Aalborg University Institute of Electronic Systems

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1 Aalborg University Institute of Electronic Systems TITLE Attitude Control System for AAUSAT-II PROJECT PERIOD IAS8, Febuary 2 nd - June 2 nd, 2004 PROJECT GROUP 830a GROUP MEMBERS Daniel René Pedersen Jacob Deleuran Grunnet Jesper Abildgaard Larsen Karl Kaas Laursen Ewa Kolakowska Isaac Pineda Amo SUPERVISOR Roozbeh Izadi-Zamanabadi Rafal Wisniewski Number of reports printed 10 Number of pages in report 140 Number of pages in appendix 26 Total number of pages 169 ABSTRACT The second student Cubesat satellite developed at Aalborg University, AAUSAT-II, has a scientific mission that requires precision attitude control. For this purpose an attitude control system is designed which, by the use of magnetic and mechanical actuation, is capable of detumbling and correcting the attitude of a CubeSat. Magnetorquers and momentum wheels have been selected resulting in an over actuated system facilitating three axis control of the spacecraft. A simulation library containing tools for simulating the orbit and attitude including disturbances has been implemented in Simulink. ADCS is integrated in the library including sensors, actuators and implementation of the attitude determination and control algorithms. A supervisory controller is developed to manage the attitude controllers to allow autonomous behavior such as momentum wheel bias control and target tracking. Classical pole-placement and optimal control is utilized to tune a state space controller for momentum wheel attitude control. The B-dot algorithm is used for detumbling using only electromagnetic actuation and a custom algorithm for momentum wheel desaturation and bias control has been developed. Simulations of the different controllers have indicated that the controllers satisfy all accuracy requirements. Further testing of the momentum wheel control will be carried out on a parabolic flight campaign.

2 Contents Nomenclature Preface v xi 1 Introduction 1 2 Mission analysis Mission objectives In-orbit operation Satellite structure Requirements Mission Definitions Functional requirements Budgets System configuration Actuator strategy Sensor analysis Configuration of momentum wheels Hardware configuration Software configuration Perspectives Actuators Magnetorquers design

3 5.2 Design of Momentum Wheels Fault Detection and Isolation system Summary Modelling Coordinate system definitions Model structure Orbit and magnetic field modelling Ephemeris model Disturbance modelling Spacecraft dynamics and kinematics Modelling of actuators Summary Perspectives Controllers Control strategies Control supervisor Detumbling controller based on B-dot Momentum wheel attitude controller Desaturation of momentum wheels Perspectives Test Introduction Feel free - feel zero-g Test strategies Conclusion Project objectives Study objectives Perspectives Bibliography 130

4 iv Attitude Control System for AAUSAT-II A Quaternion 135 A.1 Axioms and definitions A.2 The time derivative of a quaternion B Implementation of simulation 139 B.1 IGRF model B.2 Orbit model B.3 Solar radiation B.4 Atmospheric drag B.5 Gravitational disturbances B.6 Magnetic residual B.7 Spacecraft dynamics and kinematics B.8 Magnetorquers B.9 Momentum wheels C Interface Control Document 151 C.1 System modes C.2 External Interfaces C.3 Internal Interfaces

5 Nomenclature Common terms Attitude The orientation of a spacecraft given as a rotation between two coordinat systems. Ecliptic plane Mean plane of the Earth s orbit around the Sun. Eclipse Transit of the Earth in front of the Sun, blocking all or a significant part of the Sun s radiation. Failure The inability of an actuator, sensor, subsystem or system to accomplish its required function. Fault A change in the characteristics of a component, such that it influences the operation mode or performance of the component in a undesired way. Geostationary A spacecraft travels above Earth s equator from west to east at an altitude of approximately 35900km and at a speed matching that of the rotation of the Earth, thus remaining stationary in relation to the Earth. Latitude The angular distance on the Earth measured north or south of the equator along the meridian of a satellite location. Longitude The angular distance measured along the Earth s equator from the Greenwich meridian to the meridian of a satellite location. Vernal Equinox The point where the ecliptic crosses the Earth s equatorial plane going from south to north. Acronyms ACS Attitude Control System ADCS Attitude Determination and Control System ADS Attitude Determination System

6 vi Attitude Control System for AAUSAT-II BGA Ball Grid Array CDH Command Data Handling COM Communication system ECI Earth Centered Inertial coordinate system ECEF Earth Centered Earth Fixed coordinate system EKF Extended Kalman Filter EPS Electric Power Supply system FMEA Failure Mode and Effect Analysis FOV Field Of View GEO GEostationary Orbit GPS Global Positioning System GRB Gamma Ray Burst GS Ground Station IGRF International Geomagnetic Reference Field INSANE INternal Satellite Area NEtwork LEO Low Earth Orbit MECH Mechanical system OBC On Board Computer P/L Payload system RMS Root Mean Square SCT Spacecraft Control Toolbox SGP4 Simplified General Perturbation version 4 TLE Two-Line Element

