Detumbling and Aerostable Control for Cubesats

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MASTER'S THESIS

Detumbling and Aerostable Control for Cubesats

Zhou Hao 2013

Master of Science (120 credits) Space Engineering - Space Master

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

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CRANFIELD UNIVERSITY

ZHOU HAO

DETUMBLING AND AEROSTABLE CONTROL FOR CUBESATS

SCHOOL OF ENGINEERING

MSc THESIS

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CRANFIELD UNIVERSITY

SCHOOL OF ENGINEERING

MSc THESIS

Academic Year 2012-13

Zhou Hao

Detumbling and aerostable control for CubeSats

Supervisor: Dr. Peter Roberts

May 2013

This thesis is submitted in partial fulfillment of the requirements for the degree of Master of Science

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i

Abstract

This master thesis describes the design of a detumbling and aerostable control system for CubeSats and the designed control system is validated by operating the simulation in Matlab.

A CubeSat named ∆Dsat has been designed to implement aerofoils and it operates in Low Earth Orbit, thus the attitude of the CubeSat can be controlled by using aerostability. In addition, ∆Dsat also needs a detumbling control system to stabilized it after deployment. Thus ∆Dsat is used to demonstrate the detumbling and aerostable control system which is able to be implemented in other CubeSats.

Firstly, a detumbling and an aerostable control system concepts for CubeSats are presented respectively, consequently each of the control scheme is explained. Then the hardware selection for the control system is carried out. Furthermore, a 6- DOF control simulation is implemented to assess and validate the control system design in Matlab environment. In addition, the simulation result was illustrated and investigated.

The results of the simulation indicate that both the detumbling and aerostable control system meet the design requirement from preliminary design review. In addition, the detumbling time has a large margin. The detailed analysis on the result of aerostable control is also carried out. Finally, the future work required to finalize the development of aerostable and detumbling control system is outlined.

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Acknowledgements

I would like to express my gratitude to my supervisor Dr. Peter Roberts for the useful comments, remarks and engagement through the learning process of this master thesis.

Furthermore I would like to thank Mr. Josep Virgili for introducing me to the topic as well for the best support without any reservation on the way.

Also, being a student of SpaceMaster - the joint Erasmus Mundus programme. I would like to thank Dr. Victoria Barabash, Dr. Jenny Kingston and Dr. Johnny Ejemalm who are using their precious time to organize such a fantastic progamme.

I would like to thank my ∆Dsat teammates, my beloved family and friends, who have supported me throughout entire process, both by keeping me harmonious and helping me putting pieces together. I will be grateful forever for your love.

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CONTENTS v

List of Figures

1.1 ∆Dsat is in operation with aerofoil panels fully deployed at the minimum drag configuration . . . 3

2.1 The complete CAD model of ∆Dsat when it is fully deployed. It includes all the components board and science unit. This is the version used in PDR.[1] . . . 6 2.2 Schematic procedure to extract the differential measurements. [1] . . 8 2.3 Minimum drag configuration, each pair of panels can be rotated si-

multaneously to a certain incident angle to the flight direction . . . . 9 2.4 Co-rotate configuration of ∆Dsat [1] . . . 9 2.5 Counter-rotate configuration of ∆Dsat [1] . . . 9 2.6 Idea spring and damper dynamic system [2]. F is the external force

acts on the system, k is the spring coefficient, c is the damping coefficient, m is the mass of the block body, x is the the oscillating distance. . . 10 2.7 Passive magnetic attitude control system, the picture on left is per-

manet magnets and the picture on right shows the hysteresis rod [3] . 12 2.8 Active magnetic actuator (magnetorquer) used for AAU CubeSat [4] . 12 2.9 Under-actuation situation for a polar orbit satellite, some portion

of the orbit can not provide actuation on all degree of freedom, the controllability will be resumed over a period. [5] . . . 15

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LIST OF FIGURES ix

3.1 Scheme of Attitude determination and control system for ∆Dsat, the control system has three different mode: detumbling, attitude acqui-

sition and aerostable control. . . 16

3.2 Scheme of B-dot control for detumbling of ∆Dsat . . . 18

3.3 Scheme of aerostable control for ∆Dsat . . . 19

4.1 ADIS16260 Gyroscope board . . . 22

4.2 NanoMindAC712D OBC board from GOMspace, it has an on-board magnetometer HMC5843 from Honeywell. . . 23

4.3 ISIS Magnetorquer [6] . . . 23

5.1 Body reference frame of ∆Dsat, x, y and z are roll, pitch and yaw axis respectively. . . 25

5.2 Side and top view of ∆Dsat with launcher case [1] . . . 25

5.3 Side view of ∆Dsat [1] . . . 26

5.4 Bottom view of ∆Dsat [1] . . . 26

5.5 Simplified geometry of ∆Dsat, unit is in (m), it has a minimum drag configuration. . . 26

5.6 Detumbling time plot, the initial Euler angular rate was random, initial attitude was 0 latitude, 0 longitude and deploying orbit. Note: this is one typical solution from simulation . . . 29

5.7 Power consumption level for detumbling, the initial Euler angular rate was random, initial attitude was 0 latitude, 0 longitude and deploying orbit. Note: this is one typical solution from simulation which is the same as figure 5.6. . . 31

5.8 Torque from magnetorquer for detumbling, the initial Euler angular rate was random, initial attitude was 0 latitude, 0 longitude and deploying orbit. Note: this is one typical solution from simulation which is the same as figure 5.6. . . 32

5.9 Torque coefficient CtA_refI_ref produced by ∆Dsat under yaw with a minimum drag configuration. [7] . . . 37

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LIST OF FIGURES x

5.10 Simulation of aerodynamic coefficient for ∆Dsat with different altitude and aerofoil panel configuration. The simulation result of other aerofoil configurations are between the curve of 90^◦and 0^◦ degrees. . . 38 5.11 Simulation of natural frequency of marginal aerostable for ∆Dsat with

different altitude and aerofoil panel configuration . . . 40 5.12 Simulation of required damping coefficient for aeostable control of

