The Attitude Determination and Control System of the Generic Nanosatellite Bus. Michael R. Greene

Transcription

1 The Attitude Determination and Control System of the Generic Nanosatellite Bus by Michael R. Greene A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Aerospace Engineering University of Toronto Institute for Aerospace Studies Supervisor: Dr. Robert E. Zee Copyright c 2009 by Michael R. Greene

2 Abstract The Attitude Determination and Control System of the Generic Nanosatellite Bus Michael R. Greene Master of Applied Science Graduate Department of Aerospace Engineering University of Toronto 2009 The Generic Nanosatellite Bus (GNB) is a spacecraft platform designed to accommodate the integration of diverse payloads in a common housing of supporting components. The development of the GNB at the Space Flight Laboratory (SFL) under the Canadian Advanced Nanospace experiment (CanX) program provides accelerated access to space while reducing non-recurring engineering (NRE) costs. The work presented herein details the development of the attitude determination and control subsystem (ADCS) of the GNB. Specific work on magnetorquer coil assembly, integration, and testing (AIT) and reaction wheel testing is included. The embedded software development and unit-level testing of the GNB sun sensors are discussed. The characterization of the AeroAstro star tracker is also a major focus, with procedures and results presented here. Hardware models were developed and incorporated into SFL s in-house high-fidelity attitude dynamics and control simulation environment. This work focuses on specific contributions to the CanX-3, CanX-4&5, and AISSat-1 nanosatellite missions. ii

3 Acknowledgements There are many people that I would like to acknowledge. First and foremost, Dr. Robert Zee. Thank you for the opportunity to be involved in this endeavour. A unique education unlike I had imagined, and an experience I will never forget. I am grateful for my time here, and your generosity throughout. I would also like to thank the following people: Adam Philip and John Gryzmisch for guiding my initial involvement with the attitude control group. Stuart Eagleson for his guidance and encouragement. Cordell Grant for his guidance. Tarun Tuli for his irreplaceable debugging help. Daniel Kekez for never being too busy to help find anything in the lab, as well as answer any question. Guy de Carufel for his tireless efforts, and friendship. Karan Sarda for the good talks. Mihail Barbu for his endless wealth of knowledge. Jake Lifshits for software help. Mark Dwyer for software help and crucial shawarma runs! Grant Bonin for his unique ability to motivate. Scott Armitage for relieving my AIT duties and being a L A TEX guru. Benoit Larouche for driving me too school during my entire first year. Without Ben I wouldn t have lasted long. Amee Shah for driving me to school in the winter of my second year. Doug Sinclair for teaching me how to solder. John Enright for the use of the Ryerson facilities. Dominic Sgro for facilitating many vibration tests. Ontario Graduate Scholarships. Professor Chris Damaren and his students Stefan LeBel, James Forbes, and Niels Roth for their genuine interest in all things dynamics and control related. Ben Mahar for making me a nerd growing up. Thomas Hartley for competing with me in High School. Dwayne Wenaas for inspiring me to become an engineer. Jacqueline Hansen for her company and support. My sisters for being all around awesome, and never letting me take too much credit. My parents for being the foundation of my resilient, loving family who have supported me throughout my life overabundantly. Thank you for teaching me about the important things in life. God, for blessing me with wonderful family and friends, and the ability to pursue my dreams. And finally, Gene Roddenberry for inventing Star Trek, Obi-Wan Kenobi for teaching me about the force, and Jedi Master Yoda for his resonating words of resolve: Do, or do not; there is no try... iii

4 Table of Contents 1 Introduction Space Flight Laboratory and the CanX program CanX Generic Nanosatellite Bus BRITE CanX-4 and CanX AISSat Attitude determination and control system overview Requirements Architecture Mirage OASYS Attitude system hardware Attitude determination hardware sensors Sun sensors AeroAstro star tracker Magnetometer Rate sensors Attitude control hardware actuators Reaction wheels iv

5 3.2.2 Magnetorquers Attitude control laws Rate damping Momentum management Three-axis control Sun avoidance Modelling and simulation AeroAstro star tracker Sun sensors Magnetorquers Conclusion Summary of contributions Future work Bibliography 92 v

6 List of Figures 1.1 CanX-2 layout [37] and mission patch The Generic Nanosatellite Bus (GNB) layout in exploded view courtesy of de Carufel [6] BRIght Target Explorer (BRITE) payload (telescope and star tracker) and mission patch CanX-4&5 payload (CNAPS) and mission patch AISSat-1 payload (Automatic Identification System (AIS) sensor and antenna) and mission patch Simplified dynamic feedback loop for spacecraft attitude control GNB ADCS architecture block diagram GNB sun sensor GNB fine sun sensor assembly layout side profile [18] CMOS active pixel (profile) sensor projection [25] FSS profile centroiding depiction Origin bias test result for FSS Resolution test result for FSS12 about each axis Accuracy map of FSS Bad sun sensor accuracy test results GNB sun sensor readout flowchart Severe pinhole filter misalignment Initial GNB sun sensor output timing profile vi

7 3.12 Initial output timing profile from FSS OUT CRC timing profile Revised timing profile of the GNB sun sensors The AeroAstro miniature star tracker A star field image taken with the MST on November 05, 2008 at 23:52 EST Rendering of the MST with body reference frame (courtesy of AeroAstro Inc.) A resolved quaternion output on November 05, 2008 at 23:55 EST Star tracker data parser GUI TXT2CSV MST accuracy plot Sept 10, ms integration time MST accuracy plot Sept 10, ms integration time MST accuracy plot Nov 5, ms integration time MST accuracy plot Nov 5, ms integration time MST accuracy plot Nov 5, ms integration time MST accuracy plot Nov 5, ms integration time MST accuracy plot Nov 5, ms integration time MST Exposure time profile Nov 5, MST test order profile Nov 5, Comparative coordinates of the MST and STK Sinclair/SFL reaction wheel GNB reaction wheel lifetime testing profile Preliminary reaction wheel design lifetest profile Lifetest profile of the second reaction wheel design (8 N preload) Lifetest profile of the third reaction wheel design (ceramic balls with diamond races) Positive speed steady-state accuracy test of N Negative speed steady-state accuracy test of N Steady-state accuracy profile of N Positive speed current draw telemetry of N Negative speed current draw telemetry of N vii

8 3.40 Power draw profile of N Axial dipole test on wheel N15 Magnetic field measurements Axial dipole test on wheel N15 Derived magnetic dipole moment UniBRITE Z-axis magnetorquer before manufacturing procedure modification UniBRITE Z-axis magnetorquer after manufacturing procedure modification Left: Clean room integration of UniBRITE flight X-axis magnetorquer. Right: Close-up of the integrated magnetorquer Centre-axis magnetic field testing of a GNB magnetorquer 25 C Mirage model of the AeroAstro star tracker AeroAstro star tracker model sample output (250ms) Mirage Simulink model for the GNB sun sensors FOV unit-sphere projection of AISSAT-1 sun sensors Fine sun sensor reference frame Simulated FSS profile of FSS07 - AISSAT-1 +X sensor Real profile of FSS07 - AISSAT-1 +X sensor DAC setting to current command relationship Mirage Simulink model for the GNB Magnetorquer GNB Magnetorquer Model - Output dipoles GNB Magnetorquer Model - Output magnetic field GNB Magnetorquer magnetic field testing results viii

9 List of Acronyms ACS Attitude Control System ADC Analogue to Digital Converter ADCS Attitude Determination and Control System ADS Attitude Determination System BRITE BRIght Target Explorer CANOE Canadian Advanced Nanospace Operating Environment CanX Canadian Advanced Nanospace experiment CMOS Complementary Metal-Oxide Semiconductor CNAPS Canadian Nanosatellite Advanced Propulsion System CSS Coarse Sun Sensors EKF Extended Kalman Filter FOV Field Of View FSS Fine Sun Sensors GCI GeoCentric Inertial reference frame GNB Generic Nanosatellite Bus GPS Global Positioning System GUI Graphical User Interface IGRF International Geomagnetic Reference Field ITRF International Terrestrial Reference Frame LEO Low Earth Orbit MOST Micro-variability and Oscillation of STars MST Miniature Star Tracker NORAD NORth-american Aerospace Defence OASYS On-orbit Attitude Subsystem Software OBC On-Board Computer PCB Printed Circuit Board PID Proportional plus Integral plus Derivative PSF Point Spread Function RMS Root Mean Square SFL Space Flight Laboratory SGP4 Simplified General Perturbations orbit model 4 STK Satellite Tool Kit TLE Two-Line Element UTC Universal Time Coordinated UTIAS University of Toronto Institute for Aerospace Studies ix

10 List of Symbols A a B C d F h i I K d K i K p m n Φ q S τ u V cc ω Area Euler-axis Magnetic field vector Rotation matrix Pinhole height Vectrix defining a particular reference frame Momentum vector Electric current moment of inertia tensor Derivative gain Integral gain Proportional gain Magnetic dipole vector Normal vector Euler-axis angle Quaternion vector Solar vector Torque vector Control torque Voltage common cathode Angular velocity vector Notation ( ˆ) Unit vector ( ) i Expression in the inertial frame ( ) b Expression in the body frame ( ) s Expression in the sensor frame ( ) Time derivative ( ) Skew-symmetric (cross) matrix ( ) e Error quantity ( ) d Desired quantity ( ) T Matrix transpose ( ) 1 Matrix inverse ( ) Vector quantity x

11 Chapter 1 Introduction The Space Flight Laboratory (SFL), located at the University of Toronto Institute for Aerospace Studies (UTIAS), is steadily developing spacecraft on the microsatellite 1 and nanosatellite 2 scale. At the heart of SFL is the Canadian Advanced Nanospace experiment (CanX) program. This program, established in 2001, educates graduate students in space systems engineering through the development of real spacecraft under the guidance of skilled engineering staff. In this unique apprentice-style environment, students are trained to become the future of Canada s space systems engineers. While SFL offers a strong graduate education, equal focus is given towards the rapid development of reliable, cost-effective spacecraft for industry, academia, and government. In order to accommodate for the desire to accelerate spacecraft development while reducing costs, the CanX program centres its focus on the development of the Generic Nanosatellite Bus (GNB) a 20 cm cube spacecraft bus which provides a common platform for a variety of current and future missions. The versatility of the GNB is achieved through an adaptable payload bay. The GNB concepts hinges on minimizing non-recurring engineering (NRE) across multiple nanosatellite missions. At present, three distinct missions make use of this bus: CanX-3 also known as BRIght Target Explorer (BRITE) is an asteroseismology mission to determine the age and histories of the most luminous stars in the sky through precise brightness and temperature 1 Microsatellites are spacecraft under 100 kg. 2 Nanosatellites are spacecraft under 10 kg. 1

12 Chapter 1. Introduction 2 variation measurements; CanX-4 and CanX-5 two identical GNB spacecraft whose mission is to demonstrate precise autonomous formation flying; and AISSat-1 a Norwegian-funded satellite is equipped with an Automatic Identification System (AIS) sensor to investigate the feasibility and performance capabilities of tracking maritime ships near the territorial waters of Norway. The success of these nanosatellites relies in part on the ability of the spacecraft to autonomously determine their orientation, and subsequently control their state. This is the role of the attitude determination and control subsystem (ADCS). The attitude of a spacecraft is defined as its orientation relative to an external frame of reference. This metric is determined autonomously in real-time using a suite of sensors which make up the attitude determination subsystem (ADS). An ensemble of electro-mechanical actuators is necessary to control the satellite s attitude to a desired reference or target; this is the function of the attitude control subsystem (ACS). A variety of conceptual ADCS architectures may be pursued for any particular mission. The GNB ADCS follows a baseline design to which sensors and actuators may be added to best accommodate specific mission requirements. Further discussion of the GNB ADCS architecture is found in Section 2.2. Reliable, consistent, and accurate performance of the ADCS is fundamental to spacecraft operations, and often critical for mission success. At present, spacecraft attitude subsystem design is a well-developed engineering practice. However, the design and development of a precise attitude control subsystem on the nanosatellite scale is a concept very much in its infancy. The increase in mission complexity at this scale drives the need for increasingly more precise attitude control on progressively smaller platforms. In order to accomplish fine pointing, the ADCS requires accurate sensors along with small-scale actuators capable of fine torque resolution. To achieve three-axis pointing control, several heuristic controllers have been pursued. For example, SFL s own CanX-2 has demonstrated three-axis control using three magnetic torque coils complemented with one reaction wheel. The GNB ADCS is required to achieve fine pointing control with rapid slewing capabilities in all three axes. To accomplish this ambitious task, three orthogonal reaction wheels are required. Presented here is a detailed discussion of the GNB ADCS hardware development, testing, and modelling. An overview of the GNB control laws are also included.