7 Group 830a vii Notation Physics parameters There are a number of physical parameters for which standard symbols are used. 1 n n The n dimensional identity matrix a Acceleration A Area I Inertia tensor. Al Altitude B Magnetic field vector c Velocity of light eu Engineering Unit (ie. a unit less scalar) F Force G Gravitational constant H, h Angular momentum h mw Angular momentum for momentum wheels h sat Angular momentum for rigid body part of the satellite I Moment of inertia I xx, I yy, I zz Moments of inertia I xy, I xz, I yz, I yx, I zx, I zy Products of inertia JD Julian Date JD E Julian Date since defined epoch La Latitude Lo Longitude M, m Mass N Torque q Quaternion

8 viii Attitude Control System for AAUSAT-II R Position r Radius r earth Mean radius of the Earth T, t Time V Velocity Φ Solar flux µ earth Gravitational constant times the mass of the Earth. θ Rotation angle S( ) Skew symmetric matrix (3 3), vectors cross product function ω Angular velocity vector x State vector e Unit rotation vector R n n dimensional real space P Payload axis Coordinate systems Coordinate systems, also known as frames, are abbreviated as below. The definition of the frames can be found in section 6.1 on page 41. E Earth centered earth fixed. I Earth centered inertia. S Spacecraft fixed. P Spacecraft fixed principal axes. O Orbit fixed attitude reference.

9 Group 830a ix Objects To ease the typesetting of equations, the following objects are abbreviated as below: sc Spacecraft s Sun e Earth m Moon Vectors, matrices and rotations Coordinate vectors are typed as E V subscript with the reference frame of the coordinates superscripted in front of the vector. Vector components are typed as E V x which denotes the x component of the V vector in the ECEF frame. Matrices are typed like vectors I M sc The above matrix M relates to the sc object (the spacecraft) in the ECI frame. Rotations (quaternions) are typed like vectors, but with a source (bottom) and destination (top) indices; I Eq m The quaternion q rotates the moon, m, from the ECEF frame to the ECI frame Subranges of eg. vectors and matrices use the following notation E V [1:3] This subrange signifies element 1, 2 and 3 of the first row of the vector V in the ECI frame. In other words, subranges selects elements in the first row. If columns are to be selected, the vector or matrix will first be transposed. Unit vectors are typed like vectors but hatted, ie. EˆV subscript

10 x Attitude Control System for AAUSAT-II Matlab notation In diagrams from Simulink for Matlab, typesetting is not possible to the same extent as in the report. Due to this, the following notation is used: Vectors are typed as V(I) where the letter in parenthesis is the reference frame. Rotations are typed like q(i E) which denotes a rotation from the ECI to the ECEF frame. Note that scalars are written in small caps, eg. i_xx

11 Preface This report documents the development of an Attitude Control System (ACS) for the AAUSAT- II which is a 8 th semester project in Intelligent Autonomous Systems specialization at Aalborg University, Department of Control Engineering. The project began on the 2nd of February 2004 and was finished on the 2nd of June Throughout the report, figures and tables are numbered consecutively according to the chapters. References to literature are done like this: [30, p. 24], which refers to Space Mission Analysis and Design by J. R. Wertz, page number 24. The bibliography can be found on page 131. The attached CD-ROM contains the Simulink models used by the ACS. It also contains the datasheets for the motors and solar panels. The nomenclature, which contains the notations used throughout the report, can be found on page v. Since this project is closely related to the Attitude Determination System project, the first part of the report has been written in conjunction with the project group which has been responsible for this subsystem (group 04gr830b). The parts that are common for the entire Attitude Determination and Control System are the mission analysis in chapter 2, system requirements in chapter 3, system configuration in chapter 4, part of the modelling in chapter 6 and the Interface Control Document in appendix C Aalborg University June 2 nd Daniel René Pedersen Jacob Deleuran Grunnet Jesper Abildgaard Larsen Karl Kaas Laursen Ewa Kolakowska Isaac Pineda Amo

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13 CHAPTER Introduction This project is part of the ongoing process at Aalborg University to design and build a picosatellite named AAUSAT-II. The satellite will be constructed by students without professional help. AAUSAT-II is part of the CubeSat concept [28] that defines a standard for pico-satellites which makes it possible to both construct and launch satellites into space at a relatively low cost. The cheap launch is achieved by sending it into space as a secondary or tertiary payload using a standardized deployment system known as a P-pod, developed by California Polytechnic State University. The primary aspects of the CubeSat concept are that the satellite must be a cube with side lengths of 10 cm 10 cm 10 cm and weigh no more than 1 kg. The low cost of the satellite has made it possible for Aalborg University to participate in the construction of satellites. On the 30 th of June 2003 the first satellite from AAU, the AAU-CubeSat, was launched, fulfilling several of its main success criteria. The goal of the satellite was to take photographic images of the Earth using its on board camera. However due to weak radio signals and failure of the batteries on board the satellite did not succeed in taking pictures. On the 22nd of September 2003 the AAU-CubeSat project announced end of operations. AAUSAT-II was started in September 2003, and a preliminary launch date is set for late The goals of the AAUSAT-II mission are to measure gamma-rays and X-ray from the Sun. Therefore the satellite has to point towards the Sun when it is required. The secondary goal include testing an attitude control system using momentum wheels. The primary goal of the AAUSAT-II project is to educate students in working with satellite construction. Several groups, spread across different semesters and specializations, are involved in designing the different parts of the satellite. Such a distributed development process makes it necessary to have a system steering committee which consists of representatives from every group involved. The system steering committee is in charge of maintaining consistency in the satellite project, and approving changes in one part of the satellite that might affect other parts of the satellite. It is also up to the system steering committee to derive the basic requirements to the different parts of the satellite. These requirements are power usage, mass, size, interfaces and the goals of the satellite mission. This project will deal with the development of the Attitude Control System (ADCS). The goal of this subsystem is to control the satellite attitude continuously, such that the satellite points in the desired direction.

