Calculation of Program Control Not Generating Singularities in Gyrosystems

Abstract

A new approach to calculating the program controls of the spacecraft (SC) attitude by single-gimbal control moment gyros (gyroscopes in English terminology or gyrodynes in Russian terminology) is described in details. The novelty of the proposed method of calculating program controls is the virtual kinematic configuration of the actuator gyrosystem and the use of the angular momentum of the SC as a state variable when describing its dynamics. The formulation of the problem of calculating the control laws, based on these innovations, made it possible to directly use the total angular momentum of all the rotors of the gyrosystem in their motion relative to the main body of the SC, rather than its derivative, as a working tool for controlling the SC, and to accept the laws of the precessions of the gyro units, rather than the velocities of these precessions. A new approach to solving the problem of reorientation enables us to obtain control laws without such special (singular) positions of the gyro units in which the execution of the calculated laws is interrupted. This feature solves the well-known singularity problem of an actuator gyrosystem consisting of gyrodynes, and suggests that the presence of a singularity problem in the process of executing the calculated laws should be due only to their calculation method rather than due to certain specific features of the gyrosystem itself. The new method of calculating the control presented in this paper uses the structure of the space trajectory given a priori and the law of the motion along this trajectory is calculated in the process of forming the control. All the calculations are carried out on the standard onboard digital computer.