∆Dsat with different altitude and aerofoil panel configuration . . . . 41 5.13 Demonstration plot shows the possible solution of scalar c to find the

minimum power consumption . . . 44 5.14 Demonstration plot shows there is no true solution for the minimum

power consumption . . . 45 5.15 Algorithm to determine actuation level for aerostable control. The

actuation level mainly depends on both of the torque required for damping angular rate and maximum actuation level which magnetorquer can provide . . . 46 5.16 Simulation algorithm of aerostable control . . . 48 5.17 Simulation result of aerostable control for 90^◦aerofoil’s panel-configuration

and 250km altitude. The Euler angle is relative to flow direction and the period of simulation covered two orbits. The top figure shows the mean attitude plot. The middle figure presents the standard deviation plot for each instance of Euler angle. The bottom figure illustrates the mean Euler angle with standard deviation as a bar, it gives a general view of the attitude changes during the simulation of aerostable control. This simulation shows the maximum aerodynamic force (most aerostable) case for ∆Dsat. . . 50 5.18 Simulation result of aerostable control for 0^◦aerofoil’s panel-configuration

and 250km altitude. The Euler angle is relative to flow direction and the period of simulation covered two orbits. The top figure shows the mean attitude plot. The middle figure presents the standard deviation plot for each instance of Euler angle. The bottom figure illustrates the mean Euler angle with standard deviation as a bar, it gives a general view of the attitude changes during the simulation of aerostable control. This simulation shows the minimum aerodynamic drag torque at an altitude of 250 km. . . 52

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LIST OF FIGURES xi

5.19 Simulation result of aerostable control for 0^◦aerofoil’s panel-configuration and 350 km altitude. The Euler angle is relative to flow direction and the period of simulation covered two orbits. The top figure shows the mean attitude plot. The middle figure presents the standard deviation plot for each instance of Euler angle. The bottom figure illustrates the mean Euler angle with standard deviation as a bar, it gives a general view of the attitude changes during the simulation of aerostable control. This simulation shows the least aerostable case. . 54

B.1 Simulation result of aerostability control for 45^◦aerofoil’s panel-configuration and 300 km altitude. The Euler angle is relative to flow direction and

the period of simulation covered two orbits. . . 65 B.2 Simulation result of aerostability control for 90^◦aerofoil’s panel-configuration

and 250 km altitude. The Euler angle is relative to flow direction and the period of simulation covered two orbits. . . 66 B.3 Simulation result of aerostability control for 90^◦aerofoil’s panel-configuration

and 300 km altitude. The Euler angle is relative to flow direction and the period of simulation covered two orbits. . . 67

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LIST OF TABLES xii

List of Tables

2.1 List of CubeSat which use active and passive magnetic control as the

primary attitude control system. . . 11

2.2 Passive magnetic control vs. active magnetic control. The pointing accuracy for active magnetic control was taken from AAUSAT[4] and COMPASS[5]. Passive control pointing accuracy was taken from CANX-1[8] and Delft-C3[9]. The power consumption was taken from Cute-1.7[10] and COMPASS-1[5]. . . 12

4.1 Gyroscope candidates for ∆Dsat control system . . . 21

5.1 Initial State of ∆Dsat and environment information for Detumbling Simulation (Standard value from [1],[11]) . . . 28

5.2 Hardware Properties and Uncertainties Used in Simulation . . . 28

5.3 Simulation Result for Detumbling . . . 34

5.4 Statistics results of changing resolution of magnetometer . . . 34

5.5 Initial State of ∆Dsat and environment information for Aerostability Control Simulation (Standard value from [1],[11]) . . . 47

5.6 Hardware properties and uncertainties used in aerostable control . . 47

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Abbreviations xiii

Abbreviations

2U 2-Unit CubeSat Size

ADCS Attitude Determination and Control System CAD Computer-aided design

CSRC Cranfield Space Research Centre FEA Finite Element Analysis

GPS Global Positioning System

IGRF International Geomagnetic Reference Field INMS Ion and Neutral Mass Spectrometer

LEO Low Earth Orbit

LVLH Local Vertical Local Horizontal MSSL Mullard Space Science Laboratory OBC On Board Computer

PCB Printed Circuit Board PDR Preliminary Design Review PID Proportional-Integral-Derivative PWM Pulse Width Modulation

VLEO Very Low Earth Orbit UK United Kingdom

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Introduction 1

Chapter 1 Introduction

This master thesis aims to design and develop an attitude control system, particularly in aerostable control system to be implemented to QB50 - ∆Dsat (pronounce Delta D) which is a double-size (2U) CubeSat developed at Cranfield University Space Research Centre (CSRC). It had been planned to be launched in 2015. The team of ∆Dsat consists of 6 MSc students, 1 premaster student and 1 PhD student supervised by Dr. Peter Roberts. Each member was in charge of one subsystem design. Recently, ∆Dsat team had passed the Preliminary Design Review (PDR) by the UK Space Agency.

The Cranfield Space Research Centre (CSRC) participated in the QB50 mission which is planning to launch 50 2U or 3U CubeSat that developed and built by 15 international institutes and space industries led by Von Karman Institute in Belgium, into Low Earth Orbit (LEO) to study the lower thermosphere property by hosting a same Ion and Neutral Mass Spectrometer (INMS) developed by Mullard Space Science Laboratory (MSSL), UK.

The primary objective of QB50 mission is to use the network of 40 2U CubeSat which carries INMS to make multi-point, in-situ measurements of the lower thermosphere.

It will be complementary to the observations from remote-sensing earth observation satellites, ground lidars and radars; thus to increase the accuracy and reliability of all current lower atmospheric models.

Furthermore, there is free space available in the functional unit for every 2U Cube- Sat (each CubeSat of QB50 has science unit and functional unit) which allows all participants to design and carry their own experimental devices.

The CSRC has been interested in Very Low Earth Orbit (VLEO) space mission and

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Introduction 2

drag sail for orbiting control for many years. The CSRC developed Icarus drag sail for TechDemoSat-1 (TDS-1) and is producing another drag sail for the ESA ESEO mission.

Therefore, The CSRC wanted to achieve a better understanding of the rarefied- gas aerodynamic property, particularly in aerodynamic drag force. Being able to understand the principles of rarefied-gas aerodynamic force and then accurately predict the aerodynamic force can have enormous benefits to a variety of space applications. For example, accurate prediction of rarefied-gas aerodynamic drag for LEO earth observation mission such as ESA’s GOCE mission can estimate the fuel margin required to compensate the aerodynamic drag. Furthermore, understanding of how the rarefied-gas aerodynamic drag is created can help to refine the design of LEO spacecraft to minimize the drag ; thus it helps to reduce the fuel consumption and increase the life of mission. In addition, knowing the drag coefficient of each material can help to design a drag sail has the maximum drag coefficient per unit surface area in order to reduce the size of drag sail. The accurate drag model can also helps to simulate de-orbit phase of satellite mission and space debris modeling.

However, there is no enough experimental data of rarefied-gas available to perform a accurate simulation to evaluate the drag profile for each spacecraft. Furthermore, it is a challenging to undertake an experiment to assess the rarefied-gas drag on the ground because the flow velocity is much higher than on the LEO and the principles to produce drag are different.