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15 CHAPTER Mission analysis This chapter will describe the background of the overall mission requirements for the AAUSAT- II satellite. These include the primary objectives, the satellite life cycle and briefly describe which subsystems the satellite is composed of. 2.1 Mission objectives The AAUSAT-II satellite is known as a student satellite. That is, the satellite is built and operated by students with help and advise from supervisors. The AAUSAT-II development team consists of several groups working on one or more specific subsystems. The Steering Committee, which can be regarded as the management group, has the overall responsibility for the AAUSAT-II team. The Steering Committee consists of one student from each of the project groups, the project manager, the technical manager, the system engineering manager and finally a representative from Aalborg University Space Center. The Steering Committee has defined the goals of the AAUSAT-II project, of which the most important have been listed below in order of priority. Detailed information about the structure of the AAUSAT-II development team can be found in the AAUSAT-II user requirement document [15] or on the official AAUSAT-II homepage, Please note that these requirements are not related to the physical satellite itself. 1. Education of students and staff The whole project should contribute to the education of the students involved in the project and assigned members of the staff. It should produce a greater insight into space engineering in general and enhance the competence of the students in the relevant engineering disciplines on which it has its foundation. 2. Primarily be built by students The project should be carried out primarily by students. This means that everything from system engineering decisions to the acquiring of electronic components should be done by students, and that the staff members assigned to the project should function only as advisors and final arbitrators. 3. Gathering of telemetry The satellite should be able to gather and provide telemetry so that internal temperatures, voltages and power consumption can be monitored from the Earth. The satellite should be able to continuously collect and store these data and send them to earth, so the performance of the satellite can be analyzed.

16 4 Chapter 2 Mission analysis Attitude Control System for AAUSAT-II 4. Conduct a scientific experiment As the payload of the satellite, AAUSAT-II should have a scientific experiment which should be conducted and the telemetry sent to earth. The actual experiment has been provided by the Danish Space Research Institute (DSRI) and features a combined Gamma Ray Burst (GRB) and X-Ray detector. 5. Active control utilizing momentum wheels A feasibility study of active control utilizing momentum or reaction wheels should be conducted to see if it is possible and/or feasible to control a pico-satellite using a electro-mechanical system. As this report is part of the Attitude Determination and Control System (ADCS), mission objective 5 is what is treated in this report. 2.2 In-orbit operation Both before, under and after the satellite is launched into space, the life cycle of the AAUSAT- II is well defined. This section will briefly describe the different phases in the life cycle of AAUSAT-II. Development During the development stage, the different subsystems of the satellite are developed and tested separately. Integration In this stage, the different subsystems are interfaced (and tested) to each other one at a time. The result is the engineering model of the AAUSAT-II. Test During the test phase, the engineering model undergoes various tests to find possible design and/or implementation flaws, which can be corrected before the flight model of AAUSAT-II is built. Pre-launch The pre-launch stage is where the flight model undergoes the final tests and is shipped to the launch site. Launch AAUSAT-II is launched into a Low-Earth Orbit (LEO) as secondary or tertiary payload. Deployment When the rocket carrying AAUSAT-II has reached the designated orbit, the satellite is deployed via the Poly Pico satellite Orbital Deployer (P-POD) [24]. Power on After e.g. 5 minutes, the satellite is powered up by the Electrical Power Supply (EPS), and the antennas are deployed (should this be needed). Detumble The ACS system detumbles the satellite, so the angular rate is close to zero. Basic beacon When detumbling is complete, the EPS starts sending out a basic beacon, containing the satellite name and battery voltage.

