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The paper purpose is to present some aspects regarding the calculus model and technical solutions for small satellites attitude control. Mathematical model is put in nonlinear and linear form. The linear form is used for attitude control system synthesis. The attitude control system obtained is used in nonlinear form in order to maintain desired attitude. A few numerical simulations are made for standard input and the satellite behavior is obtained. The satellite model presented will be with six DOF and use Cartesian coordinates. At this item, as novelty of the work we will use the rotation angles to describe the kinematical equations. Also this paper proposes a Fourier linearising of Trigger Schmidt element used for applying the command moment. The results analyzed will be the rotation angles of the satellite as well the rotation velocity. The conclusions will focus the comparison between results obtained using optimal attitude control system, and the possibility to use such system for small satellite.