Attitude Control System Design For Ion, The Illinois Observing .

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ATTITUDE CONTROL SYSTEM DESIGN FOR ION, THE ILLINOISOBSERVING NANOSATELLITEBYBRYAN SCOTT GREGORYB.S., Marquette University, 2001THESISSubmitted in partial fulfillment of the requirementsfor the degree of Master of Science in Electrical Engineeringin the Graduate College of theUniversity of Illinois at Urbana-Champaign, 2004Urbana, Illinois

TABLE OF CONTENTSLIST OF TABLES. viLIST OF FIGURES . vii1INTRODUCTION . 12CUBESAT OVERVIEW. 22.1 History of the CubeSat Program. 22.2 The History of ION . 32.3 ION’s Dimensions . 32.4 ION’s Payload . 43THE ATTITUDE CONTROL HARDWARE. 63.1 Torque Coils . 63.1.1 Overview of torque coil theory . 63.1.2 Sizing the torque coils. 83.2 The Magnetometer. 93.3 The Flight Computer . 104ATTITUDE CONTROL BASICS. 124.1 Coordinate Systems . 124.1.1 The geocentric celestial inertial coordinate system . 134.1.2 The geocentric fixed coordinate system . 134.1.3 The satellite fixed body coordinate system. 154.1.4 The satellite orbital reference coordinate system. 164.2 Attitude Systems. 174.2.1 The attitude or rotation matrix . 184.2.2 Quaternions . 204.2.3 Euler angles. 224.3 Angular Velocity . 234.4 Angular Momentum . 244.5 Modeling the Satellite Dynamics . 254.5.1 Rotational dynamics. 264.5.2 Rotational kinematics. 265ATTITUDE CONTROL ALGORITHMS . 285.1 Position Determination. 285.1.1 The orbital elements. 295.1.2 Kepler’s second law. 315.1.3 Orbit propagation algorithm . 325.2 The Geomagnetic Field . 335.2.1 Generating the magnetic field. 345.2.2 Magnetic field algorithm. 365.3 Attitude Estimation. 365.3.1 Extended Kalman filter . 38iii

5.3.2 ION’s attitude estimation via the extended Kalman filter . 405.4 Convergence Issues . 445.5 Extended Kalman Filter Algorithm . 455.6 The Linear Quadratic Regulator Control Law. 455.6.1 Linear quadratic regulator theory. 465.6.1.1 Asymptotic periodic linear quadratic regulator . 475.6.2 ION’s asymptotic periodic linear quadratic regulator design . 485.6.2.1 Integral control. 505.6.2.2 Calculating the C matrix . 515.6.2.3 Control algorithms . 515.6.2.4 Results. 526FUTURE WORK AND OPEN ISSUES . 556.1 Extended Kalman Filter Convergence Issues. 556.2 Implementation Issues . 556.3 Detumbling Mode. 566.4 Simulation With Real Magnetometer Data . 566.5 Reducing the Order of Harmonics in the Magnetic Field Model. 576.6 Flight Torque Coils. 576.7 Testing . 57APPENDIX A : TORQUE COIL IMPLEMENTATION . 59A.1 Torque Coil Circuitry . 59A.2 Calculating Inputs for Torque Coil Circuitry . 61APPENDIX B : MAGNETOMETER IMPLEMENTATION. 63B.1 Magnetometer Circuitry . 63B.1.1 Hardware. 63B.1.2 Signals 63B.2 Calibration . 65B.2.1 Temperature and local magnetic effects . 66B.2.2 Hard and soft metal calibration. 66B.3 Normal Operation Procedure. 68APPENDIX C : OVERVIEW OF THE ATTITUDE CONTROL SYSTEM . 70APPENDIX D : CONVERSION BETWEEN THE RADIUS AND VELOCITY VECTORSAND THE ORBITAL ELMENTS . 72D.1 From the Radius and Velocity to the Orbital Elements. 72D.2 From the Orbital Elements to the Radius and Velocity. 73APPENDIX E : CONVERSIONS BETWEEN COORDINATE SYSTEMS . 75E.1 The Attitude Matrix for Converting Between the Geocentric Celestial Inertial andOrbital Reference Coordinate Systems . 75E.2 Obtaining the Angular Velocity of the Reference Frame With Respect to the InertialFrame. 76iv

