Adcs orbit intro

Chapter1 ALEXSAT
CHAPTER (1)
1.1
Satellite Orbits
After a satellite is separated from launching vehicle, it moves in a path
around the Earth called an orbit. Satellite orbiting Earth due to the balance
between two forces, gravitational force which attracts the satellite towards the
Earth and centrifugal force (due to linear velocity of the satellite in orbit )
which causes repulsion of the satellite out from Earth,see Figure ( 1-1.) During
satellite mission design, the orbit is chosen which is appropriate to its mission.
So, a satellite that is in a very high orbit will not be able to see objects on Earth
as many details as orbits that are lower, and closer to the Earth's surface.
Similarly, the satellite velocity in orbit, the areas observed by the satellite, and
the frequency with which the satellite passes over the same portions of the
Earth are all important factors in satellite orbit selection. Essentially, there are
six orbital parameter called classical Keplerian orbital elements define the orbit
as shown in Figure ( 1-3).
Figure ( 1-1) Gravitational force and the centrifugal force acting on bodies
orbiting Earth
1.
Semi-major axis. a This is a geometrical parameter of the elliptical orbit. It can, however, be computed from known values of apogee and perigee distances as for definition of apogee and perigee see Figure ( 1-2).
By Ahmad Farrag 2011 faraagahmad@hotmail.com

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( 1.1)
2perigeeapogeea+ =
2.
Eccentricity.e The orbit eccentricity is the ratio of the distance between the centre of the ellipse and its focus to the semi-major axis of the ellipse see Figure ( 1-2).
3.
Right ascension of the ascending node Ω. it tells about the orientation of the line of nodes, which is the line joining the ascending and descending -nodes, with respect to the direction of the vernal equinox See Figure ( 1-3).
Vernal equinox is the line that intersects the Earth's equatorial plane and the Earth's orbital plane, which passes through the centre of the Earth with respect to the direction of the sun on 21 MarchError! Reference source not found..
(a)
(b)
4.
Inclinationi. is the angle that the normal to the orbital plane of the satellite makes with the normal to the equatorial plane , Figure ( 1-4).
5.
Argument of the perigee W. This parameter defines the location of the major axis of the satellite orbit. It is measured as the angle ω between the line joining the perigee and the focus of the ellipse and the line of nodes in the same direction as that of the satellite orbit, see Figure ( 1-4).

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Figure ( 1-2) apogee ,perigee of the orbit and semi-major axis
Figure ( 1-3) Right ascension of the ascending node
6.
True anomaly of the satellite fo. This parameter is used to indicate the position of the satellite in its orbit. It is defined as the angle, between the line joining the perigee and the centre of the Earth with the line joining the satellite and the centre of the Earth, see Figure ( 1-4)
Orbits can be classified according to different criteria, such as
1.
According to orbit Altitude
o
Low Earth Orbit (LEO): orbit altitude ranging in altitude from 200–1000 km
o
Medium Earth Orbit (MEO): orbit altitude ranging from 1000 km to just below geosynchronous orbit at 35786 km.
o
High Earth Orbit (HEO): orbit altitude above 35786 km.

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Figure ( 1-4) Keplerian orbital elements
2.
according to inclination
o
Equatorial orbit : an orbit that co-planed with the equator i.e. orbit with zero inclination
o
Polar orbit: An orbit that passes above or nearly above both poles of the Earth on each revolution. Therefore it has an inclination of about 90 degrees
o
Inclined orbit: An orbit whose inclination between 0 and 90 degrees.
3.
according to Eccentricity
o
Circular orbit: An orbit that has an eccentricity of 0 and whose path traces a circle
o
Elliptic orbit: An orbit with an eccentricity greater than 0 and less than 1 whose orbit traces the path of an ellipse

Chapter1 ALEXSAT
1.1.1
Special Orbits
An important consideration in space mission design is determining the type of Earth Orbit that best suits the design goals and purpose of the mission. A brief description for the special orbits which frequently used such as; low Earth orbit, medium Earth orbit, geostationary orbit, polar orbit, Sun- synchronous orbit and Molniya orbit, is presented.
1.1.1.1
Low Earth Orbit (LEO)
Orbiting the Earth at roughly 200-1000 Km altitude: Almost 90 percent of all satellites in orbit are in LEO. LEO is often utilized because of the low launch requirements that are needed to place a satellite into orbit. LEO satellites orbit the Earth in roughly 90 minute periods. This means that they are fast moving, and sophisticated ground equipment must be used to track the satellite, LEO is used for such missions as flight tests, Earth observations, astronomical observations, space stations and scientific.
Figure ( 1-5) LEO, MEO and GEO
1.1.1.2
Medium Earth Orbit (MEO)
MEO sometimes called Intermediate Circular Orbit (ICO), is the region of space around the Earth above low Earth orbit (1,000 kilometers) and below geostationary orbit (35,786 Km).The most common use for satellites in this region is for navigation, such as the GPS (20,200 Km) and Galileo By Ahmad Farrag 2011 faraagahmad@hotmail.com