13 Chapter 1. Introduction Space Flight Laboratory and the CanX program The UTIAS Space Flight Laboratory was established in It was founded on the principle that a small, tightly-integrated, multidisciplinary team of skilled spacecraft engineers working together in a less formal environment is effective in achieving severely cost- and scheduleconstrained mission objectives. This is the foundation for the revolution within the space industry, adopting what is known as the microspace philosophy [13, 39, 41]. Included in this initiative is the suggestion to use commercially available components as opposed to more expensive and less available radiation-hardened components, and to select and validate these components through comparative radiation testing. Parts are derated using conservative margins, and must consider typical mission design lifetimes of 1 3 years [42]. Thorough testing at every level of spacecraft development is paramount, and intelligent design is preferred over part redundancy. In its first year, SFL was entrusted with the responsibility to design, build, and test the structural, thermal, computer, and communication subsystems for the MOST (Micro-variability and Oscillation of STars) microsatellite. Developed as Canada s first space telescope and first home-built satellite in over 30 years, MOST is a 53 kg microsatellite designed to perform longduration stellar photometry [29]. SFL continues to head mission control operations for MOST. Upon the success of MOST, SFL continued to build spacecraft, in particular within the CanX program. CanX-1 is a 1 kg, 10 cm cubesat launched in 2003 with MOST as a programmatic pathfinder mission. CanX-2 and CanX-6 were both launched on April 27, 2008 on board the Indian Space Research Organization (ISRO) Polar Satellite Launch Vehicle C9 (PSLV- C9). CanX-2 is a multi-mission bus whose objectives are to demonstrate technologies vital for formation flying and to operate a suite of payloads which are currently gathering science data for the academic community. CanX-2 is covered in more detail in Section CanX-6 also known as Nanosatellite Tracking Ships (NTS) is a 6.5 kg nanosatellite demonstrating and testing space-based AIS detection technology. The NTS spacecraft bus was developed by UTIAS/SFL under contract from COM DEV International Ltd. who supplied the payload (AIS sensor). In order to conform to tight scheduling, NTS was build using the GNB structure

14 Chapter 1. Introduction 4 with CanX-2 electronics, and a passive ACS scheme (permanent magnets and hysteresis rods). Spanning seven months from conception to launch, NTS is an excellent example of rapid, responsive spacecraft development. SFL is also involved in research regarding electric propulsion, deep space communications, and mitigation of radiation effects on commercial off-the-self (COTS) components. Each area of research is geared towards advancing microspace development. In addition, SFL provides the Nanosatellite Launch Services (NLS) to facilitate launches for other nanosatellite programs [42] CanX-2 The CanX-2 nanosatellite, shown in Figure 1.1, was launched in April of 2008 on board the PSLV-C9 launch vehicle from Sriharikota, India. On a bus measuring 10 cm 10 cm 34 cm and a mass of 3.5 kg, CanX-2 houses a plethora of scientific and engineering payloads that push the envelope of capabilities for this class of spacecraft. Figure 1.1: CanX-2 layout [37] and mission patch The primary mission objective of CanX-2 is to test and demonstrate several enabling technologies for the CanX-4&5 autonomous formation flying mission. These technologies include a custom cold-gas propulsion system, a 30 mn m s nanosatellite reaction wheel as part of a threeaxis stabilized momentum-bias attitude control system, and a commercially available Global Positioning System (GPS) receiver. The secondary objective of CanX-2 is to fly a number of

15 Chapter 1. Introduction 5 university experiments including an atmospheric spectrometer from York University, a GPS radio occultation experiment from the University of Calgary and an atomic oxygen material degradation experiment from the University of Toronto. At present (August 2009), CanX-2 has been in orbit for over 15 months and has achieved success by accomplishing many of its science and technology demonstration objectives [19]. The ADCS of the GNB has obtained significant flight heritage from CanX-2. The GNB sun sensors, magnetometer, reaction wheel, magnetorquers, and on-board software (OASYS) are all derived from the CanX-2. Flight heritage and lessons learned from CanX-2 have proved invaluable for GNB design, testing, and integration. 1.2 Generic Nanosatellite Bus The design of the GNB platform, shown in Figure 1.2, was initially conceived as a means of reducing cost, conforming to tight scheduling, and providing confidence in spacecraft reliability through the acquisition of space flight heritage. It was originally designed around two missions BRITE and CanX-4&5 and has since been applied to accommodate the AISSat-1 mission. In order for the GNB to successfully encapsulate the multi-mission bus concept, it was designed such that it could envelope performance and functionality of all current and projected missions. As a result, the GNB is a robust design, supported through highly adaptable subsystem design and validated through rigorous testing BRITE BRITE is a four-satellite constellation whose mission is to conduct long-term stellar observations. The objective of BRITE is to detect the variations in apparent luminosity of certain stars in order to infer their history, core composition, and internal structure. This is accomplished through asteroseismology [14]. The brightness of a particular star will oscillate as a result of internal pressure and gravity wave effects. Fourier analysis is applied to the long-duration photometric time series obtained from the BRITE telescope to extract the frequency of these oscillations, which are estimated to be on the order of a few hours, up to several months. The BRITE constellation will be operated in two distinct pairs of satellites, each of which

16 Chapter 1. Introduction 6 Figure 1.2: The GNB layout in exploded view courtesy of de Carufel [6] will have one satellite operate an optical filter passing 390 nm to 460 nm and the other passing 550 nm to 700 nm. This allows for dual-broadband high-precision differential photometric observations providing increased time coverage [40]. Every orbit, each pair of BRITE satellites will monitor a specific star field for a duration of up to 15 minutes. The total observational period for each target star field will be up to 100 days. BRITE scientists have selected several target star fields to be observed during the planned mission life of at least 2 years. The information obtained from the BRITE mission will provide insight into the generation of heavy elements, the creation of planets, and the ecology of the Universe essentially outlining the life-cycle of matter which makes up life as we know it. BRITE s primary targets are hot luminous stars (O and B stars found in the upper left region of the H-R diagram), massive stars, and stellar supernovae. As a secondary objective, BRITE is to observe cool luminous stars, such as Red Giants, which are rich in carbon and neutron production. BRITE will determine the timescales of surface fluctuations and infer internal convective behaviour of these stars. BRITE is the first mission conceived to employ the GNB design. In addition to the baseline GNB design, each BRITE satellite will be equipped with a small-aperture telescope and a star

17 Chapter 1. Introduction 7 tracker located in the payload bay. The BRITE payload assembly is shown in Figure 1.3. The BRITE telescope has a field of view (FOV) of 24 and is designed to detect stars with an apparent magnitude of +3.5 using an 11 megapixel charge-coupled device (CCD) detector array and optical band-pass filter. The star tracker, built by AeroAstro, provides high-precision 3-axis attitude estimates. More on the BRITE star tracker in Section Figure 1.3: BRITE payload (telescope and star tracker) and mission patch CanX-4 and CanX-5 Funded in part by the Canadian government, CanX-4 and CanX-5 are identical GNB satellites designed to execute precise formation flying in low-earth orbit (LEO). Their mission objectives are to demonstrate sub-centimetre relative position determination, sub-metre relative position control and autonomous formation maintenance in multiple orbital configurations at various separation distances. The latter objective requires the development of fuel-efficient autonomous formation flight algorithms [15]. In order to achieve precise formation flying, CanX-4&5 are equipped with the Canadian Nanosatellite Advanced Propulsion System (CNAPS), a GPS receiver, an inter-satellite radio link, and a third computer to provide formation flying control. CNAPS, located in the GNB payload bay, is shown in Figure 1.4. It uses sulfur hexafluoride (SF 6 ) as propellant, thus

18 Chapter 1. Introduction 8 operating as a cold-gas propulsion system. Attempts to reduce any misalignment between the CNAPS thrust axis and the spacecraft centre of mass are made during the design and integration phase, however complete mitigation is unlikely. For this reason, CNAPS has four adjustable nozzles which act to regulate the thrust vector in order to account for any misalignment thereby reducing the latent momentum build-up on the reaction wheels. Figure 1.4: CanX-4&5 payload (CNAPS) and mission patch CanX-4&5 will obtain precise relative positioning information through real-time kinematical (RTK) double-differencing of the GPS L1 carrier phase. The computer algorithms required for this technique were developed at the University of Calgary under the supervision of Professor Elizabeth Cannon. Determination of the relative position and velocities between CanX-4 and CanX-5 will be resolved to centimetre-level accuracy using an extended Kalman filter (EKF) for filtered estimation. In order to accomplish this mission objective, the absolute position of each satellite as obtained from identical GPS satellites will be acquired using a COTS receiver from Novatel inc., and then exchanged between CanX-4 and CanX-5 using the intersatellite link (ISL) radio. CanX-4&5 will maintain identical attitudes in order to ensure that the same GPS satellites are in view, as required to properly perform this type of differential GPS. CanX-4&5 will be launched and commissioned while physically connected. They will then be separated on-orbit using the intersatellite separation system (ISS). Once separated, they

19 Chapter 1. Introduction 9 will drift out to a relative distance of 1 km, at which point formation flying is scheduled to begin. During the projected mission life of two years, CanX-4&5 will demonstrate two distinct formations: an along-track orbit (ATO) and a projected circular orbit (PCO). CanX-4&5 will also have the capability to preform an autonomous re-configuration manoeuvre between the two formations. In the ATO, one satellite will lead the other in the same orbit by a fixed separation distance. This formation is particularly beneficial for several remote sensing applications such as interferometry, stereoscopic photogrammetry and synthetic-aperture radar (SAR). In a PCO, one satellite appears to fully encircle the other once per orbit. This effectively demonstrates the ability to perform on-orbit inspection of one satellite by the other, potentially leading to applications of on-orbit servicing. While CanX-4&5 execute formation flying, one satellite will be referred to as the chief and the other as the deputy. The role of the deputy is to follow the chief in the desired formation, expelling propellant as needed in order to actively control their relative position. The deputy will also determine and control its attitude appropriate for thrusting, while maintaining GPS lock. Thus, the deputy is responsible for all orbital station keeping throughout the duration of the formation flying demonstration. The role of the chief is therefore, to broadcast its position to the deputy, and also control its attitude to maintain an identical orientation as that of the deputy satellite. Orientation and timing of formation flying control thrusts are directed by the Formation-flying Integrated On-board Nanosatellite Algorithm (FIONA), a precise formation flying algorithm developed by Jesse Eyer [11, 12] and Niels Roth, students of the Spacecraft Dynamics and Control Laboratory at UTIAS, directed by Dr. Chris Damaren. In the event that one satellite is damaged or exhausts its fuel supply, roles may be quickly reversed in order to prolong the mission. In this case, a reconfiguration manoeuvre will take place. The ability to perform an efficient reconfiguration manoeuvre is a fundamental system driver to the CanX-4&5 mission. CanX-4&5 are also capable of performing a recovery manoeuvre. This is required if the satellites drift too far apart, beyond the limited sphere where formation flying is practical. This may occur in a variety of anticipated ways, be it a loadshed condition where the formation flying computer is inactive for a prolonged period of time or a GPS outage occurs long enough to cause the EKF solution to diverge beyond reasonable limits.

20 Chapter 1. Introduction 10 These situations cause FIONA to rely on degraded estimates, potentially leading to excessive drift. The recovery manoeuvre is designed to handle these foreseeable circumstances and, more importantly, will be robust against the unforeseeable ones. This additional functionality is also included in FIONA, and will be tested thoroughly prior to launch. Upon the success of CanX-4&5, Canada will be among the first nations to successfully demonstrate formation flying capabilities AISSat-1 Funded by the Norwegian Space Centre (NSC) and led by FFI (Forsvarets Forskningsinstitutt Norwegian Defence Research Establishment), AISSat-1 is the third nanosatellite conceived to use the GNB architecture. Although AISSat-1 is the third GNB mission, it is scheduled to be launched in Q4 2009, before any other GNB satellite. This is due to the urgency of the mission as expressed by FFI, the prime contractor. AISSat-1 will investigate the feasibility and performance capability of tracking maritime ships near the territorial waters of Norway from LEO [34]. AIS is a system used by ships and Vessel Traffic Services (VTS) primarily for identifying and locating seafaring vessels. All ships registered to use this system are equipped with a VHF transponder which transmits and receives the AIS signal. Located in these signals are the identification, position, course, and destination of the ship from which it originates. A common limitation to AIS is that the stations which receive this signal are found on coastal land and may only receive signals within a limited radius about the coast. Therefore, relying solely on terrestrial based stations will likely cause many ships to go undetected. The country of Norway in particular, which has large fishing zones under their jurisdiction, does not presently have the capability to detect these signals over their entire precinct. As a result, FFI has pursued the GNB as the nanosatellite platform from which to test the feasibility of detecting these signals from space. Complementary to the primary objective, AISSat-1 will be equipped with a GPS receiver in order to perform a particular method of triangulation. If successful, AISSat-1 will also be able to verify the location of the vessels from whom the signal was received. This estimation will be coarse, however it is expected to provide sufficient information for a general validation.

21 Chapter 1. Introduction 11 In order to successfully detect AIS signals from space, AISSat-1 is equipped with a VHF monopole antenna. The electronics to operate this antenna are designed to mount in the GNB payload bay. The AISSat-1 payload, shown in Figure 1.5, was built by Kongsberg Seatex (KSX) through funding provided by NSC. Figure 1.5: AISSat-1 payload (AIS sensor and antenna) and mission patch A primary concern for AISSat-1 surrounds an intrinsic difficulty in processing AIS signals. That is, when there are a large number of AIS signals being received by the same antenna simultaneously, it is very difficult and in some cases impossible to distinguish them. This will unfortunately cause all of the signals to be lost. In LEO, at an altitude ranging from 500 km to 950 km, the field of view (FOV) of the AIS signals increases dramatically compared to that of a terrestrial station, and consequently the ability to discern each signal decreases considerably. The density of naval vessels in the ocean is highly dependent on the particular region of interest. In order to ensure that the VHF transmissions from different transponders are not analyzed concurrently, the signals are time-multiplexed using self-organized time division multiple access (SOTDMA).

