Gain Selection for Attitude Stabilization of Earth-Pointing Spacecraft Using Magnetorquers

Abstract

This paper considers a feedback control law that achieves attitude stabilization for Earth-pointing spacecraft using only magnetorquers as torque actuators. The control law is proportional derivative (PD)-like with matrix gains, and it guarantees asymptotic stability. The PD matrix gains are determined through the numerical solution of a periodic linear quadric regulator problem. A case study shows the effectiveness of the considered control law, and specifically of the gain selection method, in a simplified simulation scenario.

Quaternion versus Rotation Matrix Feedback for Spacecraft Attitude Stabilization Using Magnetorquers

“…Table A1 reports the values selected for those matrices as well as the initial guesses K p0 K d0 for K p and K d , respectively. Thus, the approach presented in [7,20] is employed for finding a solution to the above linear quadratic problem, and the following gains are obtained. the integration interval and are equal to b b (t k ), m b rm (t k ), m coils (t k ), w 1 (t k ), and w 2 (t k ), respectively.…”

“…For what follows, it useful to rewrite Equation (7) in terms of ω b bo instead of ω b bi . For that purpose, note that from Equations ( 5) and ( 6) it follows that ω b bi = ω b bo + R bo ω o oi .…”

“…The goal of this appendix to present a method for determining effective values for the 3 × 3 matrix gains K p and K d . The method was obtained in [20] (see also [7]).…”

“…Simple control algorithms that achieves attitude stabilization using only magnetorquers, are based on quaternion and attitude rate feedback. It has been shown that such control laws achieves stabilization for both inertial pointing spacecraft [2][3][4][5] and Earth (or nadir) pointing spacecraft [6][7][8][9][10]. However, using quaternion and attitude rate feedback can result in undesired unwinding phenomenon for the spacecraft.…”

Comparative Cost Functions Analysis in the Construction of a Reference Angular Motion Implemented by Magnetorquers

“…The main problem here is the correct choice of the control gains. The papers [14][15][16][17][18] offer different solutions. However, even the most accurate selection of the control gains does not allow a simple feedback law to provide effective suppression of local disturbances.…”