.1 The Magnetic Attitude Control of ABRIXAS I Hans 1. Komgsmann, Matthias Wiegand, Oliver Matthews

ZARMJUniversity of Bremen I AmFaI1turm 28359 Bremen I Germany Abstract I ABRIXAS is a small astronomical planned by the Astrophysical Institute Potsdam (AIP) and the German Space Agency DARA. Its main scientific objective is to survey the total hemisphere; the satellite rotates once per orbit along the sun line, and after half a year the sur­ vey mission will be fulfilled. The attitude control system is one of the critical subsystems with respect to cost and mission success, and an independent study was done. With a momen­ tum biased system, three magnetic torquers and a sun sensor the mission requirement of 10 arc-minutes accuracy can be achieved, if the torquer current is controlled by an analogous driver unit. Using the BREM-SAT simulation software (which has been verified by flight results), the "onboard" software module had been developed and tested thoroughly. For the momentum wheel discharge new procedures had to be developed which work even at equatorial orbits. As a result of this study, hardware cost reduction and early software implementation and testing I had become possible.

:1 Introduction ABRIXAS is a small satellite proposed by three Germans institutes l to the German I Space Agency DARA. Its prime mission is a complete deep sky survey with an imag­ ing X-ray in a wide and hard X­ I ray energy band (0.5-10 ke V). The scien­ tific payload consists of seven 27-fold nested gold-coated mirror systems. All I seven systems share a single 60 x 60 nnn2 pn CCD detector, which is a copy of the XMM camera. The length is 1600 I rum, and each mirror system has an outer diameter2 of 160 mm. The field of view is 40 arc-minutes, and the seven different I sight lines are separated by 7°. Figure 1 (Right): ABRIXAS configuration (from [2]), the seven are visible in the lower I part of the satellite. inside the launch adapter. I

1 Astrophysical Institute Potsdam, Max- Institute for Extraterrestrical Physics, Garching., I and Institute for Astronomy, Tiibingen 2 The numbers may still change due to design I changes. I

The satellite has 2.5 to 3m length and a Accuracy in scan-motion ±2° diameter of approximately 1.2 m The total Accuracy of scan-axis ±lOarCmin I mass is approximately 400 kg, and the con­ Accuracy of attitude de- better than figuration is dominated by the telescope termination (post-mission) 30 arcsec (Figure 1). These data are the results from Orbit 500-600 kIn, I two independent system studies [2,9]. 0°_53° inel ZARMlUniversity of Bremen performed an Table 1: Attitude requIrements additional analysis for the attitude control I system Without thrusters, we had to use magnetic The proposed circular orbit has up to 53° attitude control, and to keep the scan-axis inclination and 600 km altitude; The ground within 10 arcmin towards the sun turned I station is preferably located in Germany, out to be a potential problem in the equa­ and the proposed lifetime is 3 years. A torial orbit, where the geomagnetic field scanning motion as shown in Figure 2 al­ variation is comparably low. Furthermore, lows a complete sky survey in 6 month; we separated attitude control and attitude following this period, special areas of inter­ determination for the science payload, est may be investigated in further detail. which could in principle be performed on One primary goal during the attitude con­ ground. The measurements for the attitude trol design was to reduce cost during de­ control system can easily be done by an velopment, tests and operations. Our basic analog sun sensor, because the scan-axis approach was to avoid thrusters and pro­ should point towards the sun. Because pulsion elements, reduce the number of during eclipse periods attitude control is components and keep the onboard software not possible, we choose a momentum I as simple as possible for the primary func­ wheel large enough to stabilize the motion tion. However, advanced filters allow when no sun sensor signal is available. much more flexibility and redundancy while Figure 3 shows the motion of the scan axis I reducing hardware costs at the same time. due to disturbance torques without control This simulation assumes an 200 mm offset between the point of aerodynamic pressure I