22 Chapter 2 Attitude determination and control system overview With very few exceptions, no modern spacecraft could successfully accomplish its mission without a functioning system able to stabilize and orient the vehicle to a desired attitude. Depending on the mission, attitude control is accomplished either through passive or active means. Earthorbiting spacecraft experience incessant physical disturbances caused by multiple sources within the orbital environment, each imparting a torque on the satellite. These torques are produced by gravity gradient effects, magnetic disturbances, solar radiation pressure, and atmospheric drag. The accumulation of these disturbance forces, either cyclical or secular in nature, act to reorient the vehicle and are therefore of direct concern to the ADCS. Through clever design, a passive attitude control system will harness one or more of these natural torques, causing the spacecraft to stabilize towards an innate equilibrium corresponding to a desired attitude. Several examples of a passive attitude control include: gravity gradient stabilization, where differential gravitational forces imparted along the body of a spacecraft will produce a moment; passive magnetic attitude control using permanent magnets with hysteresis rods, which will act to align the spacecraft to the local magnetic field of the Earth; and spin stabilization which makes use of conservation of angular momentum, whereby gyroscopic stiffness of a spinning spacecraft is used to maintain a constant attitude relative to a specific inertial vector in one spacecraft axis. In a passive attitude control scheme the environmental torques are not only 12

23 Chapter 2. Attitude determination and control system overview 13 tolerable, but required. Each passive scheme will align the vehicle to a specific equilibrium, with typical accuracies no greater than 5. For those missions where the stable equilibrium point of a passive scheme is non-ideal, the accuracies obtained will simply not satisfy requirements, or the mission requires a continuously varying attitude, a means of active control must be pursued. An active ACS works to resist the disturbance torques imparted on the spacecraft by the external environmental factors. In many cases, such as for inertially pointed spacecraft, the sole purpose of the ACS during nominal operations is to perform disturbance rejection. Active attitude control relies on feedback of information detailing the state of the spacecraft. Therefore, the use of attitude sensors are required, with actuators providing control authority based on prescribed control laws. This concept of feedback control is illustrated in Figure 2.1. θ T arget + Controller Control Torque Disturbance Torque N d N c + + N net Spacecraft θ Out Dynamics θ Measured Sensors Figure 2.1: Simplified dynamic feedback loop for spacecraft attitude control Active attitude determination and control systems are capable of achieving extremely precise pointing control, depending heavily on the calibre of hardware used. However, ADCS hardware with the proven capability of providing accurate 3-axis determination and control at the nanospace scale has simply not been available until recently. Section 3 outlines the ADCS hardware used on the GNB, most of which are considered highly innovative technologies, pushing the envelope in micro- and nano-space capabilities. The design of an ADCS is a non-intuitive task. Relying initially on the study of rigidbody dynamics is favourable, however it can often be a poor assumption. In many cases, consideration of structural dynamic effects caused by the influence of flexible body appendages,

24 Chapter 2. Attitude determination and control system overview 14 such as antennas or large booms, is necessary. Fluid dynamic effects, such as those caused by the sloshing of fuel, also impact spacecraft dynamics and result in energy dissipation [26]. In some cases, these factors must be considered in order to obtain a representative model, and thus to design an appropriate ADCS. When designing the attitude subsystem for a nanosatellite such as the GNB, any structural appendages are typically small and sufficiently stiff such that the attitude dynamics may be adequately modelled as a rigid body. The equations governing the motion of a satellite used for ADCS design are inherently non-linear and moving noninertial frames lead to temporal derivatives of moving vectors, thereby adding another degree of complexity. There are several ways to define the attitude of a satellite. A three-parameter set such as the Euler angle set analogous to roll, pitch, and yaw is attractive as it contains as many variables as degrees of freedom and is therefore easy to visualize. However, like any three-parameter set, Euler angles are subject to singularities [26]. By contrast, Euler parameters also known as quaternions are a four-parameter set used to describe spacecraft attitude. They originate from Euler s theorem that states: the most general motion of a rigid body with one point fixed is a rotation about an axis through that point [26]. Euler parameters are advantageous for describing spacecraft attitude in that they avoid the singularities encountered with the use of three-parameter sets. They are also much more computationally efficient as they avoid complex trigonometric routines. For this reason, Euler parameters are of great interest in the field of spacecraft attitude dynamics and are used to describe the attitude of the GNB. Euler parameters (quaternions) The following section defines quaternions along with some other important parameters used throughout this dissertation. Consider an angle of rotation φ about a fixed axis a, referred to as the screw axis. The screw axis has components a = [a 1 a 2 a 3 ] T such that a T a = 1. The quaternion q = {ε, η} is then given by ε = a sin φ 2 and η = cos φ 2. (2.1) We can state without proving it here that, for a given rotation, the angular rate ω is given

25 Chapter 2. Attitude determination and control system overview 15 by It can then be shown that ω = φa (1 cos φ) a ȧ + (sin φ) ȧ. (2.2) φ = a T ω and ȧ = 1 2 [a φ2 a a ] ω. (2.3) Taking the temporal derivative of (2.1) and using the results of (2.2) and (2.3), the kinematical equations for Euler parameters lead to q = 1 η1 + ε ω. (2.4) 2 ε T This relationship is more useful for our purposes when solved in terms of the rates as shown by η ε 3 ε 2 ε 1 ω = 2 ε 3 η ε 1 ε 2 q. (2.5) ε 2 ε 1 η ε 3 We have now defined the necessary parameters to use quaternions in spacecraft attitude control applications. 2.1 Requirements The GNB ADCS requirements vary considerably for each mission. As an astronomy mission, BRITE is focused on precise pointing control and stability with robust disturbance rejection. Conversely, the ADCS of CanX-4&5 will focus on performing rapid slewing with a relaxed requirement on stability and pointing accuracy. CanX-4&5 also has the constraint of pointing the GPS receiver to Zenith, while BRITE must avoid pointing the telescope towards the Sun. The AISSat-1 ADCS requirements fall in between these two extremes. The goal is to develop a system capable of encapsulating the requirements of all current and potential GNB missions, thus truly adopting a multi-mission architecture. This is accomplished by designing for the worst-case environmental conditions, adopting conservative margins, and allowing for versatility within the design. The initial GNB ADCS design will encapsulate the stability requirements of

26 Chapter 2. Attitude determination and control system overview 16 BRITE with the slewing and momentum dumping capabilities of CanX-4&5. This will ensure that future redesign is avoided as much as possible. ADCS requirements are defined in several ways. Pointing error, accuracy, jitter, and stability are often misunderstood and found to be ambiguous in many cases. For brevity they are listed here pertaining specifically to spacecraft attitude. A full description can be found in [33]. Pointing error: the angular offset from a desired attitude defined as a rotation about each body axis. Accuracy: the root-mean-square (RMS) of the pointing error over an extended period of time. Jitter: the RMS of the pointing error within a specific interval of time. This period is much shorter than that defined for accuracy, typically lasting the duration of a measurement e.g. for optical applications, this time period would refer to the integration time of the camera. Stability: the RMS change in the attitude from one end of an interval of time to the other. In order to verify that the attitude subsystem is capable of satisfying all requirements, rigorous hardware characterization testing and simulation is pursued. Specific mission requirements are detailed in subsequent sections. BRITE Upon initial acquisition, the star-field must enter the FOV of the BRITE telescope CCD array with pointing error that results in an accuracy of 0.5 RMS [8]. During the imaging period of approximately 15 minutes, each pair of BRITE satellites must remain inertially fixed on a particular star-field with a stability of 2 3 pixels (50 75 arcseconds) RMS (3σ). However, some wander may be desirable to smooth out sharp peaks in the point spread function (PSF) of the telescope. Every orbit, the target star field will be occulted from the telescope and star tracker, and hence the attitude will drift slightly (although sun sensors and magnetometer will remain active). Upon reacquisition, it is desired that the star field lie within 1 pixel (25 arcseconds) RMS (3σ), thus ensuring that the total accuracy and stability to remain within 3 pixels during

27 Chapter 2. Attitude determination and control system overview 17 image capture. The star tracker will initially be used for attitude determination, however the 1 pixel repeatability will be accomplished using feedback from the telescope in order to ensure each star lies on the appropriate pixel [8]. Along with pointing and stability requirements, BRITE has the added requirement of solar avoidance imposed by the telescope. This is primarily of concern when slewing to a new starfield, however it is also of concern during reacquisition in the case that the spacecraft drifts sufficiently that a direct eigenaxis rotation would pass the imager FOV through the Sun. Control laws developed for this are discussed in Section 4. CanX-4 and CanX-5 As a formation flying mission, CanX-4&5 do not require the stringent stability and accuracy sought by the BRITE mission. An accuracy of 2 is required when pointing CNAPS prior to thrusting. Any greater will cause the exhausted fuel to result in the required delta-v exceeding practical limits, severely limiting the mission life. Moreover, during commissioning while CanX-4&5 are attached in their pre-separation configuration a pointing accuracy of 5 shall be maintained [10], in order to validate the ADCS. The CanX-4&5 requirements focus primarily on rapid slewing capability: each spacecraft must be able to complete a worst-case slew of 180 within a 45 second period. Typical expected slews are on the order or 20 to 30 [36]. In addition, the ADCS must help to maintain GPS lock to the best of its ability. This will typically imply a zenith-facing GPS antenna in order to ensure that the maximum number of available GPS satellites are continuously view. However, there may be occasions where maintaining an attitude slightly off zenith will be beneficial in the case where a lock is already achieved, as opposed to foregoing a current GPS lock in order to point to zenith. As a result, the worst-case slewing requirement imposed on CanX-4&5 becomes a slew between two vectors which are 180 apart in a trajectory while ensuring GPS lock is maintained. As previously mentioned, the attitude of both CanX-4 and CanX-5 will be mirrored in order to ensure the position, velocity, and time (PVT) solution is determined through signals from identical GPS satellites.

28 Chapter 2. Attitude determination and control system overview 18 AISSat-1 The receiver gain corresponding to the detected AIS signal is directly correlated to the attitude of AISSat-1. This is due to the fact that the VHF antenna beam pattern is fixed to the spacecraft body frame. The desired apparent antenna gain is, at present, an undetermined quantity, as it is highly situationally dependent. This is due to the fact that, at any given time, a large number of ships may be in view, which in turn causes overall signal degradation thereby increasing the probability of lost signals. In order to account for this, a reduction in receiver antenna gain may be desired to provide a means of filtering out several of the weaker signals resulting in fewer signal collisions and better overall reception. Development of this technique is, in part, a mission objective for AISSat-1 [2]. That being said there are concrete requirements imposed on the AISSat-1 attitude control subsystem. A full tabulation of these requirement can be found in [9], with the most pertinent listed here: The ADS shall be capable of estimating attitude with an accuracy of at least 2.5. This includes when the payload is active, regardless of eclipses. The ACS shall be able to provide full three-axis, full sphere, control with an accuracy of at least 3.3. The ACS shall keep the satellite from spinning at a rate greater than 90 /s or the Nyquist limit of the EKF, using the slowest-update sensors. ADCS requirements summary To summarize, the ADCS of the GNB is required to be suitable for missions of varying performance requirements. BRITE is focused on fine pointing control and stability. CanX-4&5 by contrast is able to afford coarse pointing and stability but requires rapid slewing capabilities. The ADCS of AISSat-1 is not driven by either extreme; however it must remain operational throughout the entire mission duration, including eclipse. This suggests the use of rate sensors to account for the loss of solar vector estimate, as discussed in Section 2.2. Table 2.1 outlines the GNB ADCS requirements for all current missions.

29 Chapter 2. Attitude determination and control system overview 19 Mission BRITE CanX-4&5 AISSat-1 Mission BRITE CanX-4&5 AISSat-1 Mission BRITE CanX-4&5 AISSat-1 Pointing Accuracy and Stability Requirements 0.5 RMS (initially) 0.5 arcminutes (reacquisition) 2 RMS when pointing CNAPS 5 RMS while joined 3.3 RMS Slewing Requirements Slew telescope to target star field within minimum time available 180 within 45 s while maintaining GPS lock Not Defined Other Constraints Telescope must remain >45 from solar vector 2-year mission life Maintain GPS lock 2-year mission life Spin rate must not exceed 90 /s 3-year mission life Table 2.1: GNB ADCS requirements summary 2.2 Architecture The GNB ACS baseline design includes three orthogonal reaction wheels and three orthogonal magnetic torque coils (magnetorquers) responsible for attitude control actuation. The GNB ADS sensor suite includes six sun sensors (one per face) and one magnetometer. Hardware development and testing for which the author was directly responsible is outlined in Section 3. In order to accommodate the requirements of both AISSat-1 and CanX-4&5 which state that attitude estimation must be available during eclipse, these satellites are equipped with rate sensing gyroscopes as an addition to the standard GNB ADCS architecture. Also augmenting the GNB design, CanX-4&5 and AISSat-1 will be equipped with a GPS receiver and antenna for accurate position determination. This is required for formation flying and AIS triangulation respectively. For BRITE, a star tracker is required in order to satisfy the stringent pointing requirements. A star tracker is capable of determining spacecraft attitude in all three axes to high accuracy, and fine precision see Section The sun sensors and magnetometer are

30 Chapter 2. Attitude determination and control system overview 20 complementary attitude sensors on BRITE. During a star-field imaging campaign, the startracker and imager will assume primary ADS responsibility, as previously discussed. During star-field occultation, the magnetometer and sun sensors will update the attitude estimate, keeping it from diverging beyond reasonable limits. Figure 2.2 illustrates the ADCS architecture for the GNB. In general, the attitude subsystem can be divided into three distinct categories: sensors, controller (OASYS), and actuators. Sensors Sun Sensors (One per face) OASYS SGP4 IGRF Solar Ephemeris (Orbital Propagator) (Magnetic Field Model) (Earth-Sun Model) Legend Magnetometer (3-axis) AeroAstro Star Tracker EKF (State Estimation) Controller Baseline GNB ADCS Components BRITE Specific Components Rate Gyros (3-axis) GPS Receiver Actuators Reaction Wheels Magnetorquers (3 Orthogonal) (3 Orthogonal) CanX4&5 and AISSAT-1 Specific Components Figure 2.2: GNB ADCS architecture block diagram Slew and pointing manoeuvres are implemented using a near-minimum-time eigen-axis rotation algorithm in OASYS (On-orbit Attitude SYstem Software). This control implementation is desired as it reduces the required actuation from three separate rotations to a single unified rotation. Further discussion of the GNB control laws are outlined in Section Mirage Mirage is SFL s high-fidelity attitude simulation environment, developed by staff and students throughout the duration of the CanX program. It is implemented in MATLAB s Simulink environment, and includes a detailed, user friendly, front end graphical user interface (GUI). Mirage uses the Simplified General Perturbations Satellite Orbit Model 4 (SGP4) to propagate the position and velocity of the spacecraft. SGP4 uses the two-line element sets (TLEs) con-

