Modeling For The Rigid-Flexible Coupling Dynamics And Attitude Control Of Flexible Spacecraft

Rigid-flexible coupling dynamics and robust control of flexible multi-body spacecraft are investigate in the paper, which involves the characteristics of complicated dynamic characters, system uncertainties, input nonlinearity, external disturbances and precision control requirements. The main contents and innovative work can be summarized as follows:(1) The first-order approximate dynamic model of a flexible spacecraft is developed, the applicability of its traditional models for simulation and control are analyzed.Firstly, the finite-element model of a flexible beam is developed by using Jourdain's velocity variational principle, in which the second-order coupling term of axial deformation displacement caused by that of transverse is included. Secondly, the first-order approximate dynamic model and control model of a flexible spacecraft with attached mass are developed by using assumed mode method and Lagrange's method. Finally, the applicability of zero-order approximate dynamic model and traditional control model are analyzed with respect to the relative error of the frequency.(2) Simulation platform of symbolic and numerical compute programs is established, dynamic stiffening is validated based on this platform.The platform consists of three modules: symbolic compute module, numerical integralization module and data analyze module. The dynamic stiffening of a flexible spacecraft undergoing large maneuvering is validated based on this platform. Numerical simulations and theoretical analysis show that, firstly, the second-order term of deformation field has a significant effect on the dynamic characteristics of the system and the dynamic stiffening is accounted for; secondly, the first-order approximate dynamic model is more adaptive than the zero-order approximate dynamic model; thirdly, the simplified first-order approximate dynamic model can be used for controller design; finally, the end mass has different effects on the model frequency according to different descriptions of deformation field.(3) Fuzzy region controller of a flexible spacecraft with parameter uncertainty is developed.Firstly, systematic design method of TS fuzzy controller is provided by using piecewise Lyapunov functions based on fuzzy region model and maximal overlapped-rules group. Secondly, a sufficient condition of quadratic stability of uncertain TS fuzzy region model is presented by using linear matrix inequality method and Schur complement theory, where the premise variables of the fuzzy model adopt standard fuzzy partition. Finally, dynamic equations of a flexible spacecraft are described as uncertain TS fuzzy model, where fuzzy region controller is obtained. Numerical simulation results show that, the fuzzy region controller can make the spacecraft accomplish the maneuvering with high precision and vibration suppression in spite of parameter uncertainty.(4) Sliding mode controller of a flexible spacecraft with bounded input is developedFirstly, the sliding mode domain and reaching domain of sliding mode control system with input nonlinearity are investigated, and the design of nonlinear switching surfaces is presented. Secondly, the step-by-step sliding mode controller and moving-surface sliding mode controller are provided with mode coordinates being taken accounted into the state space equations. Finally, adaptive sliding mode controller with fuzzy boundary layer is provided, strain rate feedback controller is designed to actively suppress the vibration of flexible appendages. Simulation results show that, the controllers are robust to parameters uncertainties and external disturbances which can make the spacecraft accomplish the maneuvering with high precision and stabilization.(5) Attitude tracking controller of flexible spacecraft is developed based on estimatorsFirstly, a nonlinear feedback tracking controller is designed by using Barbalat lemma and Lyapunov function, where the tracked attitude velocity is bounded and its derivation not only is bounded but also has limited energy. Secondly, both of inertia-estimator and disturbance-estimator are constructed. Finally, a nonlinear feedback controller based on estimators is developed, which only requires the feedback of the attitude angle and angular velocity of the flexible spacecraft. Simulation results show that, the nonlinear feedback tracking controller is effective.In the paper, the first-order approximate dynamic model of a flexible spacecraft is developed, and the applicability of traditional models is analyzed. Then, TS fuzzy region controller, sliding mode controller and attitude tracking controller are provided for the attitude control of a flexible spacecraft, where mode coordinates are immeasurable, the inertia matrix is unknown, external disturbances exits and the control inputs are bounded. These conclusions can provide reference for modeling and attitude control of flexible spacecraft in the future.