and the center of mass and a 0.1 A.Jn2 re- L sidual dipole. Solar pressure is calculated with a similar offset as for aerodynamic I pressure, and·the moments of inertia are Winter 243 0 26] I 1= 0 144 0 [kgm2]. 53· orbit of ABRIXAS [ 26 0 159 It can be shown, that even with the compa­ I rably large offset the disturbance torque due to gravitational torque is dominant. y I F(N During less than half of the , the scan-axis changes its direction by more lUll dl~ - ft.-- .pIn IXiI than 10 arc-minutes. Variations of the or­ I Earth orbit around sun y/ l~ bital inclination cause mainly a change in FOV the direction of motion, not in the total value. Figure 2: Scanning motion of ABRIXAS [1] I The attitude requirements have been de­ fined earlier and are given in table 1. 00 ~------~ 1ar torquers, each of them having a ­ -23' Inclination mum dipole moment of 120 Am2, and an 50 ...... 53' Indination - O' Indination analog driver unit are at least able to pro­ I duce any control torque perpendicular to the geomagnetic field vector. With the spin­ axis of the wheel pointing towards the sun, I the sun sensor measures directly the errors in two spacecraft axes. A correcting mo­ ment can be derived using I o dB ·1 0 L...'-'-'.....L..~...... !...... -..L...... ~.....L...'-'-'-'-'...... -'-'--!-o -'-'--'--':'10 - = Ninert , Ninert = Dinert x Binert (1) ~o -50 -40 -30 ·20 ·10 dt inert i Right Ascension [arcminl with H: Correcting angular momen- I Figure 3: Motion of the scan-axis without control, tum due to disturbance torque's, for two orbits (500 km N: Torque circular). Please note the initial push (at 0,0) D: Dipole moment caused by momentum wheel speed adjustment to B: Geomagnetic field vector I start the scan motion. Hardware concept Measuring the geomagnetic field, we know the plane of all possible torque (Figure 4). I Because the attitude control system should In most cases, the correcting torque can be inherently stable, a momentum biased not be generated directly. system using a single wheel and three mag­ I netic torquers had been selected. The wheel B spin direction is pointed towards the sun, and speed changes are made to control the I scan rate. Only two sensors are required, a two axis sun sensor and a magnetometer to determine the earth magnetic field polarity. Correcting torque j I.... If the magnetometer is used for scan rate determination, software estimating the Plane of possible sate~te's position and the geomagnetic I field is required onboard; instead, a laser gyro may be used, which needs to be up­ dated from time to time. If the magnetome­ I Figure 4: Required correcting torque and plane of ter is used, the star sensor, pointing in the all possible moments due to the Earth magnetic direction of the telescope, is not necessary field (B). for the attitude control system and the gyro Assuming the momentum wheel spins in the I update. Z-direction, we add a Z-component to the The complete attitude control system re­ correcting torque, until it is in the plane of quires a nutation damping device3 and an the possible torques. Geometrically, the I analog driver unit for the magnetic correcting torque is transferred in the plane torquers. perpendicular to the field vector B. I Control Concept Due to H and D perpendicular B, equation The main disadvantage of magnetic attitude (1) yields control is its dependency from the Earth I magnetic field. Three mutually perpendicu-

I 3 This has not be a dedicated damper, small amounts offluids would be sufficient. I 3 bits. An initial error of 40° in declination and right ascension has been chosen, and I the error correction with the torquers causes the momentum wheel speed to ex-. ceed the hard-charge limit after 25-30° of I angular error has been corrected. During hard-charge, attitude correction is much slower, and 16 orbits (app. 1 day) are nec­ I essary to slew the telescope axis to the tar­ which gives the required correcting torque. get attitude. During the following orbits, The time t is usually ten seconds. the momentum wheel speed is slowly, but When the torquers are switched on, the constantly corrected. additional Z-component causes a change in the scan-rate, which is compensated di­ rectly by the momentum wheel. The mo­ 40 mentum wheel acts as a storage device, and special charge/discharge procedures had 30 I been developed to avoid angular momen­ L. tum over- or underflow. g 20 w ~ecllnation I 10 Right Ascension / ChargelDischarge Procedures Our 0 I flight experience from BREM-SAT 0 5 10 15 20 was, that the momentum wheel is unloaded Orbits or loaded more time than initially expected [4]. We therefor tried to integrate this pro­ Figure 5: Simulation of 20 orbits with an initial I cedure in the nominal attitude control al­ error of 40° in declination and right ascension. gorithms, using geomagnetic field constel­ The torquer activity during the simulation lations that are inefficient for attitude con­ (Figure 6) reflects the changes for the hard­ I trol. If the geomagnetic field vector B is charge mode and after the nominal attitude close to the XN-plane (Figure 4), a large is reached. Z-component is required even for a small I4' correction. Usually, these regions have been excluded, but if the torque changes 17.2 17.4 17.6 17.8 18 the momentum wheel speed towards nomi­ I nal speed, the torquers are activated. This ll mode is called IIsoft-charge and expands 120 I the region where control torques can be 90 used. It: for example during slew maneu­ 'f60 ::t30 vers, soft-charge is not efficient enough, we C switch to a more consequent mode called ~ 0 ~HlIrt'~ I ~ "hard-charge". Hard-charge does only .!l!,30

II allow" control torques if the momentum !.so wheel speed is changed towards nominal ..9() I .120 .I.:.a....u..,.J..L.JI..L-.lJ...... JI<...-.Il<..J...Jo....LL-.LL.JL.L...1.Il-UI"-"III...IIIIl...ill-"""'-'J..L...I.JL.L..J speed. o 5 10 lS 20 During nominal operations, soft-charge is Orbits I very efficient to keep the momentum wheel speed close to its limits. Figure 6: Torquer dipole moment during the 20- orbits simulation (compare to Figure 5), enlarge­ Simulation Results ment shows the activity after the maneuver is fin­ I Demonstrating the efficiency of the ished for a single orbit. charge/discharge procedures, Figure 5 shows the results of a simulation of 20 or- I 4 I )