17 Group 830a 2.3 Satellite structure 5 Establish two-way communication Once the ground station intercepts the basic beacon, twoway communication should be initiated to allow for download of advanced telemetry and upload of new parameters and/or software. Mission start Once two-way communication is achieved (when the satellite is over a suitable ground station), the science experiment and the active actuation test should start, and telemetry should be gathered. End of operation When the experiments are completed, and there is no point in continuing support of the satellite, end of operation should be declared, and the satellite should be shut down. Depending on the orbit altitude, the satellite will eventually burn up in the upper atmosphere. This report is carried out in the first phase, development. 2.3 Satellite structure The satellite consists of several different subsystems with each specific task. The subsystem abbreviations and the overall tasks of the particular system are listed below. ACS Attitude Control System. Control of the orientation of the satellite using electro magnetic coils and momentum wheels. ADCS Attitude Determination and Control System. Since ACS and ADS (below) are tightly coupled, the two subsystems are sometimes regarded as a single entity. ADS Attitude Determination System. Subsystem with the purpose of calculating the orientation of the satellite using rate gyros, solar panels and magnetometers. COM Communication. This subsystem consists of the radio and power-amplifiers needed to get two-way communication with earth. It also includes the antennas for the radios. EPS Electrical Power Supply. The system must charge the on board batteries with power generated by the solar panels. EPS is also responsible for sending out the basic beacon, which is a simple telemetry radio signal (for example using Morse code). GS Ground Station. This subsystem is not a part of the satellite itself, but is situated on earth as the main communication channel to the satellite. INSANE INternal Satellite Area NEtwork. This subsystem is the on board satellite communication channel between the different subsystems and consists of the physical communication layer (wires) and a protocol stack, which all subsystems must use to ensure compatibility. MECH Mechanical subsystem. The mechanical system must provide the satellite frame and casing, in which the other subsystems can be integrated.

18 6 Chapter 2 Mission analysis Attitude Control System for AAUSAT-II OBC On Board Computer. The on board computer is the main processing facility on board, and features most of the on board software like the flight planner and ADCS algorithms. P/L Payload. The payload consists of the DSRI-supplied Gamma Ray Burst (GRB) detector and controller, which is the key scientific experiment. CDH Command Data and Handling. This subsystem consists of the flight planner, which is the in-orbit scheduler for the various events which is to take place. CDH also includes the various telecommand and telemetry handles. The internal structure of the satellite is depicted on figure 2.1 on the next page, showing the different busses and communication channels on the satellite, namely the network bus named INSANE, and the power bus that delivers power to the systems which is the responsibility of the EPS. As can be seen on figure 2.1 on the facing page, the INSANE is used both as the satellite network between physical subsystems via a CAN bus and as the communication channel internally in the OBC via a mailbox system. The satellite link to earth is via a radio link between the radio unit and the GS. The EPS subsystem is directly connected to the solar cells and batteries, and all subsystems are connected to the EPS, which is responsible for monitoring the power usage. In the OBC subsystem two subsystems (SS) can be found. These represent a physical subsystem which will have a software system running on the OBC as well, for example the P/L, which needs data storage, and the ADCS system which might be too computational demanding to run on the decentralized physical subsystem itself.

19 Group 830a 2.3 Satellite structure 7 MECH OBC CDH SS SS INSANE (mailbox) INSANE (can) COM ADS ACS P/L EPS Power RADIO SOLAR PANEL BAT TERIES Radio link GS Figure 2.1: Overall satellite structure.

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21 CHAPTER Requirements This document states the requirements for the Attitude Determination and Control Systems for the AAUSAT-II satellite. 3.1 Mission The following two prioritized scientific missions for AAUSAT-II are: 1. Performance study of a single CdZnTe (CZT) detector 2. Gamma ray burst detection 3. Solar X-ray detection These missions prompt a need to adjust the attitude of the satellite which requires an attitude determination and control system. Requirements to the following subjects are set: Detumbling Pointing Fault detection and handling Autonomy 3.2 Definitions This section contains the prerequisites for the functional requirements Modes The term mode is used to indicate the requested state of the ADCS. The modes to be implemented are:

22 10 Chapter 3 Requirements Attitude Control System for AAUSAT-II Idle The ADCS is idle. Sensors and actuators use minimal power and the required computational demands are minimal. Detumbling The ADCS is performing angular rate reduction of the spacecraft. Pointing The ADCS is acquiring a requested attitude and maintaining this attitude. This mode has three submodes: Attitude control The ADCS is acquiring a requested attitude and maintaining this attitude. Direction control The ADCS is pointing the payload in a direction given by a target vector. Autonomous pointing The ADCS is pointing the payload in the direction of a target which is continuously calculated by the ADs States The term state is used to indicate the actual physical state of the spacecraft. The states referenced in the requirements to ADCS are: Detumbled state The satellite is detumbled and requirement [ADCS 1.2] in section applies. Stable pointing state The satellite is in detumbled state and a requested attitude has been acquired. Requirement [ADCS 2.2] in section applies Pointing The term pointing is defined to describe the act of acquiring and maintaining a given attitude referenced in the inertial coordinate system. This also includes direction control where the rotation around the payload axis is free. The term attitude error given as an angle is defined using the error quaternion in (3.1). q err q err[4] = q att q 1 = cos ref ( θerr 2 ) θ err = 2 cos 1 (q err[4] ) (3.1) The term pointing error is given as an angle between the payload axis and the vector indicating the requested direction in which to point.

