Comparative Stability Analysis and Performance of Magnetic Controllers for Bias Momentum Satellites

This paper reexamines magnetic controllers for roll/yaw control of Earth-pointing bias momentum satellites in circular orbits using pitch dipoles. A general magnetic controller employs three gains, first for controlling precession, second for damping nutations, and third for stiffening the roll/yaw motion directly, using attitude angles and rates for feedback. For an orbit-averaged magnetic field, dependence on these gains of the closed-loop roots associated with precession and nutation and their damping coefficients is investigated via eigenanalysis and root loci. Stability inequalities constraining the three gains are developed by applying Routh-Hurwitz criteria, and the stability boundaries so obtained are spot checked with Floquet theory. The stability and performance of a three-gain controller is compared with that of 1) the classical A/t x B controller and 2) controllers having zero stiffness gain with or without yaw feedback for precession. Faster transient performance and improved pointing accuracy attributed to yaw feedback and stiffness gain are clearly brought forth in this study. Simple formulas are developed to calculate the gains for desired precession rate and nutation damping coefficient.