This document summarizes a presentation about attitude control of a satellite test setup using reaction wheels. It describes the mathematical models of DC motors, reaction wheels, and the satellite test setup. It also discusses the implementation of a PID controller to control the satellite's orientation by generating angular velocity references for the reaction wheels. Simulation results show that the settling time of the system was decreased from 21.5 seconds to 6.1 seconds by optimizing the PID gains. Future work is planned to consider effects like vibrations and actuator saturations when testing the system.

1. Ankara Yıldırım Beyazıt University
Faculty of Engineering and Natural Sciences, Department of Mechanical Engineering
BILTEK
International Symposium on New Development in Science, Technology, and Social Science
«ATTITUDE CONTROL OF SATELLITE TEST SETUP
USING REACTION WHEELS»
Speaker: Abdurrahim Bilal ÖZCAN
Date: December 20, 2019

2. CHAPTER 1 - INTRODUCTION
CHAPTER 2 - ABSTRACT
CHAPTER 3 - LITERATURE REVIEW
CHAPTER 4 – DC MOTOR MODEL
CHAPTER 5 - MATHEMATICAL MODEL OF SATELLITE TEST SETUP
CHAPTER 6 – REACTION WHEEL MODEL
CHAPTER 7 - CONTROL OF SATELLITE TEST SETUP
CHAPTER 8 - SIMULATION RESULTS
CHAPTER 9 - CONCLUSION
CHAPTER 10 - FUTURE WORKS
REFERENCES
OVERVIEW

3. 1.INTRODUCTION
Satellite is the name of a planet which spins on the orbit of a planet or a vehicle that spins around the
earth is launched for various purpose. For example, Earth is an satellite because it rotates around the
Sun. It is called as a natural satellite. Human-made satellites are called as artificial satellites.
In recent years, the importance of satellites increases in both civil and military area. In civil area, many
satellites were launched in order to make weather prediction, to understand the universe better, to gather
information about planets, telecommunication, etc. Observing military area, mapping, and data
transmission can be given as examples for military applications

4. 1.INTRODUCTION
With the cold war, spacecraft systems have been developed actively all around the world since the
1950s. Sputnik-1 was launched by Russia in 1957 and following that the USA launched Explorer
satellite in 1958.
• 1957 – The first satellite (Sputnik-1)
• 1961 – The First Person to space
• 1964 – The First telecommunication satellite (TELSAR)
• 1965 – The first Intelsat satellite
• 1969 – The first human to the moon
• 1981 – The first shuttle with human (STS1)

5. 1.INTRODUCTION
In Turkey, the first satellite was launched in 1994 and it was produced by Alcatel Alenia Space Industries.

6. 2.ABSTRACT
 Satellites which are exposed to many external forces and must be used in space for
many years are used in many tasks such as meteorology, observation, intelligence,
communication etc.
 Satellites need a highly accurate attitude control system. In this study, reaction wheels
are used in order to control the satellite test setup in 3-axis.
 Mathematical model of DC motors with reaction wheels to be used is obtained
 Mathematical model of the satellite test platform is obtained.
 Conventional PID controller is selected for attitude control.
 By selecting the optimum PID gains, signal was generated to bring the satellite test
setup to the reference value.
 Simulation results are compared and discussed.

7. 3.LITERATURE REVIEW
Satellite attitude control was realized many times by using different
platforms, actuators, control algorithms.
[1]- Optimum tilt angle study - PD Controller
[2]- System performance study - PD + Neural Networks
[3]- System performance study - PD + Genetic Algorithm
[4]- Delay in sensors - PD vs. FVRC & modified FVRC
(Bulanık Değişken Yapılı Kontrolcü) & LQR
[5]- Reaction wheel configuration - PD Controller

8. 4.DC MOTOR MODEL
V Voltage 18
R Terminal Resistance (Ohm) 0.199
L Terminal Inductance (H) 0.000113
𝐊 𝐦 Torque Constant (Nm/A) 0.0217
𝐊 𝐛 Back emf Constant (Vs/rad) 0.0219
𝐊 𝐟 Viscous Friction (Nms/rad) 0.0023873
J Rotor Inertia (kgm2) 0.0000023
 Angular Velocity (rad/s) 821

9. 4.DC MOTOR MODEL
V = E + iR + L
di
dt
J
dω
dt
= Ti
Te = Kf + J
dω
dt
+ TL= i*Km
• Te is the electrical torque,
• Kf is the viscous friction constant,
• J is the rotor inertia,
•  is the angular velocity,
• TL is the mechanical load,
• Km is the torque constant
The transfer function from the input voltage (V), to the angular velocity is expressed as follows :
𝜔 𝑠
𝑉 𝑠
=
Km
𝐿𝑠+𝑅 𝐽𝑠+Kf +KmKb

10. 4.DC MOTOR MODEL IN MATLAB SIMULINK

11. 4.DC MOTOR MODEL IN MATLAB SIMULINK
Kp=0.05
Ki=1
Kd=0.0025
Rise Time 1.2 s
Peak Time 1.26 s
Settling Time 1.6 s

