Monoaxial Electrodynamic Stabilization of a Spacecraft Using PID Controller

One of the actual problems of modern cosmic dynamics is the development of systems for controlling the angular orientation of spacecrafts with respect to their centers of mass. To solve this problem, magnetic control systems based on the interaction of their executive devices with the Earth’s magnetic field are widely and effectively used. An important class of problems for controlling the angular spacecraft orientation is that of problems of monoaxial stabilization. This paper considers a satellite whose center of mass moves in a circular equatorial low Earth orbit. It is assumed that it is equipped with a controlled electrostatic charge distributed over a certain volume and a controlled magnetic moment. The rotational motion of a satellite with respect to its center of mass in the orbital frame is studied. The problem of monoaxial stabilization of a satellite in an arbitrary equilibrium position is solved. The electrodynamic control method is used which is based on the simultaneous application of a magnetic moment and the moment of Lorentz forces. Each of these moments is selected as a sum of damping, restoring and compensating components. To improve the characteristics of transient processes (damping unwanted oscillations and increasing the speed of convergence to program motion), PID controller of a special type is constructed. The stability analysis of the closed-loop system is carried out on the basis of the Lyapunov direct method. An original construction of the Lyapunov—Krasovskii functional is proposed, with the help of which the conditions on the control parameters are determined that guarantee the asymptotic stability of the program motion. The results of numerical simulation are presented confirming the obtained theoretical conclusions and demonstrating the advantage of the developed approach compared to the use of previously constructed controllers. It is shown that due to the appropriate choice of control parameters, the characteristics of transient processes can be significantly improved