23 Group 830a 3.3 Functional requirements Functional requirements This section states the functional requirements to the ADCS Detumbling ADCS 1 The ADCS has to be able to detumble the satellite in order to stabilize the attitude of the satellite. ADCS 1.1 The ADCS must be able to detumble the satellite from an angular velocity of 0.1 rad s down to rad within 5 orbits. s ADCS 1.2 In detumbled state the ADCS must keep the angular velocity below rad s axes. on all Pointing The GRB detection mission has no accuracy requirements for the attitude of the satellites other than is mst be able to point away from the Sun; but the X-ray detector alone determines how accurate the satellites attitude must be adjusted. The requirement for pointing accuracy from the X-ray mission is below 5, see [9]. A prerequisite for switching to pointing mode is that the satellite is in detumbled state and the ADCS is fully operational. ADCS 2 The ADCS must be able to turn the satellite to an attitude or direction given by the flight planner in pointing mode. ADCS 2.1 The ADCS must be able to maintain a stable pointing state continuously for 25% of an orbit. ADCS 2.2 The ADCS must be able to maintain a stable attitude of the satellite with an attitude error below 5 for 99% of the time in stable pointing state when in attitude control mode. ADCS 2.3 The ADCS must be able to maintain a stable direction of the pauload axis with a pointing error below 5 for 99% of the time in stable pointing state when in direction control mode. ADCS 2.4 The ADCS must be able to maintain a stable direction of the pauload axis with a pointing error below 5 for 99% of the time in stable pointing state when in autonomous pointing mode.

24 12 Chapter 3 Requirements Attitude Control System for AAUSAT-II Fault detection and handling ADCS 3 The ADCS must be able to detect sensor and actuator faults. ADCS 3.1 The ADS is in charge of monitoring the sensors and notifying the ADCS in case of a fault or failure. ADCS 3.2 The ACS is in charge of monitoring the actuators and notifying the ADCS in case of a fault or failure. ADCS 3.3 In case of failure in the redundant sensor system the ADS must still be able to determine the attitude of the satellite with an rough accuracy of 15. ADCS 3.4 The ACS must have at least one redundant actuator system. ADCS 3.5 In case of failure in the redundant actuator system the ACS must still be able to keep the satellite in detumbled state Autonomy ADCS 4 The ADCS must be able to autonomously point the payload in a direction given by a vector. ADCS 4.1 The ADCS must be able to autonomously point the payload at the Sun in pointing mode. 3.4 Budgets The budgets for the joint ADS and ACS is currently only a draft with a 200 g buffer for the mass, but the limits should not be exceeded Power The power budget of the ADCS system is 225 mw in active mode and 25 mw in idle mode. The expected average power generated by the EPS is 2.5 W Mass The mass budget for ADCS is 200 g. The maximum total mass of the satellite is 1000 g.

25 CHAPTER System configuration In this chapter the configuration of the sensors, actuators and other hardware of the ADCS is discussed. This is done by defining some basic design parameters such as the actuation strategy and which sensors to use. Following this, the physical configuration of sensors and actuators is set and considerations on electronic circuits and software design are made. 4.1 Actuator strategy To be able to control the attitude of the spacecraft at least one actuator system is needed. Actuators must be able to cause an angular acceleration of the spacecraft. According to equation (4.1) they must assert a torque on the spacecraft. N = ωi (4.1) As the torque is the derivative of the angular momentum, the actuator must change the angular momentum of the spacecraft, which according to Newtons law must be constant when the spacecraft is not affected by external forces. As a result there are only two ways to alter the attitude of the spacecraft. 1. By transferring angular momentum to an external object. 2. By transferring angular momentum to another part of the spacecraft. They can be achieved by a number of different methods. The most common ones are discussed below Chemical thrusters Chemical thrusters utilize a chemical reaction which accelerates a propellant and expels it from the spacecraft. In other words, momentum is transfered from the spacecraft to the propellant, thus chemical thrusters belong to the second group of actuators. They can be used to exert a torque on the spacecraft but they have a limited operational time which depends on the amount of fuel. As the chemical thrusters use propellant, they can not be used on a Cubesat, [24].