12. • The orientation of spacecraft in space is called its attitude.
• Almost all spacecraft missions require attitude determination and control.
• The satellite operators must be able to determine the current attitude.
• The error between current attitude and reference attitude, and produce control torque in order to
remove errors.
5.MATHEMATICAL MODEL OF SATELLITE TEST SETUP

13. 5.MATHEMATICAL MODEL OF SATELLITE TEST SETUP
Euler’s moment equations are used for understanding dynamic behavior of the system. In this equation, the subscript “I”
indicates a derivative in the inertial frame, while the subscript “B” indicates a derivative in the rotating body frame.
M= 𝐡I = 𝐡B +  𝐱 𝐡
𝑀 𝑥 = 𝑰 𝑥 𝜔 𝑥 + (𝑰 𝑧 − 𝑰 𝑦)𝜔 𝑦 𝜔𝑧
𝑀 𝑦 = 𝑰 𝑦 𝜔 𝑦 + (𝑰 𝑥 − 𝑰 𝑧)𝜔 𝑥 𝜔𝑧
𝑀𝑧 = 𝑰 𝑧 𝜔𝑧 + (𝑰 𝑦 − 𝑰 𝑥)𝜔 𝑥 𝜔 𝑦
Mx, My, M 𝑧are the torques on each axes,ωx, ωy, ωz are the angular velocity components and their derivatives as accelerations
of each axes, and Ix, Iy, Iz are the moment of inertias of the system around each axes.
5. 1 System Dynamics

14. 5.MATHEMATICAL MODEL OF SATELLITE TEST SETUP
Quaternion is used for kinematic calculations.
• It is harder to interpret.
• Euler’s angles are very important for the human perception.
• Singularity might cause in Euler’s angular representation.
5. 2 System Kinematics
The kinematic differential equation for quaternions are
given as
𝑑
𝑑𝑡
𝑞 =
1
2
′ 𝑞
′ is the skew matrix. It is used for getting scalar
product converting from vector product.
′ =
0 𝜔 𝑧 −𝜔 𝑦 𝜔 𝑥
−𝜔 𝑧 0 𝜔 𝑥 𝜔 𝑦
𝜔 𝑦 −𝜔 𝑥 0 𝜔 𝑧
−𝜔 𝑥 −𝜔 𝑦 −𝜔 𝑧 0
Quaternions can be converted into Euler’s angles as
follows.

𝜃

=
𝑡𝑎𝑛−1 2(𝑞1 𝑞4+𝑞2 𝑞3)
1−2(𝑞1
2+𝑞2
2)
𝑡𝑎𝑛−1 2(𝑞4 𝑞2 + 𝑞3 𝑞1)
𝑡𝑎𝑛−1 2(𝑞4 𝑞3+𝑞1 𝑞3)
1−2(𝑞2
2+𝑞3
2)

15. 6.REACTION WHEEL MODEL
• Reaction wheels are used to control a spacecraft's attitude by transferring angular momentum
• To control the attitude in space, at least three reaction wheels are required.
• Three reaction wheels, with each one's rotational axis parallel to one of the satellite's body axes, make up the simplest
control system.
𝐓rw = 𝐡rw + B 𝐱 𝐡rw
𝐓rw = 𝐈rwrw +  𝐁 𝐱 𝐈rwrw
• 𝐓rw is the produced total torque by reaction wheel.𝐈rw is the reaction wheel’ moment of inertia,  𝒓𝒘 is the angular
velocity of the reaction wheel, 𝐡rw is the angular momentum of reaction wheel, and  𝑩 is the satellite angular velocity.
• When DC motor which is connected to reaction wheel produces a torque which accelerates or decelerates it, a reaction
torque occurs on satellite body.

16. 𝐓rw − 𝐓B = 𝛕
𝛕 = 𝐈rwrw +  𝐁 𝐱 𝐈rwrw − 𝐡B +  𝐁 𝐱 𝐡 𝐁
𝑑
𝑑𝑡
 𝐁 = 𝐈−1
𝛕
Changing the angular momentum of the reaction wheel to make equal the total of the
total angular momentum has to make a change in orientation.

17. 7. CONTROL OF SATELLITE TEST SETUP
• PID controls have proven to be most helpful in the field of process control systems.
• PID controller is widely used because of its simple structure and it can be established easily.
• In the system, PID controller of satellite test setup generates angular velocity reference value for DC motor.
• In real systems, this reference value states as PWM (Pulse Width Modulation) value applied on motor controller
in order to change the motor direction or to accelerate or decelerate in correct value.