Therefore, The CSRC has been developing a QB50 CubeSat named as ∆Dsat which carries a payload and two pairs of aerofoil panels to study how the flow incidence angle, the surface material and surface roughness affects rarefied-gas aerodynamic drag force. The aerofoil panels are made by different material which commonly used for space missions and the aerofoil panels can be rotated to various incident angles to the flow direction.

Figure 1.1 illustrates ∆Dsat in an operation with aerofoil panel parallel to the flow direction. In this case, the CubeSat experiences minimum aerodynamic drag force.

By rotating the panels to expose a certain surface material at an incident angle to the flow direction, the drag force can be extracted after one orbit by use of GPS and orbit determination. And then the extracted drag force can be used along with the measurement of flow density from INMS payload to calculate the drag coefficient.

Each extracted drag coefficient will be compared differentially (e.g. ^C_C^d1_d2) to minimize the bias and error from measurements. This is the reason that the 2U QB50 satellite developed at the CRSC named as ∆Dsat (∆ is for differential, and D is for drag)[1].

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Introduction 3

Figure 1.1: ∆Dsat is in operation with aerofoil panels fully deployed at the minimum drag configuration

In order to make the measurement more accurate, the CubeSat has to be travel exactly along to the incident flow direction. The deployed aerofoil panels can provide restoring torque to make the CubeSat marginally stable to the flow direction with oscillations, a control system is required to damp this oscillation. This is one of the most important scientific demonstrations of ∆Dsat mission.

A more detailed discussion about science objectives of ∆Dsat mission is covered in Chapter 2.

This control method is called aerostable control. The objective of this Master thesis is to achieve a conceptual design of aerostable control system for ∆Dsat. The control algorithm design, hardware selection and the comprehensive simulation to evaluate the aerostable control are covered in this project.

In addition, the B-dot detumbling control design and simulation are also included for the first control phase after deployment of the CubeSat.

The outcomes of this Master thesis will directly contribute to the whole ∆Dsat project, particularly in control system design and programming. Furthermore, the product of aerostable control system can be potentially implemented as a primary control system for LEO spacecraft to reduce the system complexity and mission cost.

Chapter 3 presented the conceptual design of ∆Dsat control system. It firstly introduced the design of B-dot control for detumbling and then discussed about aerostable

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Introduction 4

control algorithm.

Based on the control system design, Chapter 4 explained the procedure for selecting hardware for the attitude control system.

In the chapter 5, the simulation procedure and result analysis were carried out to validate the control system design.

Finally in the last chapter, the conclusion to this thesis was made and the possible future work was discussed.

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Literature Review 5

Chapter 2 Literature Review

2.1 Current Progress of QB50 - ∆Dsat Project

QB50 project is an leading intentional project that aims to launch 50 cubesat into lower earth orbit to study rarefied atmosphere region. On the latest official doc- ument of QB50 mission, it is scheduled to be launched in 2015 from Brazil. The launch altitude is 350 − 380km, the inclination angle is 98^◦, The design and development of each cubesat have been carried out among 15 universities and institutes around the world but mainly are from European countries. Apart from carrying the same Ion and Neutral Mass Spectrometer (INMS) provided by QB50 consortium, each participant is encouraged to design its own payload to demonstrate individual scientific objectives.[1]

The Cranfield Space Research Centre agreed to design a CubeSat named ∆Dsat for QB50 project, which aims to study how the aerodynamic drag force is affected by surface material and flow incident angle for spacecraft which operates in Low Earth Orbit (LEO), by using two pairs of aerofoil made by different material. Each pair of aerofoil can be rotated to aline the edge of aerofoil to a certain incident angle to the orbiting direction.

The preliminary design report had been approved by UK space agency by the date of submission of this report. It covered initial conceptual design and the simulation result to check compliancy for each subsystem.

The work had been done for ∆Dsat includes:

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Literature Review 6

Spacecraft System Configuration

Initial Aerofoil and Deployment System Design

Initial Attitude Determination and Control System (ADCS) Design and Simulation Electric Power Subsystem (EPS) Design

Structure Design

Initial Thermal Control Design Budgets Analysis

Hardware Selection

Figure 2.1 shows the Computer-aided Design (CAD) model of ∆Dsat system configuration. It presents a basic scope of the present design of ∆Dsat.

The cylinder on top is the INMS science device. The Printed Circuit Board (PCB) in the middle with two sun sensors is the CubeSense board which is used for attitude determination. And the PCB below is the interstate board with gyroscope and data interfaces following by the On Board Computer (OBC) and then ISIS Magnetorquer Board as the only actuator for attitude control. The bottom part includes step motors to control the aerofoil deflection and thermocutter to deploy the antenna and the aerofoil panels after deployment.

Figure 2.1: The complete CAD model of ∆Dsat when it is fully deployed. It includes all the components board and science unit. This is the version used in PDR.[1]

For the ADCS of ∆Dat, it was split up into two sections: Attitude Determination and Attitude Control. This thesis only covers the progress on attitude control system design.

However, since the ADCS normally works as an whole system e.g. attitude control

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Literature Review 7

system requires the attitude information from the attitude determination system, the ADCS hardware selection and system configuration were actually done within the ∆Dsat team.

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Literature Review 8

2.1.1 Methodology to Extract Rarefied-gas Aerodynamic Coefficient Before starting the design of attitude control system for ∆Dsat, particularly in aerostable control, it is crucial to understand the reason that ∆Dsat requires a aerostable control system and it is essential for accurately measuring the differential drag coefficient.

The primary scientific objective of ∆Dsat mission is to determine how the following factors affect aerodynamic drag coefficient of a satellite operating in LEO.

1. Flow incidence angle to spacecraft

2. Surface roughness and cleanliness on gas–surface interactions on spacecraft in low Earth orbits

3. Surface material property (e.g. molecular composition, reflectiveness, lattice configuration and particle level flow coherence ratio )

The drag coefficient extracted for each material or incident angle will be compared in differential form (i.e. measured drag coefficient Cd1 and Cd2, compare ^C_C^d1_d2). This is because each measurement will contain significant bias from the sources of current atmosphere model, disturbance on control system or the INMS science device.

The detailed algorithm to extra the differential drag coefficient had been developed by the CSRC[7]. Figure 2.2 presents the schematic procedure to extract the differential measurement. However, a detailed discussion about this post data processing is beyond the scope of this thesis.

Figure 2.2: Schematic procedure to extract the differential measurements. [1]

In order to make measurement on various material and different incident angles,

∆Dsat is designed to use two pairs of panels which are mounted separately on each

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Literature Review 9

surfaces of the 2U cube structure (Shown in figure 2.3). The two panels, which are on the opposite surfaces, are linked along the central axis of the panel and thus can be rotated simultaneously. In addition, the aerofoil panels are made by nominated materials which are commonly used in spacecraft.