31 Chapter 2. Attitude determination and control system overview 21 taining the mean orbital elements issued by the North American Aerospace Defense Command (NORAD) and outputs the propagated state vector in discrete time intervals. The SGP4 model considers the secular effects of the J 2, J 4, and J 2 2 gravity terms, long-periodic effects of J 3 and short-periodic effects of J 2, as well as atmospheric drag. This is the identical orbital propagator used onboard each GNB spacecraft. Mirage will then compare the position and velocity state vector to the International Geomagnetic Reference Field (IGRF) model in order to estimate the magnetic disturbance torques exerted on the satellite and to provide a model of the Earth s magnetic field. The simulated magnetometer measurements are differenced against this magnetic field model as a means to calculate the attitude of the satellite, however this attitude measurement is constrained to two axes due to ambiguity about the local magnetic field line. Also included in Mirage is a solar ephemeris model. This model propagates the Earth-Sun vector against which the sun sensor measurements may be compared in order to provide a complementary two-axis attitude estimate, with ambiguity about the solar vector. Solar radiation pressure effects are also calculated from the solar ephemeris, taking into account the estimated attitude at each time step. The expected behaviour of the sensors and actuators are modelled based on characterization testing in order to consider the expected noise and measurement biases of these components. The purpose of Mirage is to validate ADCS design parameters through realistic simulation. Mirage, therefore, uses a direct interface to the OASYS flight-code, written in the C programming language. This Simulink-to-C interface is realized through MATLAB s MEX-function capability, allowing the actual GNB flight code in-the-loop of every control sequence of each simulation. This is desired as it provides a means to co-validate mission parameters as well as the flight code itself. During run time, Mirage outputs telemetry such as sensor measurements and positional information which is then passed to the ACS exchange structure, an array which acts as an interface between the simulated environment and OASYS. The ACS exchange structure contains all necessary information for OASYS to update the spacecraft attitude estimate and subsequently issue appropriate control torque commands as governed by the mission-specific control laws. Control commands are then placed back into the ACS exchange structure, which are then issued to the actuator models. Mirage continuously simulates the resulting attitude

32 Chapter 2. Attitude determination and control system overview 22 in the plant dynamics block. On orbit, the on-board operating system (CANOE) will be responsible for managing the ACS exchange structure to and from the hardware. Naturally, the plant dynamics and environmental models will be replaced with actual spacecraft dynamics and on-orbit environments once the particular spacecraft has been launched. The plant is a model describes the physical dynamics of the spacecraft. It is governed by Euler s equations of motion, which are continuously integrated numerically in Simulink using ode45, a Runge-Kutta-based variable-step solver. A time step of 1 s is used for all simulations as OASYS is expected to operate at this rate. At present, the plant in Mirage is governed by Euler s equations, and hence considers a rigid-body approximation. Flexible body appendages such as antennas are not included, and fuel concerns of CanX-4&5 such as sloshing and mass loss are not considered as their inclusion would cause simulation time to run being practical limits, with very little benefit OASYS OASYS, the GNB attitude control software, acts as the controller in the full ADCS feedback loop. It is responsible for implementing robust control laws while operating efficiently on the attitude determination and control computer (ADCC). OASYS will continue propagating the spacecraft attitude state estimate through an EKF corrected with discrete sensor measurements. As a result, OASYS is responsible for issuing appropriate mission-specific control torque commands to the reaction wheels and magnetorquers. The control laws by which OASYS computes these control torques are outlined in Section 4. OASYS includes a common library of algebraic mathematical operations to perform matrix and vector manipulation, written in the C programming language. The full GNB attitude control sequence operates on a sequential timing profile. Within each time step all sensors are read, the EKF is updated, OASYS computes the required control torques, and the actuators execute their respective commands. This timing profile will operate with a minimum baseline frequency of 1 Hz. However, magnetorquers will not preform momentum dumping during a BRITE imaging campaign or during a slew manoeuvre of any GNB spacecraft in order to reduce the noise induced on the system inherent to this operation.

33 Chapter 3 Attitude system hardware In order to achieve precise three-axis control at the nanosatellite scale, the design and development of small-scale ADCS hardware is required. This hardware must be reliable while providing robust means of attitude sensing and actuation. As mentioned, ADCS hardware of this size and capability is not readily available. As a result, SFL has pursued the in-house development of several ADCS components. The GNB magnetorquers, magnetometers, rate sensors, and sun sensors were all developed by SFL. In addition, the GNB reaction wheels were developed as a collaborative effort between SFL and Sinclair Interplanetary. Each unit is subjected to rigorous testing at the unit and system levels for flight qualification. Test results are also used to characterize the design of a particular component, information which is then used to develop high-fidelity hardware models for integration into Mirage. Simulations are the primary means to evaluate mission-level performance prior to flight. As a result, the ADCS hardware and control scheme is co-validated through this process. In many cases, several design iterations are applied to a particular unit as a result of the testing procedure. Testing, analysis, and in some cases simulation followed by necessary design modifications are repeated until there is sufficient confidence that the hardware will perform as required. Development and testing of the GNB ADCS hardware is discussed in the remaining sections of this chapter. 23

34 Chapter 3. Attitude system hardware Attitude determination hardware sensors The degree of accuracy to which spacecraft attitude must be known is governed largely by the required accuracy to which the ACS must control its state. The approach pursued at SFL is the following: provided that high-fidelity simulations validate the ability of the ACS to control the attitude within given requirements, determination is sufficient. As a result, this implies that determination must be greater than the required pointing accuracy by some factor to account for ACS inaccuracies. This guideline is subject to mission-specific requirements. GNB attitude determination is performed using a mission-specific combination of sun sensors, a magnetometer, rate sensors, and a star tracker. These components are discussed here with specific details on those contributions made by the author Sun sensors Sun sensors operate using visual imagery sensing, whose processed results determine the location of the Sun relative to the spacecraft body frame, on which the sensors are rigidly fixed. Over the course of one full year, the apparent solar motion relative to the Earth traces out a line known as the ecliptic. In order to determine the inertially defined attitude of a spacecraft relative to the sun sensor generated solar vector, a solar ephemeris must therefore be included, from which the relative location of the Sun can be obtained. Sun sensors are a common attitude sensor and are typically capable of accuracies on the order of 1. The resultant solar vector constrains the spacecraft attitude estimate in two of the three axes. The ambiguity of the third axis is seen as the roll about the solar vector. For this reason, whenever sun sensors are used, another attitude sensor should be employed in conjunction to fix the third axis, thereby achieving a full threeaxis solution. As mentioned, a magnetometer is included as part of the baseline GNB ADS architecture, thereby offering the ability to fully constrain the attitude in three dimensions. A particular disadvantage of sun sensors is that they are unusable during eclipse that is, when the Sun is eclipsed by the Earth relative to the spacecraft. Eclipse durations are dependent on the particular spacecraft orbit and occur once per orbit. Despite their disadvantages, sun sensors are still among of the most popular ADS sensor. This is due to their relatively high

35 Chapter 3. Attitude system hardware 25 accuracy, low power consumption, small form factor, and low cost. As a result they are a clear choice for nanosatellites. The GNB sun sensors build upon flight heritage earned from the CanX-2, with a nearidentical hardware implementation. Each sensor is equipped with a fine and coarse sun sensor (FSS and CSS), a temperature sensor, an external oscillator, and an 8-bit microcontroller. A GNB sun sensor is shown in Figure 3.1. Figure 3.1: GNB sun sensor The coarse sun sensor is a simple photo-transistor whose output current depends on the intensity of incoming light. Using optical filtering techniques and supporting circuity, the CSS circuit voltage displays an inverse cosine dependency on the incoming light, as described by V out = V cc ( 1 ŜS ˆn S ) (3.1) where ŜS is the solar vector in the sensor frame, ˆn S is the vector normal to the sun sensor array in the sensor frame, and V out and V cc are the output and source voltages, respectfully. This sensor is dark activated that is, the output voltage is greatest when there is minimal incident light. The coarse sun sensor voltage, temperature sensor, source voltage (V cc ) and ground (GND) pins are read by the 10-bit analogue to digital converter (ADC) on the microcontroller.

36 Chapter 3. Attitude system hardware 26 V cc and GND are read internally using the built-in V monitor. The ADC port operates as a multiplexer where only one channel can be read at any given time. All four ADC channels use V as the external voltage reference. On CanX-2, all coarse sun sensors are read as a means to determine which spacecraft face is most illuminated by the Sun. This result is then used to determine which particular fine sun sensor is read. This sun sensing scheme is followed because the coarse sun sensors have much lower readout times, whereas the fine sun sensors provide much more accurate solar vector estimates. At the time of writing, CanX-2 has had over one full year of successful on-orbit operations. Part of CanX-2 s success is attributed to the ADCS, which is particularly complex for its size. In fact, CanX-2 was the first nanosatellite to demonstrate precise three-axis control. The space heritage obtained from this mission has provided a great degree of insight into the GNB design through lessons learned, in particular with regards to the sun sensors. As previously alluded to, the coarse sun sensors are phototransistors which demonstrate a nonlinear dependency on the incident angle of light. In order to rectify this issue, and smooth out the profile, a diffuse filter is used. This filter consists of several layers of films and adhesive tapes, which combine to provide an optical band-pass filter in the near-ir. It is only with this filter that the sinusoidal response is possible. This filter was tested thoroughly on the ground prior to launch. Unfortunately, there were several issues surrounding them. Through analysis of on-orbit data it is believed that the CSS optical filters on Canx-2 are tenting 1, and therefore providing a skewed reading. Also, the FSS selection voltage threshold from the CSS reading was initially set too low, resulting in stray albedo light causing the incorrect fine sun sensor to be selected on occasion. Both issues resulted in degraded ADCS performance, however the latter was rectified through a software update. To avoid these issues, the GNB will not use the coarse sun sensors as a primary means of FSS selection. Instead, the GNB selection scheme uses the panel voltages generated by the solar cells to determine to general location of the sun relative to the spacecraft, consequently determining which fine sun sensors should be read. Hence, the solar cells will provide a means of coarse attitude determination. On the CanX-2, one FSS is used to determine the location 1 Tenting refers to a condition where the filter protrudes out from the centre, where it would otherwise lie flat.

37 Chapter 3. Attitude system hardware 27 of the sun. For the GNB missions, up to three fine sun sensors will be read each cycle in order to greatly reduce the possibility of false readings. There was concern that this method could potentially increase the overall sun sensor operation time beyond a reasonable limit, however through software timing optimization efforts by the author (described in Section 3.1.1), the overall sun sensor readout cycle will not increase substantially. Future SFL sun sensors will use phototransistors which demonstrate the desired cosine relationship, thereby forgoing the need for custom band-pass filters. The fine sun sensor uses a complementary metal-oxide semiconductor (CMOS) active pixel sensor to provide a pair of one-dimensional projected light profiles, one for each axis. The 256-by-256 pixel CMOS array is integrated with timing and voltage generators and a 10-bit ADC on-chip. This ADC can be set to 8-bit mode, as it is on the GNB sun sensors in order to achieve a pixel depth of 1 byte, thereby simplifying readout and packet buffering. In operation, the incident light will first pass through a neutral-density filter which is fixed to the GNB panel in front of the sun sensor to attenuate solar flux over all wavelengths as a means to avoid saturation. Each GNB sun sensor has the ability to vary the exposure time of the CMOS active pixel sensor. In order to project a small, definitive light source onto the image sensor and obtain the desired point spread function (PSF), a pinhole filter is required. The pinholes used, supplied by Edmond Optics, have a 300 µm diameter aperture. A side profile of the GNB sun sensor design is illustrated in Figure 3.2. Incident Light θ max ND Filter Body Panel Panel Pinhole Filter Sun Sensor PCB CMOS Active Pixel Sensor Figure 3.2: GNB fine sun sensor assembly layout side profile [18]

38 Chapter 3. Attitude system hardware 28 Each pinhole filter is precisely aligned and fixed to the FSS using a small PSF laser and CV-1142 RTV respectively. This process is described in more detail in [24]. When a light source passes through the pinhole filter, it appears as a point on the CMOS array. This point is then projected onto the X and Y profiles. Figure 3.3 illustrates the profile sensing concept, using a 12-by-12 pixel array as an example. Reading each profile from the array will produce outputs illustrated in Figure 3.4. Figure 3.3: CMOS active pixel (profile) sensor projection [25] Figure 3.4: FSS profile centroiding depiction

39 Chapter 3. Attitude system hardware 29 Using the technique of central tendency described by Grzymisch [23], the centroid of each profile is calculated by ˆ S S = 1 Cx 2 + Cy 2 + d 2 C x C y d (3.2) where ˆ S S is the solar vector in the sensor frame, C x and C y are the centroids for the X and Y profiles respectively, and d is the pinhole hight above the CMOS array. Ideally, the centroid would correspond to the pixel of maximum intensity; in reality, the noise characteristics of the sensor preclude making that assumption. The pinhole filter height is required in order for this method to produce accurate results. This height will vary between sensors due to the tolerances in fabrication and variations in the amount and distribution of the RTV bonding agent. The location of the centre of each pinhole relative to the origin of the CMOS array must also be known in order to account for pinhole misalignment. These quantities are determined through unit-level testing. Unit-level flight acceptance testing In order to qualify each sun sensor for flight and to characterize their behaviour, a series of rigorous acceptance tests are preformed. The complete GNB sun sensor test plan, procedure, and results are found in [20]. The most significant tests are described here. As mentioned, a variation in pinhole height will have a direct effect on the accuracy of solar vector estimation, and hence attitude determination. This quantity must be known for each sun sensor prior to launch. This metric, along with the pinhole origin bias, sensor resolution, and overall accuracy, is determined through testing preformed at Ryerson University. Located there is the Space Avionics and Instrumentation Laboratory (SAIL), supervised by Professor Jon Enright. There each sensor is calibrated using a robotic manipulator and a Xenon lamp, which provides a spectral output approximating that of the Sun, though at one third of the intensity. The end effector of the robotic arm, on which each sun sensor is mounted, exhibits three-axis of rotary motion with high precision capabilities.

40 Chapter 3. Attitude system hardware 30 Origin Bias: During pinhole filter mounting, careful precautions must be taken in order to ensure the pinhole remains aligned over the origin of the image sensor, located at the pixel (128,128). Pinhole alignment is a very meticulous process, where exact precision is difficult; therefore, some degree of error is expected. This alignment error shows up as an origin bias, which must be determined and accounted for in order to refine the sun vector estimate. In order to determine this value, each sun sensor is rotated about its boresight over 360, taking measurements in 10 increments. In general, the pinhole lens will not be perfectly centred. In this case, the rotation will cause the sunspots to trace out an ellipse, whose centre reveals the true origin of the fine sun sensor, and hence the bias in the pinhole filter alignment. An example of the result of this test is shown in Figure 3.5, from which the origin of FSS12 the AISSat-1-X sun sensor is determined to be (127.7,124.6)pix. Figure 3.5: Origin bias test result for FSS12 The results of this test are accounted for in OASYS during profile centroid calculations, thus ensuring pinhole misalignment has minimal effect on solar vector estimation. This metric is also used in the Mirage sun sensor model for FOV calculations see Section 5.2.