18. 7. CONTROL OF SATELLITE TEST SETUP
𝜔𝑐𝑥 = 𝑘 𝑝𝑥  𝑟𝑒𝑓 −  𝑚𝑒𝑎 + 𝑘𝑖𝑥 𝑑
𝑑𝑡
 𝑟𝑒𝑓 −  𝑚𝑒𝑎 + 𝑘 𝑑𝑥  𝑟𝑒𝑓 −  𝑚𝑒𝑎 𝑑𝑡
𝜔𝑐𝑦 = 𝑘 𝑝𝑦 𝜃 𝑟𝑒𝑓 − 𝜃 𝑚𝑒𝑎 + 𝑘𝑖𝑦 𝑑
𝑑𝑡
𝜃 𝑟𝑒𝑓 − 𝜃 𝑚𝑒𝑎 + 𝑘 𝑑𝑦 𝜃 𝑟𝑒𝑓 − 𝜃 𝑚𝑒𝑎 𝑑𝑡
𝜔𝑐𝑧 = 𝑘 𝑝𝑧  𝑟𝑒𝑓 −  𝑚𝑒𝑎 + 𝑘𝑖𝑧 𝑑
𝑑𝑡
 𝑟𝑒𝑓 −  𝑚𝑒𝑎 + 𝑘 𝑑𝑧  𝑟𝑒𝑓 −  𝑚𝑒𝑎 𝑑𝑡
The variables kp, kd, ki are the proportional, integral, and derivative gains. Where  𝑟𝑒𝑓,𝜃 𝑟𝑒𝑓,
and  𝑟𝑒𝑓 are the Euler references.𝜔𝑐 is angular velocity reference value generated by PID
controller.

19. Overall System View

20. 8. SIMULATION RESULTS
Parameter Description Value
𝐼 𝑥, 𝐼 𝑦, 𝐼𝑧
System’s moment of inertias 0.0036,0.0064,0.004 kgm2
 𝑟𝑒𝑓, 𝜃𝑟𝑒𝑓,  𝑟𝑒𝑓
Attitude angle commands 30, −30,60 deg
0, 𝜃0, 0 Initial conditions 0,0,0 deg
𝑘 𝑝, 𝑘𝑖, 𝑘 𝑑 PID controller gains of DC Motors 0.5,1,0.0025
𝑘 𝑝, 𝑘𝑖, 𝑘 𝑑 𝑥
𝑘 𝑝, 𝑘𝑖, 𝑘 𝑑 𝑦
𝑘 𝑝, 𝑘𝑖, 𝑘 𝑑 𝑧
PID controller gains of the system on
three axes
25,15,1
15,0.7,15
25,15,5
𝐼𝑟𝑤 Reaction wheels’ moment of inertias 0.0004118 kgm2
t Simulation time” 25 sec.
P I D Settling Time
1
X 25 25 0.001 19 sn
Y 25 25 0.001 21.5 sn
Z 25 25 0.001 12.5 sn
2
X 25 5 0.001 5 sn
Y 25 5 0.001 9.3 sn
Z 25 5 0.001 8.5 sn
3
X 25 5 1 5.05 sn
Y 25 5 1 9.29 sn
Z 25 5 1 8.06 sn
4
X 25 15 1 4.9 sn
Y 15 0.7 15 6.1 sn
Z 25 15 5 5 sn
Many experiments were done to decrease settling time of the satellite test setup.
But 4 crucial experiments were shown.

21. Angular Position of Satellite Test Setup in Three Axes

22. Angular Velocity of Satellite Test Setup in Three Axes

23. Occured Torques on Satellite Test Setup in Three Axes

24. Produced Torques by Reaction Wheels in Three Axes

25. Angular Velocities of the Reaction Wheels

26. 9. CONCLUSION
• In this paper, attitude control of the satellite test setup is aimed in optimal settling time.
• Attitude control is realised using classical PID controller to stabilize and orient the
system.
• Finally, many experiments are done to obtain optimal settling time.
• Overall settling time is decreased from 21.5 sec to 6.1 sec using correnct PID gains.

27. 10. FUTURE WORKS
• Design of satellite test setup will be finished and obtained simulation results will be compared with the
real system.
• In real system, vibrations, saturation of DC motors, command delay etc. will be considered.
• Different control algorithm, especially nonlinear controllers such as sliding mode controller, will be
carried out to compare each other.

28. REFERENCES
[1] Shirazi, A., Mirshams, M., “Pyramidal Reaction Wheel Arrangement Optimization of Satellite
Attitude Control System For Minimizing Power Consumption", International Journal of
Aeronautical & Space Sciences, 2014.
[2] Moradi, Murtaza, Satellite Neuro-PD Three-Axis Stabilization Based on Three Reaction Wheels,
2014.
[3] B.J. KIM, H.Lee, S.D. Choi, "Three-axis Reaction Wheel Attitude Control System For KITSAT-3
Microsatellite”, Satellite Technology Research Center (SaTReC), KAIST.
[4] Erkal, Bilgehan, Kaynak, Okyay, “Design of a Fuzzy Variable Structure Controller for Controlling
Satellite Attitude Suffering From Sensor Data Delay”, International Electric and Electronic
Engineers IEEE,2011.
[5] Ismail, Z., "Spacecraft Attitude and Control", Master Thesis, Department of Aerospace Engineering,
University Putra Malaysia, 2016.