Figure 2.3: Minimum drag configuration, each pair of panels can be rotated simultaneously to a certain incident angle to the flight direction

There are two options to rotate the two pairs of panels: co-rotate or counter-rotate.

co-rotate shown in figure 2.4 is to rotate both panels to the same direction. It will generate lift force to let the CubeSat fly at an angle to the flow direction. The counter-rotate of panels shown in figure 2.5 is to rotate each panel to the opposite direction, it can help the CubeSat to fly along with the flow direction but the generated torque will also roll the CubeSat.

Figure 2.4: Co-rotate configuration of

∆Dsat [1] Figure 2.5: Counter-rotate configuration of

∆Dsat [1]

Flying ∆Dsat by using of co-rotate is not idea for measuring the drag coefficient.

Because, firstly, the incident flow density measured by INMS in this case is not the same as the one on the flow direction. Furthermore, the relationship between rarefied drag coefficient respects to flow incident angle is still unknown.

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Literature Review 10

Therefore, it had been decided to use counter-rotate method to operate the panels on ∆Dsat. However, in order to cancel the undesired roll induced by counter-rotate panels, a control torque is required. This should be considered in the attitude control system design.

2.1.2 Accurate Measurement of Drag Coefficient and Aerostability Con- trol

If migrating the concept of Euler angle for aircraft to CubeSat, the aerodynamic drag coefficient is a function of pitch, yaw and roll angle. Therefore, estimation of aerodynamic drag coefficient would be considerably effected by the current attitude of spacecraft related to flow direction.

However, to measure the pitch roll and yaw angles relative to flow direction is rather difficult because the CubeSat operates in a environment which experiences co-rotation of atmosphere and rarefied wind that will deflect the satellite from orbital velocity direction to the incident flow direction.

Fortunately, the aerofoil mounted on ∆Dsat can provide a restoring torque that forces the CubeSat to fly towards the incident flow direction. However, the dynam- ics of satellite would behave elastically to this torque. Therefore, ∆Dsat is only marginally stable to the flow direction. (i.e. oscillating around the flow direction)

Figure 2.6: Idea spring and damper dynamic system [2]. F is the external force acts on the system, kis the spring coefficient, c is the damping coefficient, m is the mass of the block body, x is the the oscillating distance.

Figure 2.6 shows an idea spring and damper system that is a analogy to explain aerostable control of ∆Dsat. The aerodynamic force that the CubeSat experiences can be considered as the restoring torque provided from the spring. It is only statical equilibrium but not dynamic equilibrium, therefore, a damping torque required to stabilize the CubeSat.

A novel control system therefore is required to provide the damping torque. Be- cause this control system is required to work with the aerodynamic force, it is called

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Literature Review 11 Active Magnetic Control Passive Magnetic Control

CANX-1 [8] UNISAT-4

COMPASS-1 [5] Delfi - C3 [9]

AAUSAT [4] CanX-6

Cute-1.7+APDII [10] MUNIN

Table 2.1: List of CubeSat which use active and passive magnetic control as the primary attitude control system.

aerostable control. Successful demonstrating aerostable control is one of the major technology objectives of ∆Dsat mission. The complete control algorithm with hardware can be potentially implemented in other future LEO space missions.

The simulation that assess the accuracy of measurement on drag coefficient had been done by Space Research Centre at Cranfield University recently. The result of simulation indicated that, by using the above algorithm, the accuracy of measurement on drag coefficient was in a range between 2.5% and 5%[7].

A detailed explanation of aerostability is covered in section 5.3.1.

2.2 Magnetic Attitude Control

Magnetic attitude control is preferable for small size satellites, especially for low cost cubesat. The main reasons to make it so popular are that magnetic control method is inexpensive, moderate reliable, relative simple installation and implementation of hardware and low consumption of energy. [12]

There are two major methods to use electromagnetic field to control spacecraft:

active control and passive control. Both of them have been theoretically studied and fully applied to CubeSat.

Table 2.1 lists the CubeSat that use these two control methods. The satellites which use active magnetic control have a similar size and control requirement to the 2U CubeSat from QB50. [1]

The most significant difference between these two methods is that passive magnetic control, shown in figure 2.7, uses a combination of permanent magnets to track magnetic field line and Hysteresis rod to damp the oscillation. While active control, shown in figure 2.8 adjusts the current level (actuation level) in magnetorquer (conductor coil) to change the output torque on different axis.

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Figure 2.7: Passive magnetic attitude control system, the picture on left is permanet magnets and the picture on right shows the hysteresis rod [3]

Figure 2.8: Active magnetic actuator (magnetorquer) used for AAU CubeSat [4]

A general comparison of active and passive magnetic control is given in the table 2.2.

The largest benefit to use passive magnetic control is because it requires no power to drive it and it can actuate continuously. However, it has unsatisfied pointing accuracy and furthermore, the design of passive magnetic control system is very sophisticated, because it demands careful calibration and mathematical modeling.

In contrast, active magnetic control consumes moderate power to drive it. And it has to wait for computing the required driving torque. But it has decent pointing accuracy and less complexity to be implemented.

Active Magnetic Control Passive Magnetic Control

Power Consumption 1 to 3 W NO

General Pointing Accuracy (β) β< 8^◦ 10^◦< β < 20 Actuation Continuity Have to wait for the

reading of magnetic field strength

Continuous actuation

Difficulties in Design Control system programming and

magnetic field measurement accuracy

Mathematics modeling and testing

Table 2.2: Passive magnetic control vs. active magnetic control. The pointing accuracy for active magnetic control was taken from AAUSAT[4] and COMPASS[5]. Passive control pointing accuracy was taken from CANX-1[8] and Delft-C3[9]. The power consumption was taken from Cute-1.7[10]

and COMPASS-1[5].

Therefore, active control is more preferable for QB50 - ∆Dsat mission, because the control system of QB50 satellites were required to achieve a relative high pointing accuracy of ±10^◦ and pointing knowledge of ±2^◦(QB50-SYS-1.2.2) [1]. In addition, the hardware for active magnetic control (magnetorquer board with Pulse Width Modulation (PWM) driver) can be directly purchased and implemented to ∆Dsat without consuming more time on mathematical modeling for design the passive magnetic control.

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2.2.1 Active Magnetic Control

The only actuator that was considered to be used for ∆Dsat is magnetic control system. Because the use of magnetic control system consume no power or less power than other traditional actuation system such as actuation wheel and no momentum dumping required. The installation and programming for magnetic control are also relative simple. In addition, there had been many CubeSats used magnetic control system as their primary control system in the past ten years.