41 Chapter 3. Attitude system hardware 31 Resolution: The resolution of the sun sensor is defined as the minimum detectable change in angular orientation. In order to determine this quantity, each mounted sun sensor is rotated about each principal axis over 2 in 0.1 increments. An example of the result of this test is shown in Figure 3.6, from which the resolution of FSS12 is determined to be /pix and /pix for the X and Y axes, respectfully. The results of resolution testing provide a means of screening sun sensor for flight acceptance testing. Figure 3.6: Resolution test result for FSS12 about each axis Accuracy: The accuracy of the GNB sun sensors, mapped over the pixels in the active region of the array, was determined. This was done by rotating the mounted sun sensor in an umbrella pattern with ribs rotated by 5, while incrementing by 1 steps. Figure 3.7 illustrates the resulting sun sensor accuracy map from this test, from which a 1.21 RMS accuracy is determined for FSS05. Accuracy test results are used as a means of screening sun sensors for flight, as well as sensor selection placement (i.e. place the least accurate sensor on the nadir facing panel etc). Embedded flight software Although the GNB sun sensors are based on those presently used on CanX-2, a major difference residing between the two designs is found in the embedded flight software. The GNB sun sensors

42 Chapter 3. Attitude system hardware 32 Figure 3.7: Accuracy map of FSS05 were modified from CanX-2 to speak the nanosatellite protocol (NSP). NSP is a communication protocol developed for the CanX nanosatellites, with ease and simplicity in mind [28]. The NSP sun sensor code was originally written by a previous SFL student nearing the end of his degree. This code required significant modification in order for it to accommodate the GNB ADCS architecture, as well as the sensor readout time optimization, as previously discussed. This section outlines these flight code modifications and debugging, with specific focus on the contributions made by the author. Sun sensor communication protocol: The GNB sun sensors use an Atmel AVR 8-bit microcontroller with a built-in serial peripheral interface (SPI) bus to control and communicate with a CMOS profile sensor (the FSS). Moreover, a built-in synchronous/asynchronous serial receiver transmitter (USART) is used to communicate over a multi-drop bus on which all six sun sensors and both OBCs (HKC and ADCC) are situated. Each GNB sun sensor communicates using KISS-encoded NSP over this asynchronous serial link, at bps, with 8-bit bytes, no parity bit, and one stop bit (8N1). The bootloader of this device uses a custom serial protocol instead of NSP, and is identical to that used on the CanX-2 sun sensors. The boatloader software was written in 2006 in the assembly programming language. To execute bootloader mode, a break on the serial line (i.e. pulling the line low) must be asserted when the device is powered on. Hence, for normal operation, the OBC s serial-transmit line must be high when

43 Chapter 3. Attitude system hardware 33 the sun sensor is turned on in order to ensure the sun sensor loads in application code, as is standard for a data bus using UART protocol. Functionality also exists which enables the ability for the sun sensor to jump into application mode directly from the bootloader. The bootloader mode is only used for (re)programming the GNB sun sensors; it is not required for nominal operations [18]. The GNB OBC operating system software (CANOE) uses a specific maximum size of 260 bytes in the data field buffer of its NSP packets, however the full sun sensor profile is 512 bytes. For this reason the sun sensors were modified to read out in two separate packets: one for the X-profile and one for the Y-profile. The OBC is responsible for managing each profile by placing them into the proper fields of OASYS s ACS exchange structure. The current GNB architecture allows for multiple sun sensors to operate on a shared serial bus. In this configuration all six sun sensors listen to the OBC. When replying, the specific sun sensor will drive the transmit line, otherwise the line will be at high impedance. The OBC must not send another command over the shared communication line until it has received a response to its last call. Any received packet which fails a cyclic redundancy check (CRC) will be ignored by the sun sensors. Currently, no CRC error count is implemented on the sun sensors [18]. The specific address assigned to each particular sun sensor is such that a given mission will not see duplication. However, there is also a common address to talk to all sun sensors simultaneously. This address can be used to command all active sun sensors to capture a profile, as is desired in the current GNB architecture. It is important to note that while commanding multiple sun sensors to capture an image, acknowledgement should not be requested, i.e. the P/F bit in the NSP packet must be set to 0. Neglecting this may result in multiple sun sensors attempting to reply to the OBC simultaneously, resulting in garbage on the bus, forcing an unwanted power cycle. Design changes and contributions: The author s first responsibility with regard to the GNB sun sensors was to qualify the AISSat-1 sun sensors for flight. This involved the acceptance testing described in Section It was discovered then that the sun sensor software post-nsp update displayed non-representative outputs. Figure 3.8 shows the resulting accuracy map of

44 Chapter 3. Attitude system hardware 34 the first sun sensor under test. It is clear when compared to the desired results illustrated in Figure 3.7 that these results are caused by bad sun sensor readout. Figure 3.8: Bad sun sensor accuracy test results As mentioned, the 8-bit microcontroller employed on the GNB sun sensor communicates to the FSS through SPI. However, this device has only one SPI port used to read data from the sensor whereas the imager has 2 data channels, one for each axis. In order to accommodate for this, a multiplexer was established in software. The flow chart in Figure 3.9 outlines typical sun sensor readout, illustrating the MUX functionality. X Profile Readout Set MUX (X-Channel Read) Flush Imager (Begin Exposure) Exposure Delay Receive Data (257 Bytes - NSP) X-Profile Y Profile Readout Set MUX (Y-Channel Read) Flush Imager (Begin Exposure) Exposure Delay Receive Data (257 Bytes - NSP) Y-Profile Figure 3.9: GNB sun sensor readout flowchart The control register responsible for toggling the logic on the pin which drives the multiplexer was not implemented properly in software. The bitwise operation performed in the function responsible for pulling the start pin low, thereby signalling to the array to begin transmitting,

45 Chapter 3. Attitude system hardware 35 was mistakenly resetting the MUX pin low, thereby reading out the X profile each time. Fortunately, only a simple fix was required: ensure the start pin function did not modify the logic on any other pin. However, this error had other implications; the alignment of the sun sensor pinhole filters was preformed using this software, unfortunately resulting in severe pinhole misalignment. As seen in Figure 3.10, a pinhole origin of (126.2,172.6) was observed. In order to remedy this misfortune, the affected pinhole filters were removed and reinstalled. Figure 3.10: Severe pinhole filter misalignment In order to avoid a similar situation, unit-level quality assurance was enforced by implementing a new requirement in the GNB sun sensor test plan and procedures document, namely a software qualification test. Prior to loading new software on any sun sensor units, it must now first undergo strenuous software qualification. The goal of this test is to qualify the most recent version of the FSS software. This is not a test that must be preformed to each unit (i.e. acceptance test). Instead it must be preformed once, on a select group of sun sensors, to qualify the software to be programmed on all flight units (i.e. qualification test). Individual unit-level software acceptance testing will occur inherently as part of all other unit-level tests [20]. This qualification test must be run for every new revision of flight code. The flight

46 Chapter 3. Attitude system hardware 36 software qualification test involves running every possible permutation of command sequences over the sun sensor multi-drop bus, with a sample of multiple sun sensors (minimum 2). In order to accommodate this testing on a PC, an array of testing software was written. The software test-code was written in MATLAB, making use of the MEX functionality in order to implement several MFC functions to enable external communication with multiple sun sensors through a USB interface. The USB port was connected to a USB-to-RS232 cable which was itself connected to a CMOS-to-RS232 converter, in order to communicate with the sun sensor. In the original sun sensor code, when readout was requested from a particular unit, both the X and Y profiles would automatically be returned, in a single NSP packet of 512 bytes. As mentioned, the data buffer size in CANOE is 260 bytes. For this reason each profile is now read out as a separate NSP packet of 257 bytes (one byte is a flag, as seen below). It is also a GNB requirement for the sun sensors to facilitate the request of multiple (up to 3) sun sensors to perform simultaneous image capture. As such, software modification was required, including a new function. The commands used to control the sun sensors are listed here, where pre-existing functionality is shown in blue, modified code in green, and new commands in red. Modification to FSS READ added the functionality of storing profiles in the sun sensor SRAM, where FSS OUT was written to output this profile. PING Returns Software Version and Compilation date and time. INIT Resets the microntroller along with all parameters. Responds with an acknowledgement. FSS READ Replies with fine sun sensor data at requested exposure time. OR Captures image profile (at requested exposure time) and stores in SRAM. FSS OUT Replies with fine sun sensor data from last FSS READ command. ADC READ Replies with ADC voltage of requested channel (ADC3 - Coarse sun sensor, ADC4 - Temperature sensor). With this new implementation, there is a concern for misuse, where the stored profiles are requested in an improper order. For example, if a call to FSS OUT is made after an INIT, power cycle, or a previous FSS OUT call, it will result in erroneous, or potentially unwanted data. For

47 Chapter 3. Attitude system hardware 37 this reason, the first byte in the data field of each NSP packet sent from the GNB FSS will be a flag byte. This byte is necessary to inform the OBC concerning a variety of situations, each of which is handled by the OBC. Flag byte definitions are found in [18]. Timing optimization: Implementing multiple sun sensor readouts during each OASYS cycle required revisiting the timing profile, in order to ensure that the time required to output up to three sun sensors was not significantly delaying attitude control operations. During initial inspection it appeared as though the sun sensor readout time was experiencing unnecessary delays. Figure 3.11 illustrates the original sun sensor timing profile, which shows a readout time of 123 ms including the command sent to the FSS from the OBC, with an exposure time of 250 ns. The readout from each sun sensor directly out of SRAM (with a call to FSS OUT) took 90 ms Figure Figure 3.11: Initial GNB sun sensor output timing profile The large delay between the two packets was originally thought to be caused by a redundant memory copy, however after further investigation it was determined that the delay in sun sensor readout was caused almost entirely by the CRC calculation. In the GNB implementation of NSP protocol, a 16-bit CRC is appended at the end of each packet as a type of check-sum to ensure correct transmission. A CRC value is calculated based on a particular arithmetic

48 Chapter 3. Attitude system hardware 38 Figure 3.12: Initial output timing profile from FSS OUT expression as a function of the binary values of the transmitted data. There are many different types of CRCs. Most GNB devices use a CRC look up table from which a CRC is selected from previously computed values. This lookup table occupies 512 bytes, which is problematic for the sun sensors as the microcontroller has only 1 kilobyte of available SRAM. For this reason, the GNB sun sensors solve the CRC equation during run time, which is a fairly extensive algorithm relative to the other operations on this chip. The CRC operation takes approximately 20 ms, as illustrated in Figure This calculation is preformed for both the X and Y profiles, on each of the three sun sensors, ultimately contributing 120 ms of readout delay, a relatively large portion of the overall OASYS timing profile. To resolve this issue, the CRC calculation function is now called immediately after the command is sent to any sun sensors on the bus. This will force the code to execute in parallel by each sun sensor behind the scenes instead of after the FSS OUT command, which had caused the time delay to add serially. The overall time required for the sun sensor to perform its operations has not changed, however it has been relocated resulting in a net increase in sun sensor readout efficiency. The FSS readout now takes 46.8 ms each (Figure 3.14) instead of 90 ms, almost halving the readout time. As opposed to losing 120 ms to CRC calculations, all three sun sensors can be read-out in approximately 200 ms (including the 40 ms attributed to the CRC calculations of the first

49 Chapter 3. Attitude system hardware 39 Figure 3.13: CRC timing profile Figure 3.14: Revised timing profile of the GNB sun sensors sun sensor to be read out, and its expected exposure time delay). The timing optimization increases both, run-time efficiency and consequently, the accuracy of GNB attitude estimation, due to a decrease in the OASYS time step. The Mirage sun sensor model has been updated to include the change mentioned above see Section 5.2.

50 Chapter 3. Attitude system hardware AeroAstro star tracker A star tracker is an optical attitude sensor much like the sun sensors, however much more complex. Star trackers are capable of determining spacecraft attitude in all three axes to very high precision, accomplished through star field observation and identification. There are several ways of performing star identification; the method used in the AeroAstro star tracker is proprietary intellectual property, and is therefore undisclosed. However, a simple heuristic to follow involves comparing the geometrical formation of the stars detected by the imager with an on-board star catalogue. This method, known as star pattern recognition, relies on the principle that any three stars in the celestial sphere, as viewed from Earth, form a mathematically unique shape, or triad. Using a fairly extensive searching algorithm, a star tracker is capable of matching the imaged triad with those found in the star catalogue, hence identifying each star by name. Star trackers typically operate in two modes: initial attitude acquisition and attitude tracking. The first method is the one previously discussed, which results is what is known as the lost-in-space (LIS) solution, as no initial information is provided. The output from this mode is the identification of each of the stars in view, their orientation relative to the star tracker, and precise determination of the star tracker attitude in GCI [35]. If done in a clever way, star trackers can also be used for interplanetary spacecraft. They may also provide coarse information for orbital guidance, navigation, and control (GN&C) [4]. Once the LIS solution is determined, the attitude of the star tracker, relative to the inertial frame, will be known to high accuracy. The star tracker will then exit the LIS mode and begin executing the tracking algorithm. In tracking mode, the location of each star is compared in successive images, to monitor the attitude as it is changing with time. The angular rates about each axis are also calculated as a result. A clever star tracker will use angular rate information it computes to approximate the location of the stars in the subsequent images, and then only observe a windowed area about this location in order to obtain information on the stars new locations [30]. This can significantly increase a star tracker s run-time efficiency. A minimum of three stars must be in view in order to determine the LIS solution in the case of the pattern recognition technique, while only two are needed to perform tracking. However,

51 Chapter 3. Attitude system hardware 41 the greater the number of observable stars in the FOV, the greater the accuracy. Moreover, stars which are situated furthest from the boresight of the star tracker contribute to higher accuracies, as those near the boresight are subjected to some degree of roll ambiguity. Another star identification technique is based on the colour spectra emitted from each star. With sufficient colour resolution, particular stars may be identified depending on their apparent spectral output. This is a technique currently being researched at Ryerson University, under Dr. John Enright. Until recently, it was infeasible to consider the use of a star tracker for a nanosatellite mission. However, due to the increasing popularity of small satellite development, as well as the obvious advantages of star trackers for attitude determination over other sensors, these devices are now being developed on platforms significantly reduced in size. AeroAstro, a small satellite company founded by Rick Fleeter (author of The Logic of Microspace), has developed the Miniature Star Tracker (MST) which meets the accuracy requirements of the BRITE mission while fitting into the volume of only one quarter of the GNB payload bay. Two AeroAstro star trackers have been purchased by SFL for their use on the Austrian UniBRITE and BRITE-Austria satellites. Figure 3.15: The AeroAstro miniature star tracker The specifications outlined in Figure 3.15 have been supplied by AeroAstro, as determined through their method of testing. In order to validate these values, and provide confidence in the BRITE mission, the author was responsible for fully characterizing the AeroAstro star tracker.

