Gain Selection for Attitude Stabilization of Earth-Pointing Spacecraft Using Magnetorquers
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ORIGINAL ARTICLE
Gain Selection for Attitude Stabilization of Earth‑Pointing Spacecraft Using Magnetorquers Fabio Celani1 Received: 21 April 2020 / Revised: 15 September 2020 / Accepted: 8 October 2020 © The Author(s) 2020
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. Keywords Spacecraft attitude stabilization · Magnetorquers · PD-like control · Matrix gains
1 Introduction Spacecraft attitude control can be obtained by adopting several actuation mechanisms. Among them electromagnetic actuators are widely used for generation of attitude control torques on satellites flying in low Earth orbits. They consist of planar current-driven coils rigidly placed on the spacecraft typically along three orthogonal axes, and they operate on the basis of the interaction between the magnetic dipole moment generated by those coils and the Earth magnetic field. In fact, the interaction with the Earth field generates a torque that attempts to align the total magnetic dipole moment in the direction of the field. Magnetic actuators, also known as magnetorquers, have the important limitation that control torque is constrained to belong to the plane orthogonal to the Earth magnetic field. As a result, usually actuators of a different type accompany magnetorquers to provide full three-axis control. Moreover, magnetorquers are often used for angular momentum dumping when reaction or momentum-bias wheels are employed for accurate attitude control (see [11, Chapter 7]). Lately, attitude stabilization using only magnetorquers has been considered as a feasible option especially for low-cost micro- and nano-satellites and for satellites with a failure in the main attitude control * Fabio Celani [email protected] 1
School of Aerospace Engineering, Sapienza University of Rome, Via Salaria 851, 00138 Roma, Italy
system. As a result, several papers have been dedicated to the design of stabilizing control laws in such a setting. In some of those works stability is achieved in the case of inertial pointing (see, e.g. [2, 4, 5, 7]), whereas in other papers it is achieved for Earth (or nadir) pointing spacecraft (see, e.g. [6, 8, 12, 16, 17]). In all of the cited papers PD-like control algorithms are employed. In [2, 4, 5, 16] the corresponding scalar control gains are determined substantially on a trialand-error basis. In [6, 7, 12] the scalar gains are selected so to maximize the degree of stability of the closed-loop system. In [8, 17] matrix gains are employed and are determined by solving linear quadratic regulator problems. In the present wor
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