The first discussion on the principles of active magnetic control is from the article [13]. It introduced the 3-axis magnetic control system by the use of a bias momentum method. And the first pure active magnetic control system used in space is designed for OERSTED which achieved a pointing accuracy about 10^◦(roll and pitch) to 20^◦ (yaw). [14]

The principal of active magnetic control is rather simple and given in equation 2.1.

τ = m × B (2.1)

The control torque provided from magnetorquer equals to the cross product of actuation level and local magnetic field strength. The actuation level is the character of magnetorquer on each axis, it can be in a form of squared metal coil or a cylinder wrapped with conductor wire. By adjusting the feeding current in the conductor, the actuation vector (generated electromagnetic field vector) changes to provide a required torque in a known strength of magnetic field.

The magnetic field strength vector can be either gained from known model or direct measurement. Although the direct measurement from magnetometer would have disturbance from other on-board devices, for ∆Dsat mission, it is preferred to use this measurement to calculate the required toque rather than using magnetic mode. This is because, in detumbling mode, devices for attitude determinations (e.g. GPS) are turned off, thus no attitude information can be fed into magnetic field mode. Furthermore, detumbling control was designed to saturate the magnetorquer as quick as possible, the dominating factor is control coefficient rather than the change of magnetic field strength. Therefore, the disturbance to magnetometer have insignificant effect to the detumbling control (detumbling control is discussed in section 3.1).

Because of the natural of earth magnetic field, active magnetic control suffers from the following problems:

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1. Under-actuation: if the direction of actuation vector is parallel to the magnetic field line vector, they they system is not able to generate any torque on that direction.

2. Uncertainty in magnetic field model (IGRF) : the magnetic field model is not accurate enough and the actual earth magnetic field changes with time and is effected by solar storm. The attitude information from other sensors induces further error to the estimation of magnetic field.

3. Uncertainty in magnetometer: the noise, bias and resolution of magnetometer will contaminate the reading of magnetic field strength and also the communi- cation device on-board will significantly increase the reading.

Figure 2.9 illustrates the period of under-actuation for a polar orbit (∆Dsat has an inclination of 98^◦). It shows in the polar region, satellite has no access to the yaw control. This is because the magnetic field line is parallel to the yaw axis thus it can not generate any torque along this axis to control yaw motion ( Because the nature of product rule shown in equation 2.1). Similarly, when the satellite travels to the equatorial region which the orbit is parallel to the longitude line, the active magnetic roll control is not achievable.

However, the above example just demonstrates the simplified and idea case of under- actuation. In real case, under-actuation can happen in any part of the orbit where the CubeSat Local Vertical Local Horizontal (LVLH) frame (the reference frame which magnetorquer uses) coincidentally align with earth magnetic field line. If this happened, the CubeSat has to wait for few minutes to restore the active magnetic attitude control.

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Figure 2.9: Under-actuation situation for a polar orbit satellite, some portion of the orbit can not provide actuation on all degree of freedom, the controllability will be resumed over a period. [5]

Therefore, for using active magnetic control as the primary control system for Cube- Sat, the control algorithm to use active control has to be carefully designed and tested. Furthermore, the sensors has to be calibrated before use. In addition, the time of actuation has to consider the period of under-actuation.

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Initial Design of ∆Dsat Control System 16

Chapter 3 Initial Design of ∆Dsat Control System

Figure 3.1 presents the scheme of Attitude Determination and Control System (ADCS) designed for ∆Dsat.

Figure 3.1: Scheme of Attitude determination and control system for ∆Dsat, the control system has three different mode: detumbling, attitude acquisition and aerostable control.

There are three independent control modes for ∆Dsat:

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1. Detumbling Mode: Detumbling mode will be initiated after the ∆Dsat deployed from the launcher and the aerofoil panels and antenna fully deployed. The control method for detumbling is B-dot method. The sensor used for this mode is magnetometer and the actuator is magnetorquer. The B-dot method can only stabilize the CubeSat in magnetic field reference frame. And the threshold to stop detumbling mode and move to the next control mode is the norm of the angular rate equals to 0.1 degree/sec. (explanation is covered in section 5.2.2.1 ) In order to further stabilize the CubeSat in inertia reference frame, attitude acquisition mode is required.

2. Attitude Acquisition Mode (had not been developed yet): Attitude acquisition mode will stabilize the CubeSat in inertia frame, and then drive the CubeSat point to the flow direction (INMS unit to flow direction). Furthermore, this mode should roll the solar panels to face to the sun. Then the control mode can move to aerostable control. This control mode can be achieved by implementing a PID controller.

3. Aerostability Control Mode: This mode is to use aerostability and damping torque to aline the CubeSat along with flow direction. The idea control torque is to provide critical damping torque. And a magnetic roll control mode is required to stop the CubeSat spinning along the flow direction and let the solar panel face to the sun by using a PID controller. The sensor used for this mode is gyroscope to monitor the angular rate. The actuator is magnetorquer.

There are two sensors supposed to be used for attitude control of ∆Dsat.:

• A group of three gyroscopes are required to provide information of angular rate on the CubeSat body axis.

• There is one magnetometer on NanoMind (Selected OBC for ∆Dsat) board, it will continuously measure the local magnetic field and then the change of magnetic field strength can be estimated by applying certain filter.

3.1 B-dot method for detumbling

The basic concept of B-dot control is to continue measuring the change of earth magnetic field which mainly due to change of attitude, therefore, minimize the change of magnetic field to zero by the use of magnetorquer can stabilize the CubeSat.

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Since the change of magnetic field can not be directly measured, in addition, the measurement from magnetometer includes noise and bias, choosing a proper algorithm to determine the change of magnetic field from the measurement from magnetometer is very crucial.

Nevertheless, this thesis does not discuss about the filter and controller design of B-dot method. It only concentrates on validation and proof of the use of B-dot method in ∆Dsat can meet the requirements of detumbling.

Figure 3.2: Scheme of B-dot control for detumbling of ∆Dsat

The control scheme of B-dot method is shown in figure 3.2. In the actual control system, ˙B is determined from various methods of estimation. (e.g continuous time estimation, discrete time estimation etc.) Periodic measurement from magnetometer and actuation can be challenging for the future B-dot controller programming.

However, in the simulation procedure, the following equations were used:

B ≈ B × ˙θ˙ (3.1)

m = −c ˙B (c is a scalar) (3.2)

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For simulation, the change of magnetic field is calculated from cross-product of local magnetic field and ˙θ (Euler angular rate matrix), shown in equation 3.1.

The actuation level m in equation 3.2 is the actuation level matrix. c is the control coefficient. Theoretically, c has to be set large enough to saturate the magnetorquer as soon as possible to shorten the damping time.

3.2 Aerostability Control System

The concept of aerostable control for ∆Dsat was discussed in section 2.1.1. It can be described as an control system to damp the oscillation along the flow direction and stop the spinning effect from the counter-rotation panels.