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(23,222 Km) constellations. Communications satellites that cover the North and South Pole are also put in MEO. The orbital periods of MEO satellites range from about 2 o 12 hours. Telstar, one of the first and most famous experimental satellites, orbited in
1.1.1.3
Geostationary/Geosynchronous Earth Orbit (GEO)
Satellite in geostationary orbit appears to remain in the same spot in the sky all the time. Really, it is simply traveling at exactly the same speed as the Earth is rotating below it, but it looks like it is staying still regardless of the direction in which it travels, east or west. A satellite in geostationary orbit is very high up, at 35,850 km above the Earth. Geostationary orbits, therefore, are also known as high orbits; GEO is used for communications satellite
Figure ( 1-6) GEO satellites appear stationary with respect to a point on Earth
1.1.1.4
Polar Earth Orbit
For full global coverage of the Earth, a ground track would have to cover latitudes up to ± 90o. The only orbit that satisfies this condition has an inclination of 90°. These types of orbits are referred to as polar orbits. Polar orbits are used extensively for the purpose of global observations.
1.1.1.5
Sun Synchronous Orbits (SSO)
A Sun-synchronous orbit (SSO) is a nearly polar orbit where the
ascending node precesses at 360 degrees per year or 0.9856 degrees per day.

Chapter1 ALEXSAT
Figure ( 1-7) Sun synchronous orbit
1.1.1.6
Molniya Orbit
Highly eccentric, inclined and elliptical orbits are used to cover higher latitudes, which are otherwise not covered by geostationary orbits. A practical example of this type of orbit is the Molniya orbit. It is a widely used satellite orbit, used by Russia and other countries of the former Soviet Union to provide communication services. Typical eccentricity and orbit inclination figures for the Molniya orbit are 0.75 and 65° respectively. The apogee and perigee points are about 40000 km and 400 km respectively from the surface of the Earth. It has a 12-hour orbit and a satellite in this orbit remains near apogee for approximately 11 hours per orbit before diving down to a low-level perigee. Usually, three satellites at different phases of the same Molniya orbit are capable of providing an uninterrupted service.

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Figure ( 1-8) Molniya orbit
1.2
Reference Coordinate Systems
Several different reference coordinate systems or reference frames are used to describe the attitude of a satellite in orbit. The most utilized coordinate systems employed in attitude control problem are the inertial, Greenwich, orbital, body, and device frames.
1.2.1
Geocentric Inertial Coordinate System
The Geocentric Inertial Coordinate System or Earth-Centered Inertial
(ECI)coordinate system has its origin in the Earth center The -axis points is
the axis of rotation of Earth. The -axis is in the direction of the vernal
equinox, and the -axis completes the right-hand rule for the coordinate
system. A demonstration for the geocentric inertial coordinate system is shown
in Figure ( 1-9).
IZIXIY
1.2.2
Greenwich Coordinate System
The Greenwich Coordinate System or Earth-centered Earth-fixed
reference frame also has its origin at the center of the Earth, but it rotates
relative to inertial space, shown in Figure ( 1-10) The -axis direction is the GZ

Chapter1 ALEXSAT
GXGY
Figure ( 1-9) Inertial coordinate system

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Figure ( 1-10) Greenwich coordinate system
1.2.3
Orbital Coordinate System
The orbital coordinate system (OCS) is located at the mass center of the satellite. This frame is non inertial because of orbital acceleration and the rotation of the frame.
The motion of the frame depends on the orbit altitude. The -axis in the
direction from the satellite to the Earth , -axis in the direction opposite to
the orbit normal, and the -axis is perpendicular to the -axis and -axes
according to the right-hand rule . In circular orbits, is the direction of the
satellite velocity. The three directions , , and are also known as the roll,
pitch, and yaw axes, respectively. Figure ( 1-11) shows a comparison of the
inertial and orbital frames in an equatorial orbit.
OZOXO OYOXOX

Chapter1 ALEXSAT
Figure ( 1-11) orbital coordinate system
1.2.4
Body Coordinate System
Like the OCS frame, the body coordinate system has its origin at the satellite’s mass center. This coordinate system is fixed in the body. The -axis in the direction from the satellite to the Earth , -axis in the direction opposite to the orbit normal, and the -axis is perpendicular to the -axis and -axes according to the right-hand rule . In circular orbits, is the direction of the satellite velocity. The relative orientation between the orbital and body frames is the satellite attitude, when the satellite is nadir pointing OCS is co-onside with BCS

Chapter1 ALEXSAT
Figure ( 1-12) Body coordinate system
1.2.5
Device Coordinate System
The device coordinate system is fixed at the device body (i.e. sensor or
actuator …). It define the orientation of the device with respect to satellite BCS
.As shown in Figure ( 1-13) the ZD- axis is Z-axis of the device 's body and XD-axis
is X-axis of the device 's body and YD-axis is perpendicular to ZD-axis and
XD-axis

