Dynamic effects of delayed feedback control on nonlinear vibration isolation floating raft systems

Vibration suppression and chaotification are the key issues in the study of the concealment capability of underwater vehicles. Time delay control is superior in chaotification, but the involved dynamics are sensitive and complex. This paper presents an analysis to obtain an analytical solution of the nonlinear delay differential equations and determine the effect of delay control on the vibration amplitude. Besides, by checking the stability of the analytical solution, dependence of chaotification upon the time delay control parameters is examined. Based on the theoretical derivation, the effects of different configurations of system parameters and delay control parameters on vibration amplitude are demonstrated in numerical simulation. What׳s more, the outcome of our results shows the significant role the time delay control plays in vibration suppression and chaotification. According to the analytical solution and stability analysis, not only can the appropriate delay be found to reduce the vibration amplitude, but also the suitable delay control setting can be selected for chaotification.