26 14 Chapter 4 System configuration Attitude Control System for AAUSAT-II Ion thrusters Ion thrusters expels an ionized propellant accelerated by an electric field. This makes the ion thrusters more fuel-efficient than the chemical thrusters, but with much lesser thrust. As with chemical thrusters the ion thruster belongs to the second group of actuators as the angular momentum of the satellite is transfered to the ionized propellant. Ion thrusters are a new and relatively unproven technology with very high complexity. The power consumption used for creating the electric field is very high and it is thus not feasible for use in a CubeSat Momentum wheels Momentum wheels consist of a motor and a flywheel. When the flywheel is accelerated by the motor it picks up angular momentum, which is transfered from the satellite frame (on which the motor is mounted). With three momentum wheels it is possible to transfer angular momentum from the satellite to the momentum wheels. Instead of using three momentum wheels it is also possible to use a single momentum wheel in a gyroscopic suspension. However there is a limit of how much angular momentum can be transferred to the momentum wheels as the motor has a saturation limit, and momentum wheels are thus often used in conjunction with another actuation system. The momentum wheels belong to the second group of actuators as the angular momentum is transfered to the momentum wheels. Momentum wheels are a viable actuation system for the satellite as it is possible to find motors of very small sizes and low power consumption Magnetorquers Magnetorquers belong to the first group of actuators as they work by generating a magnetic field, which through interaction with the Earth s magnetic field, transfers angular momentum to the Earth. Magnetorquers consists of a set of coils which generates a magnetic field when current runs through them. Three coils are needed to achieve control in all spatial directions. Their operation is limited since the torque produced depends on the cross product of Earth s magnetic field and the magnetic dipole generated by the coils. Thus the magnetorquers ability to control the spacecraft to a certain attitude is dependent on the position of the spacecraft relative to the Earth. It means that the precision, in which the attitude can be controlled, can vary substantially. Apart from varying accuracy of the magnetorquer attitude control, the coils are the ideal attitude actuator system for a CubeSat, as it has no mechanical parts and can be constructed arbitrarily small.

27 Group 830a 4.2 Sensor analysis Summary A magnetorquer is a mechanically simple actuator which has been proven to be very reliable for low Earth orbiting spacecraft like e.g. Ørsted and AAU CubeSat. Due to its capabilities to excert external torques on the spacecraft body and its availability the magnetorqer is chosen as an attitude control actuator for AAUSAT-II. The accuracy of magnetorquers is, however, limited so in order to achieve fine pointing control another actuator system is needed. For this purpose momentum wheels is seen to be the best choice as they do not involve propellant and it is possible to control the amount of angular momentum stored in the momentum wheels to a very high degree of accuracy. 4.2 Sensor analysis This document describes the possible sensors that can be used on the satellite. The section is based on information from [30, p.376] Sun sensor A sun sensor is a reference sensor which measures a direction in a known reference coordinate system. Sun sensors are visible light detectors which measure one or two angles between their mounting base and the incident sunlight. Sun sensors are popular, accurate and reliable but requires a clear field of view and are very expensive for the small scale of a CubeSat. Instead of using sun sensors, solar panels can be used. The angle of the Sun is calculated from measurements of the power generated by each of the panels. Solar panels are less precise than sun sensors as they are not designed to be used as sensors. However, as solar panels are the only mean for generating power on-board the satellite Star sensors Star sensors can be either scanners or trackers. Scanners work on spinning satellites where the attitude is determined by the light of stars passing through multiple slits in the field of view of the scanner. Star trackers recognize star patterns in the field of view of the sensor. Camera technologies as Charged-Coupled Devices (CCD), Active Pixel Sensors (APS) and CMOS could be considered for this task. The location of two or more stars is enough to determine the attitude of the satellite. This means that a star tracker alone can determine a three axis attitude when pointing towards the sky. For recognizing star patterns, an on-board star database is necessary. However, the problem with star trackers is they require the satellite to be stabilized to some extent before the tracker works. This stabilization may require extra sensors which increases the overall cost of the mission.

28 16 Chapter 4 System configuration Attitude Control System for AAUSAT-II Gyros A gyro is a sensor which measures the angular rate of the satellite or the angle of rotation from an initial reference, without any knowledge of external references. A gyro measures the angular velocity by means of the Coriolis effect which is defined by Newton s first law of motion: A body in motion continues to move at a constant speed along a straight line unless acted upon by an unbalanced force. The advantage using gyros is that they can provide high frequency angular rate information (up to hundreds of Hertz), which the other types of sensor may not be able to do. Also, gyros measure angular velocity directly, which eg. sun sensors and star sensors can not. When grouped together gyros can provide full 3-axis information Magnetometer Magnetometers are simple lightweight sensors that measure the direction and size of the magnetic field (eg. the magnetic field of the Earth). The precision of a magnetometer is not as high as that of a star sensor. Due to this, it is desirable to combine it with another type of sensor. Since the magnetic field of the Earth is limited to the vicinity of the Earth, the magnetometers can only be used in LEO. When the satellite uses magnetorquers to control the attitude, the magnetometer and the magnetorquer should be synchronized, so that the magnetorquer is not turned on when the magnetometer is measuring. Magnetometers can be used to get three axis attitude information GPS GPS is the most accurate positioning sensor. It communicates with satellites in GEO to calculate the current position and velocity of the sensor. The attitude of the satellite can be calculated using the difference between the measurements from two or more sensors. However the price of a GPS receiver, small enough to fit on a Cubesat, is very high Horizon sensor Horizon sensors detect the threshold between infrared light emitted from the atmosphere of the Earth and space by utilizing an infrared diode and a lens. There are two kinds of horizon sensors; scanners and horizon crossing indicators [21]. A horizon crossing sensor is fixed in the satellite structure and can provide valuable attitude information only when the sensors line of sight crosses the mentioned threshold. Due to the size, weight and complexity only static horizon crossing indicators are considered suitable for a Cubesat.