E.3 The Attitude Matrix for Converting Between the Geocentric Celestial Inertial andGeocentric Fixed Coordinate Systems . 77E.4 The Satellite Fixed Body Coordinate System . 78APPENDIX F : CONVERSIONS BETWEEN ATTITUDE REPRESENTATIONS . 79F.1 Conversion from the Quaternion Vector to the Attitude Matrix . 79F.2 Conversion from the Attitude Matrix to the Quaternion Vector . 80F.3 Conversion from the Euler Angles to the Attitude Matrix . 81F.4 Conversion from the Attitude Matrix to the Euler Angles . 81APPENDIX G : QUATERNION MATHEMATICS . 83APPENDIX H : SIMULATION OVERVIEW. 85H.1 Flow Diagram of the Simulations. 85H.2 Magnetometer Simulation . 85H.3 Modeling Disturbance Torques . 87H.4 Gravity Gradient Torque . 87H.5 Aerodynamic Torque. 88H.6 Disturbance Torque Results . 92H.7 Attitude Propagation Algorithm . 93APPENDIX I : DERIVATION OF THE LINEARIZATIONS FOR THE EXTENDEDKALMAN FILTER AND LINEAR QUADRATIC REGULATOR . 94I.1 Linear Representation of the Extended Kalman Filter . 94I.2 Linear System for the Linear Quadratic Regulator . 98REFERENCES . 104v

LIST OF TABLESTABLE 1: ION’s Numerical Parameters. 5TABLE 2: Torque Coil Parameters . 59vi

LIST OF FIGURESFigure 1: Torque Coil. 7Figure 2: Intuitive Torque Coil Operation . 8Figure 3: HMC2003 Magnetometer. 10Figure 4: Small Integrated Data Logger (SID) . 11Figure 5: Geocentric Celestial Inertial Coordinate System . 14Figure 6: Geocentric Fixed Coordinate System. 14Figure 7: The Fixed Body Coordinate System . 15Figure 8: Satellite Reference Frame Coordinate System. 16Figure 9: Yaw Pitch and Roll Angles . 23Figure 10: The Three-Dimensional Orbit . 29Figure 11: Circumscribed Two-Dimensional Elliptical Plane. 31Figure 12: Orbit Propagation Algorithm. 33Figure 13: The Magnetic Field Algorithm. 36Figure 14: Attitude Ambiguity. 37Figure 15: Attitude Estimation Algorithm. 45Figure 16: Pss Calculation . 51Figure 17: Attitude Control Algorithm . 52Figure 18: Typical Steady State Yaw, Pitch, and Roll Angles for Linear Quadratic RegulatorControl . 53Figure 19: Typical Yaw, Pitch, and Roll Angles for an Initial 90 Attitude Deviation. 54Figure 20: Torque Coil Schematic. 60Figure 21: Magnetometer Circuit Schematic. 64Figure 22: Signal Specifications for “Set,” “Reset,” and “S/R ”. 64Figure 23: Magnetometer Coordinate System . 65Figure 24: Attitude Control System Flow Diagram. 71Figure 25: The Earth’s Equatorial Plane. 78Figure 26: Simulation Flow Diagram . 86Figure 27: Attitude Propagation Algorithm. 93vii

1 INTRODUCTIONWertz defines an attitude control system as “both the process and the hardware by whichthe attitude [of a spacecraft] is controlled” [1]. This thesis consists of the attitude control systemdesign for the CubeSat class satellite designed and built by students at the University of Illinois,which is known as ION, Illinois Observing Nanosatellite. As such, both of these aspects(process and hardware) of the attitude control system will be explored in detail.The attitude control hardware consists of a three-axis magnetometer to sample the Earth’smagnetic field, three torque coils mounted on each of ION’s three axes, and the microprocessorupon which the algorithms are implemented. The process by which this hardware is used by theattitude control system will be explained in detail throughout the second section of the paper.This thesis will begin with a short introduction to CubeSat satellites in general. It willthen provide a short overview of ION in particular. In the second section of the thesis, theattitude control hardware will be reviewed in detail. The third section of the thesis will introducesome of the basic theory necessary to address attitude control problems. The final section willinclude the algorithms that are implemented in the attitude control design.1