52 Chapter 3. Attitude system hardware 42 Characterization and qualification testing Star tracker performance depends on the detection threshold and sensitivity, the field of view, the accuracy of the centroiding method used, the number of stars detected, the type of star catalogue and searching algorithm, and the method of calibration [30]. In order to qualify each star tracker for flight, and confirm the accuracy claimed by AeroAstro, several field testing campaigns were preformed at night. A sample image from the UniBRITE star tracker taken during one of these testing campaign is shown in Figure The stars in this figure are somewhat hazy, which is desired as star tracker optics are intentionally defocused slightly in order to blur the image. This will cause the PSF of each star to spread over multiple pixels, thereby increasing the precision resulting from centroiding, to provide sub-pixel accuracy. Figure 3.16: A star field image taken with the MST on November 05, 2008 at 23:52 EST During each testing campaign, the star tracker was fixed to a testing platform and pointed to zenith. The LIS and tracking algorithms were then continuously run for a time span of up to three hours. Over the observational period, as the Earth rotated, the star tracker orientation would vary relative to the celestial sphere, outputting its calculated attitude in the Geocentric Inertial (GCI) reference frame. The output of this test is a log file containing the star tracker 2 Note: star intensities are augmented to distinguish them in printed publication.

53 Chapter 3. Attitude system hardware 43 quaternions, describing the rotation from the GCI (J200) to the MST body frame. The MST frame is shown in Figure 3.17, where the roll, pitch, and yaw angles are defined about the Z, X, and Y axes respectively. Once integrated, the star tracker X, Y, and Z axes will correspond to BRITE s Z, Y, and -X axes respectively. Figure 3.17: Rendering of the MST with body reference frame (courtesy of AeroAstro Inc.) Included as part of the star tracker output file are the date and time stamps for each observation, as well as a certainty value for each solution ranging from 0 (least certain) to 1 (most certain). An example of the MST output is shown in Figure The MST communicates Figure 3.18: A resolved quaternion output on November 05, 2008 at 23:55 EST over RS422 (3.3 V signals, 5.0 V tolerant) through a DB9 (micro-d) connector. It is capable of standard baud rates up to In order to parse the MST output, the author wrote Star Tracker TXT2CSV, a Windows application written in Visual C++, whose GUI is shown in Figure The MST quaternion output was then compared with Satellite Tool Kit (STK). In STK, the local astronomical (LA) reference frame was propagated over the same time period

54 Chapter 3. Attitude system hardware 44 Figure 3.19: Star tracker data parser GUI TXT2CSV as the star tracker observations. The output quaternion, describing the rotation from GCI to LA, was used as the truth model, which was compared to the MST quaternion outputs. The following listing shows the MATLAB analysis code. %Retrieve star tracker quaternion 0084 q st(:,i) = [MST(i,6:8) ;MST(i,5)]; 0085 q st(:,i) = q st(:,i)./ norm(q st(:,i)); % Enforces normality eta MST = q st(4,i); 0088 epsilon MST = q st(1:3,i); %Skew-symmetric matrix 0091 epsilon MST cross = [0 -epsilon MST(3) epsilon MST(2); 0092 epsilon MST(3) 0 -epsilon MST(1); epsilon MST(2) epsilon MST(1) 0]; Once the star tracker quaternions were extracted, the direction cosine matrix, defining the angular displacement from the GCI frame to the MST body frame, is computed following the relationship C bi = (η 2 ε T ε)1 + 2εε T 2ηε (3.3)

55 Chapter 3. Attitude system hardware 45 whose components can be written as 1 2 ( ε ) ε3 3 2 (ε 1 ε 2 + ε 3 η) 2 (ε 1 ε 3 ε 2 η) C bi = 2 (ε 2 ε 1 ε 3 η) 1 2 ( ε ) ε2 1 2 (ε 2 ε 3 + ε 1 η) 2 (ε 3 ε 1 + ε 2 η) 2 (ε 3 ε 2 ε 1 η) 1 2 ( ε ) ε2 2 (3.4) The roll, pitch, and yaw angles may then be extracted from C bi as a Euler rotation sequence defined by c 2 c 3 c 2 s 3 s 2 C (θ) C 1 (θ 1 ) C 2 (θ 2 ) C 3 (θ 3 ) = s 1 s 2 c 3 c 1 s 3 s 1 s 2 s 3 + c 1 c 3 s 1 c 2 c 1 s 2 c 3 + s 1 s 3 c 1 s 2 s 3 s 1 c 3 c 1 c 2 (3.5) where c i = cos θ i and s i = sin θ i. The following listing shows the relevant MATLAB code %Calculate star tracker Yaw, Pitch and Roll from C bi 0100 %pitch = 1, yaw = 2, roll = yaw MST(i) = asin(-c bi(1,3)); 0102 pitch MST(i) = asin(c bi(2,3)/cos(yaw MST(i))); 0103 roll MST(i) = asin(c bi(1,2)/cos(yaw MST(i))); 0112 %Local frame vectrix 0113 F l = [East Vector J2000(j,4:6); 0114 North Vector J2000(j,4:6); 0115 Zenith Vector J2000(j,4:6)]; Similarly, the direction cosine matrix defining the rotation from Geocentric Inertial reference frame (GCI) to International Terrestrial reference frame (ITRF) is ˆl1 î 1 ˆl1 î 2 ˆl1 î 3 C li F l F T i = ˆl2 î 1 ˆl2 î 2 ˆl2 î 3 ˆl3 î 1 ˆl3 î 2 ˆl3 î 3 (3.6) where C li is defined by the dot product between the GCI and ITRF vectrices 3. 3 Vectrices follow from the work of Hughes [27]. They describe a frame of reference as a matrix of three orthogonal vectors, each of which defines a principal axis of that frame.

56 Chapter 3. Attitude system hardware 46 The Euler angles of the STK-generated LA frame are extracted by a rotation, as in the following listing %Calculate STK Yaw, Pitch and Roll from C li 0127 yaw l(i) = asin(-c li(1,3)); 0128 pitch l(i) = asin(c li(2,3)/cos(yaw l(i))); 0129 roll l(i) = asin(c li(1,2)/cos(yaw l(i))); The resulting set of roll, pitch, and yaw angles from each source were then differenced in order to determine the MST accuracy. Figures 3.20 and 3.21 illustrate the AeroAstro star tracker field testing results of the night of Sept 10, Initially, the star tracker exposure time was set to 500 ms as recommended by AeroAstro for urban night sky conditions [1]. Later that night, the exposure time was changed to 250 ms, in order to obtain a separate metric that is, how the star tracker performs at different exposure times. Figure 3.20: MST accuracy plot Sept 10, ms integration time

57 Chapter 3. Attitude system hardware 47 Figure 3.21: MST accuracy plot Sept 10, ms integration time A handheld GPS receiver, referenced to the WGS84 ellipsoid, was used to determine the UTC time and precise location on the Earth from which the observations were made. Star tracker measurements were taken for observational periods of up to three hours in the northern region of the Greater Toronto Area, specifically just outside the David Dunlop Observatory (DDO). It should be noted that the star tracker was not levelled with the Geoid or local datum. made. In general, no attempt to align the star tracker with the local reference frame was This is not a concern, however; the misalignment of the star tracker with the local reference frame is represented as a constant bias in the quaternion results. Likewise, any error in the recorded time from the GPS receiver is a constant offset. As the Earth rotates, the star tracker measures a quaternion representing the rotation matrix between the two frames. Time offset, like constraint frame misalignment, will also be subtracted as a constant error bias. A bias in the star tracker is not a major concern for BRITE, as the desired 1-pixel repeatability will be implemented through feedback of the telescope imager itself. For this reason, only the variance and hence, standard deviation are of interest.

58 Chapter 3. Attitude system hardware 48 The procedure described above was repeated for several testing campaigns, varying optical integration period in order to further characterize the star tracker performance with respect to exposure time. Characterization testing of this form produced results which were then used to create the star tracker model for use in Mirage see Section 5.1. It is clear from Figure 3.21 that a greater accuracy is achieved with the exposure time reduced from 500 ms to 250 ms. All noise values represent the 1-σ standard deviation from the mean. On the night of November 5, 2008, another test campaign was carried out. The purpose of this test was to obtain a profile describing the star tracker s behaviour as a function of integration time. The star tracker was tested at 50 ms (no solutions captured), 100 ms, 150 ms, 225 ms, 350 ms, and 500 ms. These results are shown in Figures , with the integration time profile and testing order profile shown in Figures 3.27 and 3.28, respectfully. Figure 3.22: MST accuracy plot Nov 5, ms integration time

59 Chapter 3. Attitude system hardware 49 Figure 3.23: MST accuracy plot Nov 5, ms integration time Figure 3.24: MST accuracy plot Nov 5, ms integration time

60 Chapter 3. Attitude system hardware 50 Figure 3.25: MST accuracy plot Nov 5, ms integration time Figure 3.26: MST accuracy plot Nov 5, ms integration time

61 Chapter 3. Attitude system hardware Pitch error Yaw error Roll Solution % 1 sigma error (arcseconds) Integration time (ms) Figure 3.27: MST Exposure time profile Nov 5, sigma error (arcseconds) Pitch Yaw Roll Solution % Test order Figure 3.28: MST test order profile Nov 5, 2008

62 Chapter 3. Attitude system hardware 52 As expected, Figure 3.27 shows solution percentage increasing with greater exposure times. However, the star tracker performance does not appear to be monotonic with exposure time. It appears as though the order that the tests were preformed have more bearing on the accuracy than the exposure times (error increases over time). This may be caused by changing conditions of light pollution over the course of the night, or perhaps condensation on the lens although this was checked periodically as part of the test procedure. Determining a correlation between exposure time and performance is desired, however not required as the results presented here contain sufficient information to construct a representative star tracker model for Mirage, whose results will determine the expected mission level performance of BRITE s ADS. The lowest errors during the testing campaign on November 5 th are achieved with a 500 ms exposure time, which agrees with the value suggested by AeroAstro [1]. An integration time seed value on orbit will therefore also follow from manufacturer s suggestions that is, 50ms exposure time in orbit. It is important to note that the accuracy about the roll vector is consistently demonstrating degraded performance. This is expected, as previously discussed, due to the ambiguity seen about the boresight of the imager, as the tracked stars centralize. Figure 3.29: Comparative coordinates of the MST and STK

63 Chapter 3. Attitude system hardware 53 Sources of error: During any type of qualification testing, one must consider all possible sources of error. The primary source of error for the method of testing described here is induced by Earth s atmosphere. While CanX-3 is in LEO, this error will not be experienced; therefore, results seen here will be degraded from the expected on-orbit performance, and hence are considered conservative values. The atmosphere will cause stars which would nominally appear as a point source to break up into specular patterns. Also, their apparent brightness will scintillate, or fluctuate, as they twinkle a phenomenon caused by the turbulent fluid flow of the upper atmosphere. The greatest source of atmospheric error is caused by atmospheric refraction. As star light refracts through the atmosphere it will bend causing stars to appear at greater elevations in the celestial sphere than they actually are. This effect is zero at zenith, and a maximum at low elevations and is also highly dependant atmospheric conditions, specifically temperature and pressure. This relationship is described by R = P tan(z) (273 + T ) (3.7) where R is the angle of refraction, z is the zenith angle, T is temperature in degrees Celsius, and P is barometric pressure in millibars [7]. On November 5th, 2008 the atmospheric conditions in Toronto were: P = millibar and T = 6 C. During each testing campaign the star tracker is pointed at zenith, therefore the effects of atmospheric refraction will be a minimum. However no attempt was made to level the camera. Considering a maximum zenith angle of 5 (boresight offset) plus 15 half-angle FOV, the refraction angle will vary from arcseconds. It is difficult to quantify the degree to which the resulting star tracker solutions would be distorted, however, from (3.7), it is conservative to expect an error of no more than 15 arcseconds in each axis. The sidereal motion of the Earth will also induce an error in this method of testing. The star tracker will capture the rotation of the Earth about its axis in discrete points in time, however through the duration of the exposure time, the stars in the FOV will appear to smear by a seemingly small amount, as the Earth rotates. The centroiding algorithm on the star tracker may not account for this smearing, thereby resulting in a measurement error. The effect this smearing has on overall accuracy depends greatly on the method AeroAstro pursued

64 Chapter 3. Attitude system hardware 54 for centroiding. It is possible that the star tracker is unaffected by this motion. It is also possible that the MST uses this streaking to obtain a more accurate estimate for angular rate (this is a relatively new concept for star trackers). However, in the case where sidereal motion is not accounted for in any way, a maximum error of 7.5 arcseconds may be induced, as determined by the angle the Earth rotates in half of a second (the largest selected integration time). This value also depends on target declination. While the LIS algorithm is running, the AeroAstro star tracker will output quaternion solutions at a rate of approximately 1 Hz to 2 Hz. In order to perform the comparison, STK requests a fixed simulation time step. The value of one second was used. However, the star tracker outputs solutions to the precision of s. These values were therefore rounded to the closest second for comparison to the STK results; no interpolation was preformed. As a result of rounding, an error is induced. This error is quantified as a maximum of 7.5 arcseconds, as defined by the arc traced out by the Earth in 0.5 s, corresponding to the largest possible roundoff. Predictable errors sum to 30 arcseconds. Averaging the results, this corresponds to approximately 30% of the MST noise, an appropriate margin for modelling. Based on the preceding results, we see that the accuracy originally claimed by AeroAstro is optimistic. A claim of ±70 arcseconds (3-σ) is approximately three times better than the accuracies determined through this process. From the testing results presented here, an accuracy of ±70 arcseconds (1-σ) per axis is a more appropriate expectation Magnetometer The GNB magnetometer is used to measure the local magnetic field vector of the Earth. It is structurally located at an offset from the body, in order to ensure minimal measurement corruption by the residual magnetic dipole of the satellite. It is equipped with three orthogonal, single-axis magneto-inductive sensors which measure variations in the inductance of the Earth s magnetic field. The magnetometer performs a measurement-differencing technique to provide noise and temperature stabilization. After filtering, this sensor suite can provide attitude knowledge in the range of ±1 [16]. The resulting magnetic vector is used directly by

