Attitude Determination And Finite Time Control Algorithms For A Satellite

With the development of the aerospace technology, the requirement for satellite attitude determination and control is getting stricter. From the point of view of a three-axis-stabilized satellite attitude determination and control system, this paper has theoretically studied the composition and algorithm of the attitude determination system and the finite-time control method for the attitude control system. The main contents are as follows:Firstly, the definitions, the calculation rules, conversion relation, advantages and disadvantages of Euler angle or quaternion description of satellite attitude are summed up systematically, and also the rigid satellite's kinematic and dynamitic equations are established for different cases. As the calculation of sun vector needs precise orbit information, the time system and simplified two-body orbit model are also established at the same time.Then, the attitude determination system of the satellite which is composed of gyros, infrared horizon sensors and digital sun sensor is designed. For theoretical development, the continuous and discretization models of gyros are derived meticulously through analyzing the correlations of the bias and measurement of gyro. The measure equations and relative analysis of infrared horizon sensors and digital sun sensor are also given at the same time. The principle of the attitude determination system using the measurement of infrared horizon sensors and digital sun sensor to modify the gyros'driftbias is proposed. The attitude estimator which is composed of error quaternion state equation and measure residual equations of infrared horizon sensors and digital sun sensor is then established. Due to the application of the extended Kalman filter (EKF) algorithm, the precision of attitude determination is improved.Lastly, the finite time control theory of nonlinear system and some control methods represented by terminal sliding mode (TSM) control are deeply investigated in this section. The definition of finite time stability based on Lyapunov stability is given, and a theorm used to determine the finite time stability of autonomous scalar system is also proved in details. Comparing with the basic concepts of sliding mode control and conventional TSM, a new type of TSM is introduced, and a finite time stable sliding mode is also designed. Both an uncontinuous and a continuous TSM finite time controllers using inverse dynamic method are then designed for the second-order dynamic system of the satellite without disturbance. The stability of the controller is then analyzed then. In order to eliminate the oscillation, a new type of symbolic function is also designed to replace the conventional symbolic function. The validity and reliability for the proposed algorithm are testified through simulations with and without constraints on the control torque.