Automatic Control of Space Vehicles' Orbit around Earth

The paper presents the design of an automatic system for the control (stabilization) of the orbit associated to a space vehicle (rocket, satellite etc.) during its motion around Earth. The dynamics of the space vehicle is expressed by using the equations describing the dynamics of the three celestial bodies (satellite, Earth, and Moon). For the design of the stabilization control law, a Lyapunov function is considered; it depends on the deviation of the satellite's position and velocity vectors with respect to Earth relative to the vectors associated to the satellite's reference orbit. From the condition of automatic control system's absolute stability, one assures the simultaneous convergence to zero of the deviations associated to the position and velocity vectors with respect to the vectors describing the satellite's reference orbit. The theoretical results are validated in Matlab/Simulink environment and the dynamic characteristics associated to the new control system are obtained.