29 Group 830a 4.3 Configuration of momentum wheels Discussion of sensors Sensor comparison Sensor type Type Precision Horizon sensor Reference 0.1 deg Star sensor Reference 2 arcsec Sun sensor Reference 0.01 deg Gyro Inertial deg/hour Magnetometer Reference deg GPS Reference 1 cm 50 m Table 4.1: Comparison between different sensor types, [4] There are several aspects to take into account when choosing the sensors for the AAUSAT- II. Mass, volume and power usage are highly important factors, and also the precision of the sensors. The requirements stated in chapter 3 say that the satellite should be able to point within an accuracy of 5, so the combination of sensors chosen for the AAUSAT-II must, at least, be able to fulfill this demand. In table 4.1 different kinds of sensors and some of their characteristics are listed Choice of sensors The AAUSAT-II will be launched into LEO. Therefore the precise available models of the Earth magnetic field can be used. Magnetometers are light and do not require much power compared to eg. star sensors. Magnetometers are also to be used together with magnetorquers for detumbling the satellite as the control strategy requires measurements of the magnetic field. One of the goals of the AAUSAT-II mission is to test momentum wheel control, and see with what precision the satellite can be controlled. To be able to measure small changes of attitude, gyros or a star sensor have to be used. Since the momentum wheels will be tested on a zero-g parabolic flight star sensors are not considered, and gyros will be used instead. 4.3 Configuration of momentum wheels Designing an attitude control system using momentum wheels it is important to consider the placement and orientation of the wheels carefully before venturing into controller design. The physical constraints of the AAUSAT-II set limitations to the mass and volume that can be consumed by motors and flywheels. The laws of physics also play a role as at least three wheels are needed to do three-axis attitude control. Normally, a reaction wheel attitude control system would employ four wheels to be able to operate the motors at a bias speed while ensuring full three-axis control which requires the ability to generate angular momentum in any direction in the spacecraft frame. However, only three momentum wheels will fit inside AAUSAT-II which gives limitations to the three-axis control if the wheels are operated around a bias. These

30 18 Chapter 4 System configuration Attitude Control System for AAUSAT-II limitations are considered in the controller strategy discussion in section on page Orientation To achieve three-axis control the rotation axes of the momentum wheels must span all three dimensions of space. This is possible in many configurations, but the lack of knowledge of the mass distribution and hence the moments of inertia of the spacecraft, leaves only one obvious solution, orthogonal alignment. Figure 4.1 shows the configuration, where the wheels are aligned parallel to the axes of the spacecraft coordinate system. Figure 4.1: Momentum wheel orientation. The wheels are aligned along the spacecraft axes Operation When using momentum wheels to exert relatively small torques at high precision, as it is needed to control a spacecraft, the motors driving the wheels are operated at a bias. This means that the motors spin at half the maximum rate when the spacecraft is stabilized and torque is generated by either spinning the motors up or down between zero the maximum. The reasons for not changing the rotation direction of the motors are first of all, to avoid the non-linear Coulomb friction that acts when crossing zero (stopping and starting the motors). Secondly, according to Maxon Motor [23] extreme start/stop, left/right operation leads to a reduction in service life. The bias of the motors is referred to as S h bias = h mw 0.5 (4.2) Hardware configuration The configuration of the hardware of ADCS is depicted in figure 4.2.

31 Group 830a 4.4 Hardware configuration 19 Figure 4.2: Overall hardware architecture of the attitude determination and control system.

32 20 Chapter 4 System configuration Attitude Control System for AAUSAT-II In celebration of modularity and reusability the ADS and ACS parts of the complete ADCS are separated into two hardware units that are individually interchangeable. These hardware units work as interfaces to sensors and actuators respectively and are connected to the on board computer via CAN. The interface units communicates through INSANE 1 [19], thus it is very generic and easy to reuse in an eventual AAUSAT-III. 4.5 Software configuration The software of ADCS is distributed on multiple processing units: On board computer ADS hardware interface ACS hardware interface All control and determination algorithms will run as threads on the on board computer along with housekeeping software and supervisory control. These software units communicate with the programs running on the hardware interface units via the INSANE protocol. The software on the hardware interface units acts as device drivers communicating with sensors and actuators and relaying information between the physical systems and the software on the on board computer. 4.6 Perspectives The configuration of the actuation system may be subject to improvements if more detailed descriptions of the mechanical properties of the spacecraft are made available. This especially applies to the orientation of the momentum wheels as the choice of configuration allows the wheels to generate angular momentum in a certain subspace of the spacecraft coordinate system. By changing the orientations to span some non-orthogonal subspace it is possible to either, have the ability to generate more angular momentum, but in a narrower range of directions, or have a directional range at the cost of smaller angular momentum. The first option might be beneficial in the case that the difference in moments of inertia of the three axes of the spacecraft is big. By orienting the wheels, such that they can generate a larger angular momentum in a subspace containing the major axis of inertia, it is possible to achieve better control by being able to exert a greater torque around the major axis. This may minimize the difference in the angular acceleration which the controller can generate on the three axes. 1 INSANE is short for INternal Satellite Area NEtwork

33 CHAPTER Actuators In this chapter the design of the magnetorquers and momentum wheels for the AAUSAT-II is presented. The chapter also covers fault detection and isolation of faults in the actuators, which is a key topic in satellite design, due to the high degree of autonomy. 5.1 Magnetorquers design The magnetorquers are designed under the assumption that all three coils are the same. That concerns their physical characteristics such as structure, material and so on. The coils are to be bounded on three perpendicular plates, inside the satellite, so that the areas they encircle are as big as possible. The dimension of the coils is limited by the mechanical structure of the satellite. All the parameters are introduced in the figure 5.1. Figure 5.1: Coil. Mechanical drawing Mathematical description of a magnetorquer In the following the equations for one coil are described.

