Математическая модель углового движения твердого тела в параметрах Родрига-Гамильтона и ее использование в задачах управления ориентацией космического аппарата

• Видавець: Kamianets-Podilskyi National Ivan Ohiienko University
• Дата: 2018
• Автор: Ефименко, Николай Владимирович
• Формат: Стаття
• Мова: rus
• Опубліковано: Kamianets-Podilskyi National Ivan Ohiienko University 2018
• Онлайн доступ: http://mcm-tech.kpnu.edu.ua/article/view/158707

Currently, the most effective way to obtain data on the Earth's surface is satellite imagery. In this case, the dynamic characteristics of the control system are very stringent requirements. The turn should occur from any current position to any given position, the orientation accuracy in the unfolded position should be units of angular minutes, and the angular rates of turn can reach a value of 2-3 degrees per second. To ensure such high dynamic characteristics, the base clock of the control system should be no more than 100 ms. This restriction imposes restrictions on reorientation algorithms. On the one hand, they should be very simple so that the time spent on calculating the control action is minimal. On the other hand, they must provide high dynamic characteristics, which is impossible to provide in the class of simple algorithms. The solution to the problem of the synthesis of reorientation algorithms for spacecraft must be sought as a solution to the optimization problem. When solving such problems, as a rule, a mathematical model of the angular motion of the spacecraft is used, in which the dynamics are described by the Euler equation and the kinematics by the equation for the quaternion. In this case, it is easy enough to obtain the equations of the two-point boundary value problem, but it is not possible to find an analytical solution of this problem. The solution can only be found using numerical methods, which is not applicable when implementing algorithms onboard the spacecraft. These difficulties can be circumvented using the spacecraft model, built on the basis of the dynamic equations of the rotational motion of a rigid body in the Rodrigues Hamilton parameters. In this paper, this approach was used to solve the main problems of controlling the angular motion of a spacecraft: stabilization problems and terminal control problems. The article may be useful to develo­pers of spacecraft attitude control systems.