Figure 3.3: Scheme of aerostable control for ∆Dsat

Figure 3.3 shows the scheme of aerostable control. The objective of aerostable control is to provide a control torque to stabilize the CubeSat in inertia frame (i.e. the angular rates on three axis should zero). Therefore, a gyroscope is used for measuring the angular rates on the CubeSat body reference frame. The required control torque to achieve critical damping is a function of local aerodynamic coefficient and angular rate. And the aerodynamic coefficient stored in the OBC database is a function of attitude and the panels configuration, therefore, OBC demands these two

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information from attitude determination and the data which stores the current state of panels configuration. Once the required critical damping torque is known, the actuation level to drive the magnetorquer can be calculated. (Detailed mathematical steps for aerostable control is covered in section 5.3.1)

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Hardware Selection for Attitude Control System 21

Chapter 4 Hardware Selection for Attitude Control System

Since ∆Dsat is the first CubeSat developed in the CSRC and the time constraint for developing the system before the launch date, it was decided to directly use the off-the-shelf components for the attitude control system of ∆Dsat.

There are two driving factors to select hardware for the attitude control system:

flight heritage and cost.

The characteristics of selected components (e.g. actuation level of magnetorquer) were used for attitude control system simulation in Chapter 5.

4.0.1 Gyroscope

The gyroscope candidates are listed in table 4.1. They were selected from the recommendation provided by QB50 consortium and other organizations.

Flight

Heritage Resolution Sensitivity Scale Range Size Price

ADIS16260 Yes 8/12 bits 0.01832 -

0.07326 °/sec per LSBs

±80/160/320

dps 11.2X11.2X5.5

mm $42.48

ITG-3200 Ingerated Board

Yes 16 bits 8.75/17.50/70 LSBs per

°/sec

±250/500/2000

dps Depends on

package size (Diameter

330 mm)

$49.95

L3G4200D Integrated

Board

No 16 bits 14.375 LSBs

per °/sec ± 2000 dps 4X4X1.1

mm $49.95

Table 4.1: Gyroscope candidates for ∆Dsat control system

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Figure 4.1: ADIS16260 Gyroscope board

The gyroscope will be used in ∆Dsat mission is ADIS16260 made by ANALOG DEVICES. This is because:

• ADIS16260 has flight heritages.

• ADIS16260 offers the highest sensitivity it can measure very low angular rate which can potentially help to maintain the CubeSat in a more stable state and also can help to calculate more accurate aerodynamic torque.

• Although the price difference is small, ADIS16260 is relative less expensive.

• Compare to ITG-3200, ADIS16260 is much smaller in size

• ADIS16260 board has temperature sensor to automatically filter the thermal noise

4.0.2 Magnetometer

NanoMindAC712D board from GOMspace was selected as the main OBC for ∆Dsat mission. It is manufactured with an on-board magnetometer which model is HMC5843 made by Honeywell. It has flight heritage in the Vega launch vehicle maiden flights and others. Therefore, no additional magnetometer needs be purchased for this mission. HMC5843 magnetometer has a resolution of 10 milli-gauss.

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Figure 4.2: NanoMindAC712D OBC board from GOMspace, it has an on-board magnetometer HMC5843 from Honeywell.

4.0.3 Magnetorquer

The recommended magnetorquer by QB50 workshop was ISIS Magnetorquer board shown in figure 4.3. It is manufactured by ISIS (Innovative Solutions In Space).

Figure 4.3: ISIS Magnetorquer [6]

It was deigned for Very Low Earth Orbit (VLEO) CubeSat missions, up to 12U.

This board includes two torque rods and one air core torquer (air core consume more power but has smaller size). The actuation level for each actuator is 0.2 Am². According to the data of previous CubeSats which used active magnetic attitude control, the actuation level of ISIS Magnetorquer is large enough to handle the detumbling control (CANX-1 is 3 × 0.106 Am², Cute-1.7 is 3 × 0.037Am²)[8][10].

Furthermore, in total, the maximum actuation power is only 0.9 W.

Therefore, the ISIS Magnetorquer Board was selected for ∆Dsat mission.

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Simulation and Validation of Attitude Control System for ∆Dsat 24

Chapter 5 Simulation and Validation of

Attitude Control System for ∆Dsat

After the attitude control system for ∆Dsat had been designed, the simulation was carried out to validate the control method. All simulation method introduced in the chapter is based on the 6-Dof simulator for LEO CubeSat, which was originally developed by the CSRC. [7] The scripts were programmed to simulate the ∆Dsat attitude control system which interacted with the 6-Dof simulator.

The simulation environment is Matlab with a variety of models (Compatible to version 2011, 2012 or 2013).

The list of m-file used for the simulation are included in the appendix A. The copy of simulation file has been available with a free license on GitHub/fancydropbear or GitHub/JosepVirgili/AstroLab (Last check was 06/2013)

5.1 Moment of Inertia of ∆Dsat

Knowing the moment of inertia of ∆Dsat is fundamental to simulation of dynamic system. Before calculating the moment of inertia tensor in the CubeSat body reference frame, there are following assumptions were made:

• ∆Dsat is complete rigid body, all deployed panels are assumed to be in-deflectable and inflexible (this model will be improved before Critical Design Review (CDR))

• The principal axes are perfectly match the ∆Dsat body frame which is shown

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in figure 5.1

Therefore, the moment of inertia tensor of ∆Dsat was given in a form of







I_xx 0 0 0 I_yy 0 0 0 Izz





 for the early stage of simulation.

Figure 5.1: Body reference frame of ∆Dsat, x, y and z are roll, pitch and yaw axis respectively.

However, an more accurate and realistic moment of inertia tensor from Finite Ele- ment Analysis (FEA) model is not applicable because that the CAD model with all material information was not available by the date of submission this report.

Figure 5.2: Side and top view of ∆Dsat with launcher case [1]

The procedure to estimate moment of inertia tensor for ∆Dsat started from con- sidering the CubeSat with fully deployed panels as a prefect double size cube with four identical panels. The aerofoil would rotate during the whole mission thus the moment of inertia varies. Since the mass of the aerofoil was smaller than the main cube structure and dynamic center of the aerofoil were locates considerably far from the main satellite, for a simple approach, the inertia of moment was taken as a fixed value that the edge of aerofoil points to front of ∆Dsat and two pairs of panels

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Figure 5.3: Side view of ∆Dsat [1] Figure 5.4: Bottom view of ∆Dsat [1]

are oriented vertically to each other. (Figure 5.25.3 and 5.4 shows the geometry of

∆Dsat)

Figure 5.5: Simplified geometry of ∆Dsat, unit is in (m), it has a minimum drag configuration.