34 22 Chapter 5 Actuators Attitude Control System for AAUSAT-II Mass of one coil Defining: M c : mass of the coil V c : volume of the coil n: number of turns ρ: density of the material of the coil a w : wire cross sectional area C: circumference The mass of one coil can be described as: M c = V c ρ = nca w ρ (5.1) Power consumption Defining: P : power dissipation U c : voltage supplied to the coil I: current in the coil R: electric resistance of the coil The power dissipation can be described as: Where the resistance of the coil is given by: P = U c I = I 2 R (5.2) R = ncσ(t) a w (5.3) where: σ(t) = σ 0 (1 + α 0 T) α 0 : wire material resistivity with the temperature coefficient α 0 σ 0 (T): resistivity at the temperature 303 K σ(t): resistivity at the temperature T K

35 Group 830a 5.1 Magnetorquers design Maximum torque to detumble the satellite The maximum torque to detumble the satellite is found as: where: N det = I a o t o = 24.7 nnm N det : is the maximum torque required to detumble a o = 0.02 rad /orbit: maximum acceleration per orbit s I = kgm 2 : the moment of inertia (in the principle frame) t o = 5739 s: orbital period at the altitude of 550 km Total magnetic moment required To calculate the satellite magnetic torquing ability (magnetic moment) both torque to detumble the satellite and disturbance torque have to be taken into consideration and evaluated to have a maximum value. The total maximum torque due to the disturbances (section 6.5.5) is 36.2 nnm and the maximum torque to detumble the satellite is 24.7 nnm. Additionally a safety factor of 5 is used. Considering the moment of inertia and the torque to be scalars, the magnetic moment, that the magnetorquers are to be able to produce, can be calculated using the equation (6.37): where: m = 5 N s B = 5N det + N dist B = 0.01 Am 2 m: total magnetic moment required in Am 2. N dist : maximum torque produced by the disturbances (36.2 nnm)(6.5.5) N det : maximum torque needed to detumble(24.7 nnm) N s : minimum actuation torque that the coils have to be able to give in Nm. (N s = N dist +N det ) B: the smallest value for the magnetic field of the Earth, which is at the equator (B = nt) Design Each coil has to be able to generate the magnetic moment that can cancel the torque from the distubances and produce the one to turn the satellite. A preanalysis concerning the effect of choosing either aluminum or copper was done. It showed that aluminum is the most suitable material, minimizing the product of mass and power consumption. The reason for this is that, even though aluminum has a bad conductivity, its density is approx. three times smaller than the one for copper. These values are shown in table 5.1

36 24 Chapter 5 Actuators Attitude Control System for AAUSAT-II ρ [ kg ] m 3 σ [ Ωm] α 0 [ K 1 ] Al Cu Table 5.1: Parameters for aluminum and copper The necessary data needed is listed in the table 5.1 where: ρ: wire material density σ: wire material resistivity α 0 : temperature coefficient of resistivity Although a design with aluminum would be optimal it is not considered in the further discussion since either, manufacturers do not work with such material or the minimum diameter of wire provided is too large. It is designed under the assumption that the maximum voltage drop across the coil is 4.5 V and the number of windings is 500. All the calculations are made for the worst case, 70 C, considered the maximum temperature inside the satellite. Parameters of the coil, such as mass, maximum power usage and current flowing through the coil, can be calculated from the equations (5.1), (5.2) and (5.3). Maximum magnetic moment generated by each coil is: m = InA (5.4) Some of the possible sets of parameters using copper are represented in the table below. where, d: diameter of wire n: number of turns M: total mass of one coil I: current in coil R: electric resistance of one coil at 70 C V : voltage applied to produce the maximum magnetic dipole P : power consumption m: maximum magnetic dipole The wire of diameter 0.1 mm is chosen for the coil. The space required fits in the structure, power consumption and mass are within the budget and the magnetic dipole is almost twice of the value required. These reasons make this wire suitable for the magnetorquer requirements.

37 Group 830a 5.1 Magnetorquers design 25 d[ mm] n M[ g] I [ ma] R[ Ω] V[ V] P[ mw] m [ Am 2 ] Table 5.2: Design of coils Temperature[ C] R [Ω] I [ma] P [mw] m [A m 2 ] T max = T normal = T min = Table 5.3: Electrical properties of the coil