$$\hbox {H}_\infty $$ H ∞ and $$\upmu $$ μ synthesis control of virtual structure satellites formation flying

Abstract

Recent developments in the space industry and the great tendency to define efficient, precise and low cost missions are the main reasons for the growing interest in satellites formation flight. Regarding the aforementioned, the study of multiple satellites control methods is the subject of the present paper. In this paper, two linear robust control strategies are applied to position control system of certain satellites in the virtual structure formation flight. The proposed controllers are designed considering different parametric uncertainties such as semimajor axis and eccentricity changes as well as some disturbances like second term of gravitational acceleration function (\(j_{2}\)) and drag acceleration which are resulted in asymmetrical shape of the Earth and low density atmosphere in high altitude. In the presence of all parametric and un-modeled dynamic uncertainties, the robust stability and performance of the nonlinear system are guaranteed and good tracking, disturbance and noise rejection characteristics are achieved. Computer simulations show that these approaches have very promising performance when position controllers are applied with PWPF modulators while they are working in their pseudo linear range.