HOPF bifurcation and stability conditions for a class of nonlinear mass regulation systems with delay

Abstract

The underwater glider platform is equipped with a mass block adjustment system, which can directly control the roll angle and pitch angle through mass block adjustment, and indirectly control the heading angle through the coupling of profile motion. As the underwater glider energy and space limitations drive the low power and low frequency control, it will inevitably lead to the underwater glider attitude adjustment process is subject to the delay problem of mass motion state signal feedback, the delay time and the nonlinear and coupling characteristics fused together more likely to cause the instability of the control system. In this paper, the time delay problem in the attitude control of underwater glider is summarized as a class of nonlinear stability problems with time delay parameters. The HOPF bifurcation phenomenon caused by the time delay parameter is discussed, and the critical time delay conditions for HOPF bifurcation generation are given. The effect of the time delay parameter on the bifurcation direction and the stability of the periodic solution is analyzed using the central flow pattern method. Finally, the correctness of the theoretical analysis is verified by numerical simulation, which provides a theoretical basis for the platform stability control and drive system design of the underwater glider.