The Overall Differential Geometry In The Satellite Control System

Nowadays, society has entered into information revolution time, the development of society and the requirement for human progress induce people to devote more and more energy to spacecraft technology, especially satellite technology. The satellite technology is the core of space technology, it is applied widely to economic field cultural field and national defense field, etc. To better develop the satellite technology, people increasingly look for better theoretical systems. For decades of development, satellite has been a combined subject, which including spherical mechanics > mathematics and cybernetics, etc.The orbit control and attitude control problems of satellite have been studied in this thesis by use of global differential geometry method. In the part of orbit control, the main ideas in study is to define the nonlinear control system on a Riemann manifold from the global viewpoint, and to build the intimate relation between the geometrical structure of state space and the state equation of nonlinear control system; In the part of attitude control, the main ideas in study is to deduce mathematical model with good character based on global differential geometry ideas as well as Li group and Li algebra, moreover, to design corresponding control schemes.This thesis deals with the following results with regard to the control systems of satellite:(1) On the basis of global geometry theory, deprive the representation of state equation for the satellite orbit control system under the geometric restraint, show that the geometrical structure of geometric restraint affect on satellite orbit control system, and study the connection between the equilibriums state of the control system and the geodesies of the geometric restraint. Moreover, discuss the local controllability and observability of the satellite orbit control system under the geometric restraint. These results provide theory and tool for the design and realization of further study the satellite orbit control system;(2) Discuss the satellite attitude and position/attitude tracking control problems. Deduce the mathematical model of satellite attitude control system and position/attitude control system respectively, then design tracking controller. The credibility and availability of the proposed control strategy is shown by theory and simulation.(3) Deduce the mathematical model of attitude and shape control of satellite witharticulated appendages by the global differential geometry theory, and design PD + adaptive compensative controller. The attitude and shape control problems of satellite have been studied by Chunlei. R[16] recently, results have been developed for the controllability analysis of the attitude and shape control problem. Based on Chunlei. R[16] we deprive the mathematical model of altitude and shape control of satellite with articulated appendages although not essential, the model formulation using Li group and Li algebra theory leads to relatively simple and available control formulas. For the model, we designed PD + adaptive compensative controller to realize trajectory tracking. This controller has some advantages: when the initial error is large, the PD feedback part plays main role, and it avoids too large initial torque output; when the initial error is small, the adaptive part plays main role, such guarantee the system has good dynamic character. Moreover, the only information required in setting up the strategy is the output and velocity states of the system, while detailed description of the inversion of the inertia matrix or estimation the bound of the inertia matrix and measure the accelerations are not need.