2 CUBESAT OVERVIEWThe section provides a brief overview of the CubSsat program. It continues bydiscussing the history of the CubeSat at the University of Illinios.2.1 History of the CubeSat ProgramThe construction of smaller satellites is currently a significant trend within the aerospacecommunity. The CubeSat program is part of this trend. Traditionally, satellites have been builton a grand scale, designed over the course of many years (sometimes even up to a decade).Typical masses for these large satellites would often exceed 1000 kg, and budgets required tobuild them were also enormous. Due to the accelerating advances of technology, many of theparts used on these satellites were obsolete before they were even launched. However, since the1990s, satellite designs have gotten smaller. Nanosatellites, or satellites with a mass between 1and 10 kg, have become more common. The advantage of these small satellites is that they canbe developed much faster and at considerably less expense. Their small size also presents manymore launch opportunities. Nanosatellites are often launched as secondary payloads on variousspace missions.The CubeSat Project started in 1999 as a collaborative effort between CaliforniaPolytechnic State University and Stanford University. The project’s goal was to standardize thedesign of these nanosatellites. The CubeSat standard specifies each satellite as a 10-cm cube of1-kg maximum mass. The standard also provides additional guidelines for the location of adiagnostic port, a remove-before-flight pin, and deployment switches. With this standardization,a number of satellites can be launched from a single deployment unit. Thus, it is possible todrastically reduce the launch cost for any single satellite. On June 30, 2003, the first six CubeSat2

class satellites were launched into space. Currently more than 30 high schools, colleges, anduniversities around the world are developing CubeSats. For more information on the CubeSatprogram, see http://cubesat.calpoly.edu/index.html.2.2 The History of IONThe CubeSat Program at the University of Illinois dates back to August of 2001. Theprogram was initiated under the guidance of Professor Gary Swenson in the Department ofElectrical and Computer Engineering and Professor Victoria Coverstone in the Department ofAerospace Engineering. CubeSat is a fundamental component of ITSI: the Illinois Tiny SatelliteInitiative. Since its conception, numerous students from various disciplines have contributed tothe design and implementation of ION. The California Polytechnic State University has been innegotiation with the Russian launch provider, Kosmotras, to launch a number of CubeSatsatellites from various universities. Kosmotras converts old Soviet SS-18 missiles into satellitelaunching vehicles. This is known as the Dnepr space launch system. ION is currently slated tobe included with a number of CubeSat satellites to go into orbit in the fall of 2004. Theprojected orbit is a 700-km circular orbit at 98 inclination with a 9:30-10:30 or 22:00-23:00local launch time. For more information on Kosmotras and the Dnepr space launch system, seehttp://www.kosmotras.ru/.2.3 ION’s DimensionsION is a CubeSat class satellite, which means it must abide by the requirements set downby Cal-Poly and Stanford. These requirements govern the physical dimensions, mass, andmaterials from which ION may be built. However, one characteristic of ION that distinguishes itfrom most CubeSats is that it is a two-cube design. In other words, the satellite consists of two3