65 Chapter 3. Attitude system hardware 55 the magnetorquers for rate damping and momentum dumping of the reaction wheels. Magnetometers provide a fixed attitude estimate in two axes instantaneously, with ambiguity along the magnetic field line. However, as the spacecraft orbits the Earth, the local magnetic fields vector will wander, allowing the magnetometer to theoretically provide 3-axis determination, provided orbital inclination is non-zero Rate sensors Although not included as part of the baseline GNB ADCS architecture, rate gyroscopes are implemented on both the CanX-4&5 and AISSat-1 nanosatellites. This is due to the mission requirements which state that the attitude solution must not degrade beyond reasonable limits during an eclipse period. As the sun sensors can not operate during eclipse, and the magnetometer can only provide coarse attitude determination in two axes, rate sensors are used as supplementary sensors during this time. The GNB uses three orthogonal single-axis rate gyroscopes from Analog Devices to measure the angular rate about each axis. These rate sensors, realized through MEMS technology, employ a vibrating test mass which, when rotated, will induce lateral motion due to Coriolis acceleration. This lateral motion varies capacitance in the circuitry, which is sensed as a change in electric potential. This voltage measurement provides information used to infer the angular rate of the sensor about each axis. Rate sensor measurements are subjected to both bias and noise terms which will accumulate in estimate error. A concern with most rate sensors is the noise bias. It is strongly desired to know the bias term and account for it as small initial errors will propagate into large attitude determination errors over the course of an eclipse. In order to determine this quantity, the GNB rate sensors will be turned on for 5 minutes prior to entering an eclipse, in order to measure this bias as compared with the angular rate estimate provided by the EKF. This bias term will be used during the eclipse in an attempt to reduce error build up. However, the rate sensor noise bias term will inevitably drift over time, and with no way to estimate this drift it will not be accounted for in any way. Therefore, although rate sensors will otherwise improve the attitude estimates, results will degrade over the course of an eclipse.

66 Chapter 3. Attitude system hardware Attitude control hardware actuators Spacecraft attitude control effort is preformed using electro-mechanical actuators. Typical hardware used to perform this function includes magnetic torque coils, reaction wheels, control moment gyroscopes, and thrusters. As mentioned, the GNB spacecraft platform is designed with three orthogonal magnetorquers and three orthogonal reaction wheels. The magnetorquers are wound in-house, designed to fit within a given form factor. The reaction wheels used on the GNB were developed as a collaborative effort between Sinclair Interplanetary and SFL as a means to enable high-performance attitude control at the nanospace scale Reaction wheels The Sinclair/SFL reaction wheels are the primary control actuator for all GNB missions. They are responsible for disturbance torque rejection and slewing the spacecraft bus to a desired attitude. With a predecessor of this wheel flown on CanX-2, which continues to demonstrate flawless performance, the GNB reaction wheel builds on significant space heritage. This custom wheel imitates a brushless DC motor, optimized for high inertia by inverting the classical design. Placing the large permanent magnets on the rotor, which itself is placed at a relatively large radius from the stator, large angular inertia is achieved. The windings are situated in the inner radius of the wheel, wrapped on a Delrin stator, placed as close to the rotor as possible in order to increase the number of windings, and hence torque capability. Three digital Hall-effect sensors are used both for commutation and speed measurement and are mounted behind the coil windings on the stator [38]. Testing In order to characterize this wheel and qualify each unit for flight, a series of unit-level tests were preformed. Lifetime testing: It is imperative that the GNB reaction wheels function nominally for at least 3 years, as this is the longest projected mission life of any GNB mission. Reaction wheel failure can be caused by either an electronic or mechanical fault; the greatest concern

67 Chapter 3. Attitude system hardware 57 Figure 3.30: Sinclair/SFL reaction wheel is the bearing life. In order to confirm the wheel bearings will survive for the entire mission duration, lifetime testing is preformed where a wheel is continuously spun through a particular speed profile until it fails. This is a design qualification test, whose results will characterize the bearing life of the wheel as well as ensure the electronics will operate nominally during end-of-life conditions. Figure 3.31 outlines the GNB reaction wheel lifetest profile. Two correlated metrics are obtained from lifetime testing: maximum obtainable speed and bearing friction. The reaction wheel kinematics are modelled as a simple rotating mass with moment of inertia I and damping coefficient β, I ω + βω = ḣ (3.8) where ḣ is the applied wheel torque. During the run-down phase of the lifetest profile, the torque on the wheel is set to zero. Setting ḣ = 0 and solving the differential equation (3.8) yields ( ) β I ω (t) = ω 0 e t (3.9) Solving for β, we see the damping relationship β = ln [ ωt ω 0 ] I t t 0 (3.10) Here, the approximation is made that all wheel damping is caused by viscous bearing friction, ignoring the fluid friction of air.

68 Chapter 3. Attitude system hardware Speed (rad/s) Run-Down Controlled Breaking Time (s) Figure 3.31: GNB reaction wheel lifetime testing profile Results from this test have led to several design iterations of the Sinclair/SFL reaction wheel. Initially, this wheel was designed using stainless steel bearings with a preload of 50 N. Lifetesting this design resulted in a failed wheel after 164 testing days, as shown in Figure This is assumed to be an accelerated test with a factor of approximately 2.04 based on bearing life calculations outlined by Philip [32]. Therefore the original wheel design lasted an equivalent of 334 days in flight, less than one full year in orbit. The second iteration lowered the bearing preload to 8 N, again using stainless steel. This design preformed much better on lifetest, resulting in a failed wheel after 293 test days, equivalent to 597 days in orbit. This wheel design, whose lifetest results are depicted in Figure 3.33, survived much closer to the 3 year requirement. It should be noted both wheel failures were caused by bearing failure. The third generation, and current design iteration, of the Sinclair/SFL reaction wheels use a hybrid bearing of ceramic balls, with diamond races. Results from this lifetest are found in Figure At the time of writing, this wheel design continues life test, has already survived for 485 test days and continues to spin. This is equivalent to 2 years, 8 months, and 20 days in orbit; very promising results.

69 Chapter 3. Attitude system hardware E-6 Speed (rad/s) Maximum Speed Damping Coefficient 1.0E E E E E-9 Damping Coefficient (N*m*s) E Time (days) Figure 3.32: Preliminary reaction wheel design lifetest profile E-6 Speed (rad/s) Maximum Speed Damping Coefficient 1.0E E E E E-9 Damping Coefficient (N*m*s) E Time (days) Figure 3.33: Lifetest profile of the second reaction wheel design (8 N preload)

70 Chapter 3. Attitude system hardware E Speed Damping 7.50E E-07 Speed (rads/s) E E E E E-07 Damping (N*m*s) 4.00E E Time (Days) 3.00E-07 Figure 3.34: Lifetest profile of the third reaction wheel design (ceramic balls with diamond races) Steady-state accuracy: In order to study the performance of the GNB reaction wheels, their ability to maintain a constant speed bias was investigated. This study quantifies the noise read by the Hall-effect sensors together with the noise contributed by the wheel controller tested under different steady-state conditions. Results of this test aid in determining a characterizing metric known as the wheel bias jitter. This test was preformed by running each wheel at a constant speed between 500 rad /s and 500 rad /s in 100 rad /s increments. Speed telemetry was recorded for 1 2 minute periods. Results, shown in Figures , illustrate a certain degree of noise associated with the constant speeds, and as expected the steady-state accuracy decreases at greater speeds. A reaction wheel bias jitter will consequently induce a jitter on the spacecraft. It is apparent that this jitter will increase with greater wheel speeds. This becomes a concern for a mission such as BRITE which would otherwise benefit from the gyroscopic stiffness gained by running a reaction wheel at a bias. Gyroscopic stiffness is a phenomenon which acts to preserve the orientation of a spinning object. It is a result of the law conservation of angular momentum.

71 Chapter 3. Attitude system hardware 61 Speed error (rad/sec) rad/sec StDev = rads/sec +200rad/sec StDev = rads/sec +300rad/sec StDev = rads/sec +400rad/sec StDev = rads/sec +500rad/sec StDev = rads/sec Time (sec) Figure 3.35: Positive speed steady-state accuracy test of N16 Speed error (rad/sec) rad/sec StDev = rads/sec -200rad/sec StDev = rads/sec -300rad/sec StDev = rads/sec -400rad/sec StDev = rads/sec -500rad/sec StDev = rads/sec Time (sec) Figure 3.36: Negative speed steady-state accuracy test of N16

72 Chapter 3. Attitude system hardware Noise (rad/s - 1 sigma) Speed (rad/sec) Figure 3.37: Steady-state accuracy profile of N16 However, as BRITE would benefit from a fairly large bias running in its wheels (in order to stabilize, and remain inertially fixed), there is an apparent trade-off between the benefits of gyroscopic stiffness and the jitter induced on the spacecraft. Mission simulations will determine the acceptable wheel bias for BRITE, along with the other GNB missions.the noise curve, recorded from Figure 3.37, is approximately (1-σ). Current and power draw: Reaction wheel power draw is another very important metric to obtain. Similar to the steady-state accuracy tests, in order to obtain a representative power draw profile, each wheel is commanded to a constant speed. The current draw telemetry is recorded for a constant voltage supply for a period of one minute.

73 Chapter 3. Attitude system hardware rad/sec: Avg = 7.43mA StDev = 1.03mA 300rad/sec: Avg = 20.29mA StDev = 4.44mA 500rad/sec: Avg = 42.76mA StDev = 11.36mA 0.01 Current (Amperes) Time (sec) Figure 3.38: Positive speed current draw telemetry of N rad/sec: Avg = 6.94mA StDev = 0.85mA -300rad/sec: Avg = 19.73mA StDev = 4.21mA -500rad/sec: Avg = 43.65mA StDev = 11.39mA 0.01 Current (Amperes) Time (sec) Figure 3.39: Negative speed current draw telemetry of N13

74 Chapter 3. Attitude system hardware Power (mw) Speed (rad/sec) Figure 3.40: Power draw profile of N13 The results in Figures 3.38 and 3.39 corresponds to the steady-state error plots. The reaction wheel controller will issue a torque command based on the speed measured by the Hall-effect sensors. Each torque command requires current, as a result we see corresponding current fluctuations. The power draw profile, illustrated in Figure 3.40, displays increasing power consumption at greater speeds, as expected. The observable quadratic behaviour of the power consumption with respect to speed may be a consequence of the wind friction (or windage), which also demonstrates this relationship. That is, windage is proportional to the rotor velocity squared: β windage ω 2. Windage is not a concern in space however, therefore the on orbit power draw will likely be slightly lower than that seen here. These results, have since been accounted for in the GNB power budget. Magnetic dipole testing: As previously mentioned, the reaction wheel design resembles that of a rather sophisticated DC motor. As such, the motion of the wheel is governed entirely by magnetics, where wounded coils rigidly attached to the stator produce a magnetic field which induces a force on the permanent magnets, fixed to the rotor. It is anticipated that the magnetic

75 Chapter 3. Attitude system hardware 65 field, both produced by the coils in the wheels and the permanent magnets, will contribute to the overall spacecraft residual magnetic dipole. Any unintentional magnetic dipole rigidly fixed to the spacecraft is a concern to the attitude control subsystem, as torques induced by the Earth s magnetic field will act to realign the spacecraft. The attitude controller must be robust against these unwanted magnetic torques, which are considered a significant environmental disturbance. As such, great care is taken while sizing and selecting hardware to account for the expected disturbance. Quantifying the spacecraft parasitic dipole is therefore, of great concern. For this reason, the magnetic dipole of the GNB reaction wheel must be well understood. Using an in-house laboratory magnetometer, the GNB reaction wheel magnetic dipole was measured under several conditions. Measured results of this test are shown in Figure 3.41, with derived magnetic dipole shown in Figure Reading (ut) Delta (ut) Axial Readings Change from Ambient Ambient Unpowerd Idle 100 rad/s 200 rad/s 500 rad/s Wheel Setting Figure 3.41: Axial dipole test on wheel N15 Magnetic field measurements The magnetic dipole test was not originally part of the standard unit-level testing. It was determined that there is a larger apparent residual dipole on CanX-2 than was initially predicted. It is clear from Figure 3.41 that the reaction wheel dipole contributes a large amount of the CanX-2 residual dipole moment. This dipole is not considered large enough to be a great

76 Chapter 3. Attitude system hardware Magnetic Dipole (Am 2 ) Calculated Moment CanX-2's Parasitic Estimate Ambient Unpowerd Idle 100 rad/s 200 rad/s 500 rad/s Wheel Setting Figure 3.42: Axial dipole test on wheel N15 Derived magnetic dipole moment concern, so long as it is well understood and accounted for. Result of these tests have helped to give insight into the source of residual dipole. Consequently, dipole values for GNB simulations have been updated in Mirage Magnetorquers Magnetic torque coils, or magnetorquers, are the second type of control actuator used on the GNB. They are coiled loops of magnet wire which produce a magnetic dipole moment proportional to the amount of electric current running through them. The magnetic dipole m produced by a magnetorquer is defined by m = NiAˆn (3.11) where N is the number of loops, i is the current, A is the projected area of the coil, and ˆn is the magnetorquer normal vector. When the magnetorquer dipole vector is misaligned with the local Earth magnetic field line B, a torque τ is induced on the coil as defined by cross product

