Tactics for Heliogyro Solar Sail Attitude Control via Blade Pitching

Abstract

Heliogyros generate attitude control moments by pitching their sail membrane blades collectively or cyclically, similar to a helicopter. Past work has focused on simple blade pitch profiles with the heliogyro normal to the sun; however, most solar sail missions will require sun angles of at least 35 deg. Furthermore, combination pitch profiles (e.g., cyclic plus collective) are needed for attitude control during all mission segments. The control moments for such situations vary in an unintuitive, nonlinear fashion. This paper explores heliogyro control moment authority with varying sun angles and combinations of pitch profiles, providing critical insight for future development of heliogyro attitude control schemes. Three tactics for generating control moments using various profile combinations are introduced for three-axis attitude control during a variety of practical mission scenarios. These tactics indicate that the heliogyro can generate control moments from any orientation, including edge-on to the sun. A restricted, nonlinear, constrained optimization is used to determine the blade pitch profile combination required to generate the desired attitude control torques. This approach could be employed for analyzing mission performance and for designing closed-loop attitude control. Nomenclature A = total sail area, m 2 a xx = collective (where xx equals co), half-p (where xx equals hp), or cyclic (where xx equals cy) profile amplitude, rad, deg D, d x = despun frame F = solar radiation pressure thrust vector, N h = sail membrane thickness, m h = orbit momentum unit vector J n = nth element mass moment of inertia, kg · m 2 M = solar radiation pressure moment vector, N · m, subscript d indicates desired moments N = number of bladeŝ l = local horizontal with respect to sun in orbit plane P = solar radiation pressurê p = reference axis for clock angle δ R = heliogyro blade radius, m S = sun framê s = sun-spacecraft unit vector t = time, s β = blade flap bending angle, rad, deg γ = sail cone angle/Sun angle, angle betweenŝ andd 1 , rad, deg δ = clock angle betweenp andd 3 , rad, deg θ = blade pitch, follows right-hand rule about blade span (radius) axis, rad, deg ϕ xx = half-p (where xx equals hp) or cyclic (where xx equals cy) phase angle, rad, deg χ i = ith blade angle relative to blade 1 in the rotation plane, where χ 1 equals zero, rad, deg Ψ = in-plane moment M 23 azimuth angle, rad, deg ψ i = ith blade azimuth angle in the spin plane, rad, deg Ω = heliogyro inertial spin rate about primary spin axis, rad∕s

Exploring the Heliogyro’s Orbital Control Capabilities for Solar Sail Halo Orbits

“…Reference [8] as well as in the use of the terms cone and clock angle. While Reference [8] refers to the heliogyro's attitude angles  and  as cone and clock angles, this paper adopts the definitions as in Reference [1], where the angles  and  are referred to as cone and clock angles that describe the direction of the solar sail acceleration vector with respect to the Sun coordinate system,  , , S s l p , see Figure 2. Note that, for an FPF solar sail, the definitions are almost interchangeable (…”

“…The blade pitch angle, i  (see Figure 1c), depends on the pitch profile selected and is required to compute the   i BL transformation matrix. Reference [6] and many following works (e.g., References [5,7,8,18]) define three different pitch profiles, which can be used independently or in combination: The 'co' profile pitches the blades constantly while the heliogyro rotates, while the 'hp'-and 'cy'-profiles pitch the blades sinusoidally with revolution. The 'hp' profile repeats after two revolutions (requiring the total acceleration vector in Eq.…”

“…Reference [8] provides the th i blade's pitch angle for any combination of the three pitch profiles itemized above:…”

“…The solar radiation pressure force that such an FPF (fixed-area) sail can achieve at 1 AU, per square meter sail area, and in the direction along the Sun line, s F , and perpendicular to it, l F , can be obtained from an equation analogous to Eq. (1) or (8). Considering an interval for the cone angle of 90 , 90…”

“…Significant research has been conducted regarding the heliogyro's blade dynamics, stability and control [7] and its attitude control moment authority [8], but much remains to be explored in its orbital dynamics and control capabilities, which appear to have some interesting possibilities. For example, the force vector with respect to the Sun-line that an FPF sail can achieve is constrained to the surface of a "force bubble".…”