10-cm cubes stacked on top of each other. Thus, the physical dimensions of ION are 10 cm x 10cm x 21.5 cm. It has a mass constraint of 2 kg.2.4 ION’s PayloadION has several important components in its mission. It will be flying two sensors aspayload. The first is a H7155 photomultiplier tube (PMT) that was manufactured byHamamatsu. This is a sensor that is used to measure an atmospheric emission known as airglowat altitudes of approximately 90 km. This data will be collected and processed under thedirection of Dr. Gary Swenson at the University of Illinois. For the PMT to acquire its data,there is a pointing requirement that the sensor should be nadir (Earth) pointing with a deviationangle of less than 10 . The pitch rate must be under 0.12 /s so that the angle deviation betweenscans is negligible. The sampling rate is a function of the altitude, but it will never be more than7 s per scan. Thus, only small changes in pitch can be made every 7 s. These are the moststringent requirements for the attitude control system. The secondary sensor is a complementarymetal-oxide semiconductor (CMOS) camera, the pb330 from Photobit. It will be used to takesnapshots of the Earth.Besides the sensor payloads, ION will also be space-qualifying hardware for a number ofits primary components. ION’s microprocessor is known as SID, the Small Integrated Datalogger. This is a single board computer designed around the Hitachi 32-bit RISC SH7045Fmicrocontroller. SID is credit card sized and runs at 15 MHz on less than 0.5 W. SID is aprototype designed by Tether Applications. The other hardware being space-qualified by ION isan electric propulsion system. This is a custom system that was designed and built by AlamedaApplied Sciences Corporation in cooperation with students at the University of Illinois. Thepropulsion system consists of a power-processing unit that controls four vacuum arc micro4

thrusters. These thrusters are small, pulsed electric thrusters, designed for attitude control ofsmall satellites. It is important to note that these thrusters represent a new technology withexciting possibilities. However, since this technology is untested, the attitude control systemdeveloped in this paper does not make use of the propulsion system as an actuation device. Onlythe torque coils are used for attitude control. See TABLE 1 for a table of some of ION’simportant parameters relating to the attitude control system. For more information regardingION, see http://courses.ece.uiuc.edu/cubesat.TABLE 1: ION’s Numerical ParametersOrbit PropertiesAltitudeEccentricityInclination700km 098 Satellite DimensionsXYZ10 cm10 cm21.5 cmDeviation From Centroid to Center of MassXYZ5.498 mm-1.079 mm4.760 mmMoments of InertiaIxIyIzIxyIxzIyz7.380 g-m27.475 g-m22.155 g-m2-0.03156 g-m2-0.09591 g-m2-0.03867 g-m25

3 THE ATTITUDE CONTROL HARDWAREThere are three main hardware components that are used in ION’s attitude controlimplementation: the magnetometer, the torque coils, and the flight computer. The first two areconcerned with magnetic fields. The first component, the magnetometer, is used to measure theEarth’s magnetic field. The second component, the torque coils, is the actuator that changes theorientation of the satellite in space. This is done by generating a magnetic field, which in turninteracts with the naturally occurring geomagnetic field of the Earth. The final hardwarecomponent is the flight computer upon which the algorithms and data processing are carried out.3.1 Torque CoilsIt is a well-known fact that running a current through a wire loop will generate amagnetic field. It is also well known that magnetic fields interact to generate torque. These arethe governing principles behind all modern motors. ION utilizes these principles in its attitudecontrol system through the use of torque coils or magnetorquers. These torque coils consist ofwire wound inside the satellite to form a large coil, as seen in Figure 1. This coil is used togenerate a magnetic field, which interacts with the geomagnetic field to change the orientation ofthe satellite. For details on the specifics of the torque coils and their required circuitry, seeAPPENDIX A. The development of the remainder of this section can be found in any standardtext on electromagnetism, such as [2].3.1.1 Overview of torque coil theoryA current flowing through the torque coils generates a magnetic dipole moment,according to the following equation:6

m NIAa n(1)Figure 1: Torque CoilThe parameter A is the cross sectional area of the coil, N is the number of turns of thecoil, and I is the current running through the coil. The direction of the dipole moment is normalto the coil, and is determined by the right-hand rule according to the direction the current ismoving in the coil. This is illustrated in Figure 2. The magnetic field at the geometric center ofthis rectangle, bm, with length a and width b is given by the following equation:bm 2µ 0 NI (a 2 b 2 )anπA(2)The parameter µ0 is known as the permeability of free space, which is 4π x 10-7H/m. Theinteraction of this magnetic dipole moment with the Earth’s magnetic field generates a torque, tm,according to the following equation:7

