system. The slave system can keep in synchronization with the movements of the master via a feedback control strategy. A stability analysis of the synchronization errors is conducted. Different synchronization motions under different system parameters are simulated, based on which discussions are made for the effects of the controller parameters.