Studies On Coupling Dynamics Of Spacecraft With Multiple Liquid-filled Tanks And Maneuvering Flexible Appendages

The sloshing of liquid fuel and vibration of the flexible appendage will inevitably happen during spacecraft orbital transfer, attitude adjustment, appendage maneuver and so on, and result in complex coupling dynamics of the spacecraft system, such as rigid-liquid couple, rigid-flexible couple, rigid-liquid-flexible couple, etc, which could lead to the instability of the spacecraft system. Based on this background, the coupling dynamics of the spacecraft with multiple liquid-filled cylindrical tanks and maneuvering flexible appendages under low gravity environment are systematically studied in this thesis,and the specific topics are shown as follows:Firstly, the curved free surface of liquid in a cylindrical tank caused by surface intension under low gravity environment is considered. The generalized state equation of liquid sloshing system is obtained by expanding the lateral and pitching sloshing boundary condition of the free surface to a Fourier-Bessel series, respectively. The formulas of sloshing characteristics including wave height, sloshing frequencies, sloshing force and sloshing moment are deduced. A new semi-analytical method for analyzing the characters of liquid sloshing in cylindrical tank under low gravity environment is obtained. The detail effects of sloshing parameters including liquid-filling depth, exciting frequency and Bond number on the sloshing characteristics are investigated by means of numerous numerical experiments, and the convergence, applicability and correctness of the present algorithm are validated.Secondly, the carrier motion equations of a representative point in liquid-filled cylindrical tank in spacecraft are deduced, and the carrier potential function equations of liquid in the tank are given according to wall boundary conditions. The rigid-liquid coupled dynamic state equations of spacecraft system are presented, in which, the state vectors of equations consist of the modal coordinates of relative potential function and the modal coordinates of wave height. The coupling dynamic state equations of the main body are deduced using the Lagrange’s equations in terms of general quasi-coordinates. Correspondingly, the rigid-liquid coupled dynamics state equations of whole systems of spacecraft are obtained. A new modular method for analyzing the dynamics of spacecraft with multiple liquid-filled cylindrical tanks is presented and relevant modularized computer simulation program is coded. Through numerical example simulations, the influences of parameters on the dynamics of spacecraft are studied, in which the parameters include layouts of multi-tanks, uneven fuel consumption, driving mode and so on. Meanwhile, the correctness of the present method is validated.Thirdly, a concise expression of rotation matrixes is given through selecting rotation plane as the working plane of the body coordinates of maneuvering flexible appendage. Partial differential equations of appendages are derived based on theory of the Bernoulli-Euler beam. The formulation for dynamic interaction forces and moments between the appendage and main body at the fixed points are obtained by using the D’Alembert’s principle. The ordinary differential rigid-flexible coupled equations of spacecraft system are given by using the Lagrange’s equations in terms of general quasi-coordinates. The correctness of the proposed theoretical deduction and the accuracy of the corresponding calculating program are both verified by comparing the results with pertinent references.Fourthly, the coupling dynamic state equations for spacecraft with multiple liquid-filled cylindrical tanks and flexible appendages are deduced by means of the uniform Lagrange’s equations in terms of general quasi-coordinates. Subsequently, a completed computing system and a simulation platform for the rigid-liquid-flexible or rigid-liquid-flexible-controlled coupled dynamics analysis for spacecraft with multiple liquid-filled cylindrical tanks and flexible appendages are obtained. The rigid-liquid-flexible coupled dynamics of the spacecraft with multiple flexible appendages when under different working conditions are studied through example simulation.Lastly, an adapted terminal sliding mode controller for the attitude maneuvering and orbit target tracking of spacecraft is designed. The rigid-liquid-controlled coupled dynamics of spacecraft with one liquid-filled cylindrical tank are studied through numerical examples and the results show that: although the attitude and orbit of spacecraft are precisely controlled and the liquid sloshing in the tank is effectively suppressed by the present controller, a rigid-liquid-control coupled resonance phenomenon is obviously occurs when the same controller is applied to a spacecraft with multiple liquid-filled tanks, and the resonance phenomenon will seriously influence the control precision and the stability of the attitude and orbit of spacecraft. However, not only the rigid-liquid-control coupled resonance has been effectively avoid, but also the orbit and attitude of the spacecraft have been precisely controlled by the proposed composite controller that combined the input shaping technology and the formal adapted terminal sliding mode controller.In conclusion, a modular full-mode method for spacecraft with multiple liquid-filled cylindrical tanks and flexible appendages is presented. The problems arising from the inadequately modeling for liquid sloshing dynamics by traditional equivalent mechanical model in studying liquid filled spacecraft dynamics are effectively avoided and thus a solid foundation is laid for the further researches.