Stability by thrust control for satellites at low altitudes

Abstract

The paper deals with the problem of flight control law synthesis to stabilize the flight behaviour of a satellite which experiences unsteady drag, in an environment with nonhomogeneous properties. The study is carried out for an unsteady evolution in the proximity of Earth. To solve such a problem we take into account the extended differential system of mechanical movement for the reference flight evolution and for the (nonlinear) perturbed evolution. The main constraint for the evolution control is that involving the damping of the state variables’ deviations, formulated as implicit algebraic equations, and used to derive restriction equations determining the control laws in algebraic or differential description. The method considers the extended differential model of the perturbed flight by side of these implicit equations, and solves this differential-algebraic system in an analytical manner. The final mathematical system regards the reference control variables, for the basic evolution to be stabilized, as external known variables and those for the perturbed evolution as the real control variables, given by an appropriate device system. The method to solve the problem may be regarded in association with the known “following model’s problem” and “dynamic inversion”. The essential advantages of the proposed viewpoint and method are the “on-line” control of the unsteady flight, the use of the complete nonlinear mathematical model, the suitable damping and the admissibility of large and almost unpredictable values for disturbances.