77 Chapter 3. Attitude system hardware 67 relation τ = m B (3.12) Using three orthogonal magnetorquers, each GNB satellite is provided with electro-magnetic torquing control about each axis. However, they can not provide instantaneous 3-axis control as it is not possible to control about the local magnetic field vector, as defined by the cross product term in (3.12). In an orbit of non-zero inclination, the local magnetic field lines will vary, and as a result the local magnetic field vector will change in magnitude and direction. Therefore, the magnetorquers provide instantaneous 2-axis control, with 3-axis orbit-average control (in theory). As previously mentioned, the GNB reaction wheels are the primary attitude control actuator on the GNB. Therefore, in the current design, the GNB magnetorquers are not responsible for providing attitude control during nominal operations. They will be used solely for rate damping and momentum management. These control modes are discussed in more detail in Section 4 Magnetorquer sizing Although each GNB mission is very different, the magnetorquers corresponding to each axis will be physically identical. Therefore, the magnetorquers must be sized in order to encapsulate all missions. This is accomplished by designing to the worst-case expected conditions. The GNB magnetorquers were sized such that they would have the capability to dump the largest expected momentum buildup on the reaction wheels, after a thrusting manoeuvre with worst-case thruster misalignment assumed. Magnetorquer sizing details are described by Grzymisch [23]. A very important consideration for magnetorquers is the current they draw. This quantity must be known to a high degree of accuracy. Like on CanX-2, the GNB magnetorquers are situated on the panels of the spacecraft. Throughout an orbit, it is expected that panel temperatures will vary from 5 C to 35 C. This in turn will cause the resistance of the magnetorquers to vary significantly. As a result, the current through the loop, and hence the magnetic field induced, will not be constant for a given voltage. The procedure followed for CanX-2 involved using temperature sensors on each panel, whose recorded temperature would be compared to a look-up table to give an approximate resistance value based on a physical equation. This

78 Chapter 3. Attitude system hardware 68 process is highly dependent on several cascading sources of error, namely, the accuracy of the temperature sensors and the equation used to estimate the resulting resistivity change of the copper in the magnetorquer wire. In order for the GNB to avoid being subjected to the same sources of error, the current through the coil is fed back to a current sensor on the power board, which then regulates it to the appropriate value. Assembly Each magnetic torque coil is assembled in-house. Standard 28 AWG copper magnetic wire is pulled through a winding jig which dispenses CV-1144 bonding agent. The wire is then manually wrapped around a mold, specific for each magnetorquer, corresponding to the panel on which it will ultimately be installed. Each magnetorquer on the GNB is designed to produce the same magnetic dipole moment, however they have different dimensions corresponding to their panel housing. Therefore, each GNB magnetorquer has a different number of loops. A digital counter used to aid in this process is discussed in greater detail by Grzymisch [23]. Integration There were several issues which arose during the integration of the GNB magnetorquers. The main problems resulted from the curing process. The original procedure was to allow each recently wound magnetorquer to allow the RTV to cure on the winding jig for 24 hours, followed by 48 hours off the jig (but on the mold), followed by a bake in the thermal chamber (off the jig and mold). Unfortunately, this process led to some fairly large warping and wire bulging. This was noticed on all three magnetorquers however the issue was the worst for the Z-axis magnetorquers. In Figure 3.43, it is clear that the bulging causes the Z-axis magnetorquers to cover screw holes making this panel impossible to integrate with the rest of the satellite. The solution was to allow the magnetorquers to cure on the jig in the thermal chambers, with the added feature of steel magnetorquer constraining rods, to minimize the bulge.

79 Chapter 3. Attitude system hardware 69 Figure 3.43: UniBRITE Z-axis magnetorquer before manufacturing procedure modification Figure 3.44: UniBRITE Z-axis magnetorquer after manufacturing procedure modification

80 Chapter 3. Attitude system hardware 70 The revised winding and curing procedure led to minimizing the unwanted wire bulge, a reduction in the warping observed, and a simplification of panel integration (Figure 3.44). In order to protect the fragile insulation of the magnetic wire, Kapton film was layed down on the GNB panels. Also, all protruding bosses or other seemingly sharp edges were first covered in Kapton tape. Figure 3.45 shows GNB magnetorquer cleanroom integration, with a close up of the UniBRITE +X panel. Figure 3.45: Left: Clean room integration of UniBRITE flight X-axis magnetorquer. Right: Close-up of the integrated magnetorquer Testing To ensure the magnetorquers behave as expected, each magnetorquer is subjected to a series of unit- and system-level tests outlined below. Low-vacuum checkout: As mentioned, CV-1144 is used as the bonding agent on the mag- netorquers. To gain confidence that no air bubbles have formed during the RTV curing process, each magnetorquer is placed in a bell jar, where the pressure is pumped down to approximately 50 mbar for 15 minutes. Centre-axis magnetic field: To verify that the magnetic field produced by each magne- torquer satisfies requirements, a known current is passed through each coil and a calibrated

81 Chapter 3. Attitude system hardware 71 magnetometer is used to measure the resulting magnetic field at the centre of the coil along the central axis. The field measured during this test is then compared with theoretical expectations, predicted by the design equations. Figure 3.46 illustrates the centre-axis magnetic field test with results weighed against expected results. Figure 3.46: Centre-axis magnetic field testing of a GNB magnetorquer 25 C Figure 3.46 demonstrates a linear increase in percent error in the magnetic field estimate of the GNB magnetorquers. This theoretical value uses the permeability of free space as the dielectric coefficient, in order to model a vacuum core. However these test are not preformed in a vacuum; moreover, there is a magnetometer situated at the centre of the coils. These are possible explanations for the error seen here. The average required torque from the GNB magnetorquers is expected to require a current in the neighbourhood of 10 ma to 20 ma. From Figure 3.46 it is clear that the magnetorquers behave sufficiently close to expected performance (i.e. less than 3% error).

82 Chapter 4 Attitude control laws As previously discussed, the use of a 3-parameter set, such as yaw, pitch, and roll, for attitude state description is an intuitive approach, as they are simple to visualize. For this reason, despite their disadvantages, Euler angles continue to be used on many spacecraft. This often implies an attitude control scheme which operate as a sequence of rotational manoeuvres about each axis. The approach for the GNB, following the use of quaternions, is to preform one eigenaxis rotation about the Euler axis in order to decrease slew time and to gain the added benefits of using quaternion, as discussed in Section 2. The GNB will therefore employ a quaternion feedback regulator for 3-axis attitude control. During nominal 3-axis control, momentum management of the reaction wheels will be performed using the magnetorquers. The GNB magnetorquers will also be used for rate damping upon orbital injection in order to null spacecraft tip-off rates. These control laws, pertaining to the GNB, were originally developed by Sarda [36]. For brevity, they are summarized here. 4.1 Rate damping Rate damping, or detumble, is an attitude mode entered after spacecraft ejection from the launch vehicle. It is also required after a loadshed condition, or any other circumstance in which active control has been delayed, and the spacecraft is tumbling in orbit. In this mode, the spacecraft will null its body rates following a detumble heuristic known as B-dot (Ḃ) control. 72

83 Chapter 4. Attitude control laws 73 This manoeuvre is preformed using the magnetorquers which produce torques as described in Section Magnetic torques applied to the GNB frame, approximated as a rigid-body, follow Euler s equation, I ω b + ω b I ω b = m b B b (4.1) which eventually leads too m b = K p Ḃ b (4.2) under the assumption that the local magnetic field vector, in the body-fixed frame B b will vary more rapidly due to the rotation of the spacecraft rather than the orbital motion [5]. B-dot control therefore relies solely on the rate of change of the local magnetic field, which can be determined using two successive magnetometer measurements. 4.2 Momentum management Reaction wheels will accumulate momentum due to secular disturbances. Magnetorquers are used to dump this momentum build-up, by the magnetic momentum management equation m b = ( ) 1 K p h b(wheel) h b(wheelref ) B b B b (4.3) 4.3 Three-axis control As mentioned, slew and pointing manoeuvres will be implemented using a linear quaternion regulator to preform near-minimum-time eigenaxis rotations. The kinematic equation of motion of the GNB spacecraft, with rigid-body assumptions, is governed by the Euler s equation, I ω + ω (Iω + h w ) = u (4.4) where the matrix h b(wheel) contains the angular momentum vector for each wheel. The control torques u issued from OASYS to the reaction wheels are governed by the PID control law t u(t) = K d ω(t) K p ε e (t) K i ε e (τ )dτ (4.5) 0

84 Chapter 4. Attitude control laws 74 where ε e are the three non-scalar terms of the attitude error quaternion. The full error quaternion, q e, is defined as two consecutive quaternion rotations from the desired quaternion [ε d T η d ] T to the true quaternion [ε T η] T which, when derived, becomes q e = ε e = η d1 η d η e ε d T ε d ε. (4.6) η η d With the preceding laws the GNB is controlled to a target quaternion defined as a rotation from GCI to the spacecraft body frame. For AISSat-1, however, it is more desirable to define attitude in terms of the orbital frame. For this reason, OASYS will also accept a target vector in terms of three Euler angles defining a rotation from the Hill frame to the body-frame. Applying a feedforward term to (4.6) in order to substract the nonlinear terms induced by gyroscopic coupling, we get t u = K p q e K d ω K i q e (τ )dτ + ω (Iω + h wheel ). (4.7) 0 However, when slew rates are sufficiently small, gyroscopic coupling effects and hence non-linear terms are typically negligible. 4.4 Sun avoidance Departing from the heuristic GNB controller, BRITE requires a method which will ensure the telescope does not pass within the cone subtended 45 from the solar vector during functional ACS operations. The sun avoidance controller for BRITE designed by Grzymisch [23] is u = K d ω K p ε e + P (4.8) where P = Kε s e ( β εs 2 ) (4.9) behaves as a penalty term analogous to a location of large potential, corresponding to the solar vector, and where the target attitude would appear as an area of low potential relative to all other attitudes. Here ε s, in 4.9 represent the three non-scalar terms of q s, the quaternion

85 Chapter 4. Attitude control laws 75 describing the Euler-axis rotation from current attitude to the solar vector. β is a gain corresponding to the size of the attitude exclusion zone at the solar vector. This value will be tuned such that a cone of at least 45 is traced out. This controller is based on the work of McInnes [31].

86 Chapter 5 Modelling and simulation Mission-level simulations are the sole means of providing insight into the on-orbit ADCS performance prior to launch. Therefore, accessibility to a high-fidelity simulating environment is strongly desired. It is the goal of the ADCS group at SFL to ensure that Mirage suits such a profile. Vital to the credibility of the results obtained from Mirage is the accurate modelling of the sensors and actuators which reside within. Section 3 gave a discussion outlining many of the testing procedures executed for a majority of the GNB ADCS hardware. The results from these tests provide a great degree of insight into the behaviour of the hardware. Through analysis of the resulting test data, each component is characterized, from which the Mirage hardware models are developed. A discussion of ADCS component modelling with supporting validation is included in the subsequent sections of this chapter. 5.1 AeroAstro star tracker The Mirage star tracker model is based on the field testing described in Section The inaccuracies observed in the star tracker attitude estimates are modelled in Mirage as Gaussiandistributed white noise, specific to each axis. As mentioned, the ADCS hardware modelling makes use of MATLAB s Simulink modelling environment. The AeroAstro star tracker model is shown in Figure 5.1. Here the variance block produces the noise value about each axis, which is subsequently converted into a quaternion. This noise quaternion is then applied as a rotation 76

87 Chapter 5. Modelling and simulation 77 from the true attitude quaternion, labelled q. The result is noise-distorted spacecraft attitude quaternion. Figure 5.1: Mirage model of the AeroAstro star tracker Figure 5.2: AeroAstro star tracker model sample output (250ms)

88 Chapter 5. Modelling and simulation 78 Figure 5.2 illustrates the output from the AeroAstro star tracker model for an exposure time of 250ms. The star tracker model appears to display a valid distribution of angular noise about each axis when compared to the results shown in Figure This model has been integrated with Mirage for the mission-level simulations of BRITE. 5.2 Sun sensors As discussed in Section 2.2.1, Mirage continuously propagates a solar ephemeris model, which provides the true solar vector in the GCI frame. Once fed to the sun sensor model shown in Figure 5.3 this vector is transformed into the spacecraft body frame using a rotation matrix and is then supplied to the GNB sun sensor model, here labelled Fb:s. This true solar vector is subjected to several sources of errors in order to account for sensor measurement noise specifically caused by thermal (Johnson) noise, sensor misalignment, refraction and dark current. Time-stamp, and measurement delay are also modelled, as they too contribute to signal inaccuracies. The solar vector magnitude is also quantized to account for the 8-bit pixel depth of the CMOS sensor. The solar vector in the body frame is converted into the sensor frame through a series of 90 degree rotations, preformed in the block labelled sensor frame sun vectors. This rotation is unique for each sensor as it corresponds to the particular spacecraft face on which it is mounted. As mentioned, the GNB ADS uses up to three fine sun sensors in order to converge on one particular sensor which provides the most accurate solar vector. The three initially selected sun sensors as determined by solar cell power generation are represented in the flag labelled F, in Figure 5.3. This flag along with the sensor frame based sun vector is supplied to the block labelled field of view which determines if the sun is indeed within the sensor s FOV, and if so, will determine the available clearance. Any sensor which does not see the entire photosphere of the sun will nullify the solar vector, returning zero. The FSS FOV is determined based on the sun sensor unit-level testing preformed at the Ryerson facility, as discussed in Section These parameters must therefore be varied for each mission simulation to retain maximum predictive capability. In particular, the pinhole height and origin bias will determine the sensor

89 Chapter 5. Modelling and simulation 79 Figure 5.3: Mirage Simulink model for the GNB sun sensors

90 Chapter 5. Modelling and simulation 80 FOV θ, for a given azimuthal angle α, by the following relationship: θ = tan 1 ( l cos α + r p d + t p where d is the pinhole height, the length l depends on the origin bias, r p is the pinhole radius (150 µm), and t p is the pinhole thickness. Figure 5.4 illustrates the effective FOV of the AISSAT- 1 sun sensors as projected on a unit sphere. ) Figure 5.4: FOV unit-sphere projection of AISSAT-1 sun sensors The solar vector in the sensor frame, labelled Fs:s, is then fed into the profile simulator block which constructs a series of profiles representative of the GNB sun sensors. The resulting profiles are sent to OASYS, from which centroid is determined, and the measured solar vector is calculated. Figure 5.5 illustrates the sun sensor reference frame and how relates to the array of the CMOS active pixel sensor.