Nonlinear dynamics model of liquid-filled spacecraft and its fuzzy wave-based PID control method

During the flight of liquid-filled spacecraft, attitude maneuvering will induce nonlinear sloshing of the liquid fuel in the storage tanks. Meanwhile, liquid sloshing can also have an innegligible impact on the attitude of main rigid body. In response to this research background, this paper investigates the dynamic modeling and control methods of liquid-filled spacecraft, an under-actuated nonlinear system. Firstly, the nonlinear characteristics of the equivalent bouncing ball model (BBM) for liquid sloshing was analyzed. The dynamic equation of the model was transformed into a non-standard form of the Duffing equation, and its amplitude-frequency characteristics were studied using the multi-scaled method, revealing the bifurcation phenomenon. Secondly, based on the engineering application background, the application working conditions of the equivalent model were extended to three-dimensional Cassini storage tanks, and a rigid-liquid coupled dynamic equation system for liquid rockets was established. Finally, an improved PID control method based on fuzzy theory and wave theory (fuzzy wave-based PID, FWPID) was proposed. Through numerical analysis, it was demonstrated that the FWPID control method can simultaneously achieve target tracking and liquid sloshing suppression. Compared to traditional PID controller, the FWBPID proposed in this paper is more suitable for controlling under-actuated systems.