Therefore, ∆Dsat geometry was then simplified as shown in figure 5.5. The mass of the main cube structure and each panel was 2.044kg and 0.084kg respectively.[1]

By using the list of moment of inertia for simple geometry [15]and applying moment of inertia parallel rule[16], the shift from center gravity of aerofoil to the ∆Dsat inertial axis was given by equation 5.1.

r_xx = (h_{aerof oil}+ w_body) 2

r_yy = (h_body − w_{aerof oil}) 2

r_zz = r_yy (5.1)

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Therefore, the moment of inertia matrix was calculated by using equation 5.2, where I_zz = I_yy because yaw and pitch motion were symmetric for ∆Dsat.

Ixx = m_body

12 (d²_body+ w_body² ) + 4 × maerof oil(h²_{aerof oil}+ d²_{aerof oil}

12 + r²_xx) I_yy = m_body

12 (h²_body+ d²_body) + 2 × m_{aerof oil}(h²_{aerof oil}+ w²_{aerof oil}

12 + r²_yy+ ...

...w²_{aerof oil}+ d²_{aerof oil}

12 + r²_xx)

I_zz = I_yy (5.2)

The estimated moment of inertia tenor (principal axes) of ∆Dsat was then gained, shown in equation 5.3.







0.0459 0 0

0 0.0328 0

0 0 0.0328





kg/m² (5.3)

5.2 Simulation of Detumbling by B-dot Method

5.2.1 Simulation Procedure for B-dot Control

Recall equation3.1, ˙B ≈ B × ˙θ. For simulation, The ˙Bwas directly calculated from the cross product of local magnetic field strength and angular rate. And then the actuation level tensor can be gained by using equation 3.2, m = −c ˙B (c is a scalar). The scalar c was set to be 2 × 10⁹ because it has to be large enough to saturate the magnetorquer as soon as possible. The next step was to use equation 2.1, τ = m×B to calculate the control torque. And then this torque was fed to the 6-Dof simulator to update the attitude of the CubeSat.

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Parameters (Unit) Value/Method Notes

Altitude (m) 380 × 10³ 350 − 380km

Initial Latitude and Longitude (Degree)

(0, 0) -

Inclination (Degree) 98 -

Initial Velocity (m/s) Calculated from altitude Assume circular orbit at deploy

altitude Initial Angular Rate

(Degree/sec) random number within ±10 -

Initial Atmosphere Co-rotation Velocity

(m/s)

Cross product of initial vector

state and earth angular velocity Initial wind velocity Initial Attitude

(Quaternion) (rx, ry, rz) random from 0 to 2π,

q0is calculated from (rx, ry, rz ) -

Simulation Period (s) 3000 50minutes

Table 5.1: Initial State of ∆Dsat and environment information for Detumbling Simulation (Stan- dard value from [1],[11])

Table 5.1 shows the initial state of the detumbling simulation. The initial angular rate was randomly generated from −10^◦ to +10^◦ (Requirement from QB50-SYS- 1.2.1). The initial attitude was also an arbitrary state from 0 to 2π. The launch altitude used is the maximum possible value because it has the least aerostability (the detumbling initiates after the aerofoil panels fully deployed).

Parameters (Unit) Value/Method Notes

Magnetometer - HMC5843

Resolution (Tesla) 0.7 × 10⁻⁶ -

- - -

Magnetorquer - ISIS Magnetorquer Board

Actuation level (Am²) 3 × 0.2 2 Coils, 1 Air Core

Actuation level bias (%) ±5 -

Resolution (bit) ±8 -

Table 5.2: Hardware Properties and Uncertainties Used in Simulation

Sensor and Actuator Resolution: For the output value of digital sensor or magnetic actuator, the value is stored as a binary format of certain number of bits(e.g 8bits,16bits). The actual value given can only be on a scale of the minimum represented value for a digital device. Therefore, the reading from magnetometer and the magnetorquer actuation level were rounded to the nearest possible value in the simulation. Equation 5.4 shows the formula to calculate resolution.

Resolution = M easurement Range

2N o.of bits (5.4)

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Figure 5.6: Detumbling time plot, the initial Euler angular rate was random, initial attitude was 0 latitude, 0 longitude and deploying orbit. Note: this is one typical solution from simulation

Actuation level bias: The actuation level of magnetorquer has a fluctuation. This bias was also programmed in the simulation. The output actuation level was either less or more than 20% of the required actuation level computed in equation 3.2.

5.2.2 Result Analysis and Validation

5.2.2.1 Analysis on detumbling plot

Figure 5.6 shows the detumbling time plot, the satellite was damping the yaw and pitch rates while it was rotating along roll axis (Nutation motion).

In order to determine the detumbling time, the rotation rate of the earth magnetic field frame relatives to the CubeSat LVLH frame, for the case when the CubeSat stabilized in the earth magnetic field frame, has to be calculated.

However, this rate is changing around the longitude line of earth. In polar region, the angular rate of change of magnetic field is relative high. In contrast, around the equator region, this rate is relative small.

Therefore, to give a coarse value of detumbling time for different scenarios from simulation, a averaged rate of change of earth magnetic field is used for determining when the detumbling is finished in earth magnetic field frame.

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In order to calculate this averaged rate, assuming the orbit is an circular orbit, the detumbling orbit is the maximum orbit which is 350 km which gives the orbital velocity of 0.0655 degree/sec from equation 5.5 (this equation and constants are from [11]).

v =r Gm_earth

h + r_earth (5.5)

The earth rotation angular velocity is we = 7.292115 × 10⁻⁵/s[11]. Therefore, sum this velocity with the orbital velocity gives a value about 0.066 degree/sec.

Therefore, in the detumbling simulation, a rounded value 0.1 degree/sec was used to determine when the detumbling mode was finished.

This is the reason that 0.1 degree/s here is used as a threshold which the CubeSat finishes detumbling and moves to the attitude acquisition control mode (Chapter 3). However, in the real control system design this threshold can be adjusted to a larger number.

Therefore, the duration for detumbling (in magnetic field frame) on this plot is 19 minutes. Furthermore, this figure also illustrates that, at relative high attitude period (more than 0.5 degrees), the plot was not affected by the system uncertainties5.2. In contrast, in the region with low attitude (less than 0.5 degrees), the uncertainties, especially the actuation level bias and resolution, induced fluctuation to the angular rates. However, this effect was minor and did not influence the tumbling time much.

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Figure 5.7: Power consumption level for detumbling, the initial Euler angular rate was random, initial attitude was 0 latitude, 0 longitude and deploying orbit. Note: this is one typical solution from simulation which is the same as figure 5.6.

