Pole-Placement Technique for Magnetic Momentum Removal of Earth-Pointing Spacecraft

Abstract

A linear pole-placement technique is presented for magnetic momentum removal of Earth-pointing spacecraft. First probed are the two most commonly used momentum removal schemes, linear and bang-bang H £ B schemes (where H is the excess angularmomentum vector and B is the geomagnetic eld vector), both based on a comparison between a constant disturbance torque and an averaged magnetic control torque acting on a spacecraft. Through analysis and illustrations, it is shown that these two methods lack a precise technique for determining control gains or strength (in ampere meter squared) of roll, pitch, and yaw electromagnets. As an alternative, a linear, closed-loop, pole-placement technique is devised, which correlates control gains with the closed-loop pole locations and steady-state amplitudes of roll/yaw and pitch momentum under an orbit-averaged magnetic controller and disturbances. Special cases of low-and high-inclination orbits where pitch and yaw electromagnets, respectively, are ineffective are formulated. This new scheme and the mentioned two classical schemes of momentum removal are compared and illustrated, and generally applicable conclusions are drawn.

Reaction Wheels Desaturation Using Magnetorquers and Static Input Allocation

“…For all our simulations, unless differently specified, the initial conditions are selected as h w0 = [0.09, 0.05, 0.04] T , ω 0 = 0, 0 = [0.10, 0.05, 0.02] T and η 0 = 1 − T 0 0 . Regarding the parameter k p inducing momentum dumping, keeping in mind that it should be strictly positive, we ran several numerical simulations of the closed-loop (15) with (16). The resulting choice was k p = 5·10 −3 .…”

“…Remark 4. Following the same philosophy, other control laws have been proposed in the literature to achieve momentum dumping by focusing on (15). For example, in [23], a periodic LQ controller has been designed relying on numerical methods to solve the periodic Riccati equation.…”

“…Despite its intuitive interpretation, it seems that formally showing desirable stabilization properties of the overall controller (6), (14), (16) is not so straightforward. Some directions are given with respect to this in [3], [4], [6], [9], [15], [23] where a frequency separation argument is required between the two loops cited above, which corresponds to selecting a very aggressive action of the attitude stabilizer (14). This can be performed, for example, by selecting sufficiently large gains c and K ω in (6).…”

“…which reveals that the momentum of the reaction wheels is indeed affected by the attitude variables due to the presence of u at the right hand side. Remarking that if (q, ω) ∈ A then (24a) reduces to (15), it appears natural to select the magnetorquers input τ m in such a way to exploit the useful stabilization result of Lemma III.1, namely…”

“…0-GES of the lower subsystem. As already said, the zero input equation of the lower subsystem corresponds to (15), (25a) (where it is recalled thatb(t) = R(q)b • (t)). Thus, Lemma III.1 can be directly applied to prove that A h is globally exponentially stable for the lower subsystem with zero input.…”