t m m be(3)The parameter m is as defined in Equation (1), and be is the earth’s magnetic field at aparticular location.For an intuitive understanding behind generating magnetic torques, see Figure 2. As canbe seen in this figure, the torque generated in this magnetic field tends to align the magneticdipole moment with the geomagnetic field. Note that there is no generated torque if themagnetic dipole moment is already aligned with the geomagnetic field.beIItmtmmtmbeIImmItmIbeFigure 2: Intuitive Torque Coil Operation3.1.2 Sizing the torque coilsAccording to Equations (1) and (3), the generated torque is proportional to the area of thecoil. So, ideally, the coils should be as large as possible. However, the physical dimensions ofthe satellite and the locations of the various components within the satellite limit the area of thecoils. Nonetheless, the coils are sized as large as possible to meet these constraints. The otherconstraint limiting the number of turns of the coil is that ION has only a finite amount of poweravailable for attitude control. After analysis of the spacecraft’s power budget, it was decided that0.1 W would be the maximum power available for each of the torque coils. As such, the coilsmay have as many turns as necessary as long as their total power dissipation is less than 0.1 W.8

The total power dissipated by the coil is given according to the well-known equation2P VbusRtotal(4)The resistance Rtotal is the total resistance of the coil and the H-bridge, which is found byRtotal Rbridge Rcoil(5)The resistance Rbridge is the resistance of the H-bridge. The resistance of the coil is given by theformulaRcoil lσS(6)The parameter σ is the conductivity of the wire, l is the length of the wire, and S is the wire’scross-sectional area. Finally, the length of the coil is related to the dimensions of the coilaccording to simple geometry:l 2 N ( a b)(7)From these equations, and the given power constraint of 0.1W for each of the torquecoils, it is possible to determine the number of turns in each of the coils. Combining Equations(4) through (7), we find the total number of turns as Vbus 2 N Rbridge 2(a b) P σS(8)3.2 The MagnetometerThe second major component of the attitude control system is the magnetometer. This isa sensor that measures magnetic fields. ION employs its magnetometer to sample the9

geomagnetic field. These field measurements are then used by the attitude control system toobtain estimates of ION’s orientation in space. Although it may be obvious, it is essential thatthe magnetometer should not be sampled while operating the torque coils. Otherwise, themagnetic field created by the torque coils will skew the measurement of the geomagnetic field.The particular magnetometer flown aboard ION is the HMC2003, which is manufactured byHoneywell. See Figure 3 for a picture of this magnetometer. As can be seen, this model is asolid-state circuit mounted on a 20-pin hybrid DIP package. This magnetometer is a three-axismagnetic sensor, which is capable of independently measuring three orthogonal components ofthe magnetic field using magnetoresistive transducers. This sensor can detect fields up to plus orminus 2 gauss, with an accuracy of 40 µgauss. Detailed information regarding theimplementation of this magnetometer may be found in APPENDIX B.Figure 3: HMC2003 Magnetometer3.3 The Flight ComputerThe flight computer is a commercial, off-the-shelf part from Tether Applications (TAI),Chula Vista, CA. They have developed the Small Integrated Data-logger, known as SID, with aneye towards its use aboard small satellites. See Figure 4 for a photograph of SID. ION will be10

the first satellite to fly SID into space, and will be providing TAI with feedback on SID’sperformance and the development experience.Figure 4: Small Integrated Data Logger (SID)SID is based on the Hitachi SH7045 microprocessor, a member of the SH-2 processorfamily. SID is only 10 x 55 x 85 mm and weighs a meager 35 grams. The microprocessor iscombined with many peripherals on a very small, heavily integrated board. In addition to its 256kB of onboard FLASH and 4 k

1 1 INTRODUCTION Wertz defines an attitude control system as "both the process and the hardware by which the attitude [of a spacecraft] is controlled" [1]. This thesis consists of the attitude control system design for the CubeSat class satellite designed and built by students at the University of Illinois,

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