Figure 5.7 presents the power consumption for detumbling, it was agree with the concept of B-dot detumbling method that the magnetorquer saturated to the maximum power as soon as the detumbling stage started. The x,y and z power in the plot represent power for damping the roll, yaw and pitch rates respectively. Since roll motion has the largest moment of inertia (5.3), it consumed the most power.

The peaks appear in the plot was because of the magnetorquer resolution. The bias on actuation level of magnetorquer rose the total power consumption from an average of 0.9 W to about 0.95 W. It agrees with the assumption of 5% bias listed in table 5.2.

5.2.2.2 Analysis on the magnetic control torque

However, when the detumbling mode is close to finish, the actuation coefficient c is not necessary to be changed to a small value because the control torque is approaching to zero (shown in figure 5.8) This is because the control torque is calculated from cross product of actuation level vector and magnetic field vector. When the Cube-

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Sat is about to finish detumbling, the magnetic control vector is approaching to the earth magnetic field vector, and thus the control torque dramatically decreases to a value close to zero (with some noise and offset from hardware).

Figure 5.8: Torque from magnetorquer for detumbling, the initial Euler angular rate was random, initial attitude was 0 latitude, 0 longitude and deploying orbit. Note: this is one typical solution from simulation which is the same as figure 5.6.

Therefore, the detumbling system is designed to use constant actuation coefficient c and it is set to zero as soon as the detumbling mode is determined to be finished. In the simulation, the indication which detumbling mode finishes is set to the angular rate is less than 0.1 degree/sec (discussed in the previous section). Nevertheless, for real system, since the change of the reading from magnetometer is mainly due to the change of angular rate in magnetic field frame. Therefore, when the change of the magnetic field strength (calculated from the reading from magnetometer) is about the few magnitudes of the resolution of magnetometer, the detumbling is considered to be completed.

5.2.2.3 Chi-Square Satisfied Interval for Statistics

According to the section 5.2.1, the simulation of ∆Dsat started tumbling with a set of random initial attitude and angular rates after deployment. Furthermore, how the uncertainties of hardware affect the detumbling time was unknown. Therefore, the statistics was required to analyze the standard distribution of the detumbling

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time.

The amount of simulations required to give a satisfied result for statistics was determined by Chi-Square satisfied interval.[17]

s√ N − 1 qx²_{1−α/2,N −1}

≤ σ ≤ s√ N − 1

qx²_{α/2,N −1} (5.6)

Firstly, the expected range of mean and standard deviation of detumbling were estimated from the result of a small scale statistics. After collecting the results of detumbling time from 10 simulations, it gave a rough estimation of detumbling time with a mean of 12minutes and a standard deviation of 9 minutes. Then it was assumed that the true standard deviation (σ)of detumbling time is within a range:

7min ≤ σ ≤ 11min, where 7min was lower one-side confidence interval, 11min was upper one-side confidence interval. Before checking the Chi-Square satisfied interval, the satisfactory margin α for upper and lower boundaries was set to 5%.

The x²_α/2 is called the α/2 critical value from the chi-square distribution with N − 1 degrees of freedom, this value can be looked up in the chi-square table in Chapter 1 of the engineering statistics handbook [17].

By giving a number of simulation intervals, if the satisfied interval test gave a result which is within the minimum acceptable satisfied interval calculated from equation 5.6. It could be said that the amount of simulations can provide a satisfactory statistics result.

Therefore, for a 10 times simulation, N = 10 and standard deviation s = 9 minutes.

By the use of equation 5.6. the tested interval has a result of 6.3min ≤ σ ≤ 16.8min.

However this interval was much larger than the estimation interval before, 10 time- simulation was not enough to provide a satisfactory statistics.

Nevertheless, if the number of simulation increased to 30, solving equation 5.6 by substitution of N = 30 and s = 8 gave an interval of 6.4min ≤ σ ≤ 11min. This is very close to the estimated standard deviation interval which is 7min ≤ σ ≤ 11min.

It is concluded that 30 time-simulations for detumbling control of ∆Dsat can give a reliable statistic result.

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5.2.2.4 Statistical Result of Detumbling

Statistics of Detumbling (Data from 30 runs of simulation) Value Mean of detumbling time (min) 16.7 Standard deviation of detumbling time (min) 9.4

Average power (W) 0.97

Table 5.3: Simulation Result for Detumbling

Table 5.3 shows the statistic result for detumbling control of ∆Dsat. The average detumbling time is 16.7 minutes and the standard deviation is 9.4 minutes. It is much shorter than the QB50 requirement for detumbling (QB50-SYS-1.2.1) which is 2 days. Therefore, there is a large margin for detumbling.

The average power is 0.97 W which is the maximum power plus bias. This is because the actuators were always saturated during detumbling control.

Magnetometer Resolution (Tesla) Statistics of detumbling time over 30 times of simulation (mean, standard deviation)

(min)

3.5 × 10⁻⁶ (16.2, 9.9)

7 × 10⁻⁶ (HMC5843) (16.7, 9.4)

7 × 10⁻⁸ (14.8, 10.7)

Table 5.4: Statistics results of changing resolution of magnetometer

Knowing how the magnetometer resolution would affect the detumbling time can decide if it is necessary to purchase a higher resolution magnetometer for detumbling control. An statistic result for detumbling control with different resolutions is shown in table 5.4.

The result presents that improving magnetometer resolution dose not affect the detumbling time. Therefore, it is not necessary to replace the magnetometer on the NanoMindAC712D OBC board.

5.2.3 Validation of Simulation Result for Detumbling

In order to validate the simulation result for detumbling control, an analytical solution was carried out.

To simplify the calculation, the dynamic behavior of the system is considered as linear (i.e. the angular acceleration is 0) and the CubeSat stays in a constant

Detumbling and Aerostable Control for Cubesats

MASTER'S THESIS

Detumbling and Aerostable Control for Cubesats

Zhou Hao 2013

CRANFIELD UNIVERSITY

ZHOU HAO

DETUMBLING AND AEROSTABLE CONTROL FOR CUBESATS

SCHOOL OF ENGINEERING

MSc THESIS

Zhou Hao

Detumbling and aerostable control for CubeSats

Abstract

Acknowledgements

Contents

List of Figures

List of Tables

Abbreviations

Chapter 1

Introduction

Chapter 2

Literature Review

2.1 Current Progress of QB50 - ∆Dsat Project

2.2 Magnetic Attitude Control

Chapter 3

Initial Design of ∆Dsat Control System

3.1 B-dot method for detumbling

3.2 Aerostability Control System

Chapter 4

Hardware Selection for Attitude Control System

Chapter 5

Simulation and Validation of

Attitude Control System for ∆Dsat

5.1 Moment of Inertia of ∆Dsat

5.2 Simulation of Detumbling by B-dot Method