I During error correction and hard-charge, the torquer is frequently switched to the maximum dipole moment, 120 Am2 in that I case. When the target attitude is reached (in 30 orbit no.16), much less torque activity is

recorded, and only a few peaks use the 10 Start with initial \ITOI' t maximum dipole moment. During nominal operation, the accuracy of the scan-axis pointing to the sun is the most I important parameter. Referring table 1, the requirement is to keep this axis within ±10 I arc-minutes. Figure 7 shows, that this re­ quirement can be fulfilled if the star sensor 0.161' is used during eclipse periods, and that the -- pointing error increases to more than 20 I -91 -9O.S -90.6 -90.4 -90.2 -90 arc-minutes if only the sun sensor is used. Right Ascension [0]

I Figure 8: Scan-axis direction during scanning ~ ~------, motion, without control in eclipse periods. Only sunsensor (no control in.edipse periods) 25 I Long-term simulations / A long-term simulation for the minimum mission time of Y2 year had been performed , to verify the independence of the magnetic attitude control from orbit/sun constellation and seasons. The results show only .small I 5 changes in performance during that period. U sing the scan-repetition accuracy as basic o ~~~~~~~~~~~~~~~~~ requirement, no star sensor is necessary, o 50 100 150 200 250 300 350 <400 <450 500 I Time [Min) and the attitude of the telescope can be L reconstructed on ground. Figure 7: Pointing accuracy of the scan-axis, with I and without control during eclipse periods. 35 The reason behind the pointing requirement I of ±10 arc-minutes is that no X-ray sources 30 must be missed by random attitude motions ~ 25 of the satellite. However, even the uncon­ ~ trolled motion during eclipse periods is g 20 w I' very regular, and very similar in two suc­ 15 cessive orbits. To illustrate this effect, the ~c: rl 10 I scan-axis direction has been recorded for a V,) simulation of 5 orbits (Figure 8). The 5 pointing requirement is given for compari­ son, and it is clearly visible that the "scan­ 20 40 60 80 100 120 140 I repetition accuracy" is much better than 10 Missiontlme [Days) arc-minutes, even during uncontrolled peri­ I ods. Figure 9: Error (arc-min) during long-term simu­ lation The wheel speed during the long-term I simulation is shown in Figure 10. The nor­ mal mode, when the wheel speed is not i 5 controlled, has been defined from 1600 to Acknowledgments I 1900 RPM. During the whole mission , the This study has been performed under con­ wheel speed is kept within that range plus tract (50QQ 9405) of the German Space an additional 50 to 70 RPM peak value. Agency DARA. We like to thank DARA I The hard-charge mode is apparently not and the experimenter's group, especially necessary, if no large slew maneuvers are Prof Hasinger from Astrophysical Institute performed. These maneuvers are, in gen­ of Potsdam, Germany. I eral, constraint by power require­ ments. References [1] G. Hasinger et. al.: ABRIXAS - A I 1900 r~---r------""'" broad-band imaging X-ray all-sky 1850 Survey, Project Report, 1995 I ~1800 Mode. Normal [2] ORB-System: "ABRIXAS - Phase 0.. !!S1750 1 Studie, Final Executive Report", Bremen, 1995 I ~1700 '5.* [3] Polites, M.E., Carrington, C.K: "A i 1650 conceptual design for the attitude ~ ~1600 control and determination system I for the Magnetospheric Imager", 1550 NASA TP 3560,1995 1500 ~~~~~~...... L...... L...... L...... L ...... L..."'-'-'-.u [4] H. Konigsmann et. al. "BREM-SAT o ~ ~ ~ 00 100 1~ 1~ 1~ 100 I Missiontime [Days) - First Flight Results", Proc. Utah State University Conference on Small , 1994 , Figure 10: Wheel speed during long-term simula­ tion [5] H. Konigsmann, "Magnetische La­ geregelung von Kleinsatelliten in Simulation software niedrigen Hohen", PhD Thesis, I The simulation tool used for ABRIXAS has 1995 been originally developed for the small [6] Bandeen, W. et al., "Angular Mo~ , tion of the Spin Axis of the TIROS " satellite BREM-SAT and adapted to the I new satellite configuration and (proposed) 1 Meteorological Satellite due to hardware. All environmental torques have Magnetic and Gravitational been modeled carefully, using models like Torques", JGR Vol. 65, No. 9 I MSIS-90 (for the atmospheric density) [7] (Letters), 1960 and IGRF-90 (for the geomagnetic field) [7] Hedin, A, "Extension of the MSIS Thermo spheric Model into the [8]. During the BREM-SAT mission , this I Middle and Lower Atmosphere", software tool had been verified to predict JGR Vol. 96, No. A2, 1991 the attitude motion ofBREM-SAT or other [8] Barraclough, D.R, "International satellites, e.g. TIROS [6] very precisely up 'I to a period of 14 days. Geomagnetic Reference Field Revi­ sion 1987", J. Geomag. Geoelectr., The control algorithms had been imple­ mented in "C" computer code, and can be 39, 1987 I run on a different PC or on the same PC as [9] Kayser-Threde, K Kemmerle: "ABRIXAS - Phase 1 Study, Final the simulation module. An output module, Report", Miinchen, 1995 based on unit spheres with zoom-capability I [10] Wertz, J. R (ed.): Spacecraft Atti­ allows a easy evaluation about the status of tude Determination and Control the (simulated) satellite. , 1978 I I 6 i