Chapter1 ALEXSAT
Figure ( 1-13) device coordinate system

Chapter 2 ALEXSAT
CHAPTER (2)
ATTITUDE DETERMINATION AND CONTROL SUBSYSTEM (ADCS)
In this chapter more detailed explanation about ADCS is introduced. The impact of other subsystems requirements on ADCS and impact of ADCS requirements on the other subsystems are presented. In addition, the tasks that ADCS must perform all over the satellite lifetime and the ADCS operational modes are describe. Then, an illustration for the physical concepts and functions of ADCS devices such as sensors and actuators are exhibited. Besides, different disturbances affecting rotational motion of the satellite are demonstrated. Finally, the general control methods applied with ADCS are presented. The control methods and
2.1
What is ADCS?
The attitude determination and control subsystem measures and controls the satellite's angular orientation (pointing direction).The simplest satellite are either uncontrolled or achieve control by passive methods such as spinning or interacting with the Earth's magnetic or gravity fields. These may or may not use sensors to measure the attitude or position. More complex systems employ controllers to process the satellite attitude information obtained from sensors and actuators torquers to control attitude, velocity, or angular momentum. SC may have several bodies or appendages, such as solar array or communication antennas, that required certain direction pointing. The complexity of the attitude control subsystem depends on the number of body axes and appendage to be controlled, control accuracy, and speed of response, maneuvering requirements and the disturbance environment.

Chapter 2 ALEXSAT
2.2
Internal influence between satellite mission and other subsystems upon ADCS
ADCS is very closely coupled with other subsystems; it is interactively influences and being influenced by other satellite’s subsystems. In the following section, a briefer description for interaction between ADCS and other subsystem is presented.
2.2.1
Internal influence between ADCS and Mission requirement
Main mission of the satellite imposes the main requirements on ADCS. Normally, the requirements associated with the mission are
Earth pointing or inertial pointing ( this will affect in ADCS control techniques)
•
Accuracy /stabilization requirements (this will affect in accuracy of selected ADCS sensors).
•
Slewing requirements (this will affect in selection of actuators types)
•
Mission life time (this will affect in life time of selected ADCS devices)
•
Orbit parameters (this will affect in the magnitude of environment disturbance which will perturb ADCS)
2.2.2
Internal influence between ADCS and Structure Subsystem
The ADCS Subsystem directly interacts with the structure subsystem. The structure of the satellite affects the space craft moment of inertia and location of its center of mass, which is affecting the dynamics and stability of the satellite. Also, the rigidity of the structure determines whether the model of the satellite will be a rigid body or a flexible one. In addition, mounting accuracies of ADCS devices are one of the main constrains upon the structural design of the satellite.

Chapter 2 ALEXSAT
2.2.3
Internal influence between ADCS and Power Subsystem
The ADCS and the power subsystem are influencing each other. The power budget of the satellite must take into account the requirements of the ADCS sensors and actuators during different operational modes. For satellite using solar panels, there are additional pointing requirements placed on the ADCS, if solar panels must be kept aligned with the Sun for optimal performance
2.2.4
Internal influence between ADCS and Communication Subsystem
If the satellite antenna is required to be pointed within a given accuracy in order to communication with ground station, the Communication subsystem will add pointing requirements on the ADCS Subsystem during communication session.
2.2.5
Internal influence between ADCS and Command and Data Handling Subsystem
Since the Command and data handling subsystem is the main brain that organizes the data flow between satellite subsystems; so it imposes requirements on the volume and rate of data transfer to ADCS or from ADCS to other subsystems.
2.2.6
Internal influence between ADCS and thermal subsystem
In order to keep temperature of the satellite’s components within specific range the thermal subsystem may impose maneuver requirements on ADCS, by pointing the hot side to deep space and pointing the cold side towards the sun
2.3
ADCS Tasks
According to the previous mutual impacts of ADCS with other subsystems, ADCS has the following tasks must to be executed all over the satellite life time. That is, ADCS executing the following tasks from the moment of separation up to de-orbiting or discarding of the mission.

Chapter 2 ALEXSAT
1.
Damping the satellite angular velocity, obtained from LV after satellite separation.
2.
Attitude acquisition of the satellite where the BCS is oriented to be coincide with the assigned RCS (in Earth observation missions OCS will be this RCS). In this attitude acquisition the satellite is initially oriented towards the RCS supports the mission requirements.
3.
The satellite three-axis stabilize in the RCS with the required accuracy during the imaging sessions.
4.
Three-axis stabilization in nadir pointing with low accuracy during non- imaging periods
5.
Attitude determination with the required accuracy during all ADCS operational modes
2.4
Satellite operational modes
According to the above required tasks from ADCS, the ADCS operational mode will be.
2.4.1
De-tumbling mode (DM)
This mode occurs after the satellite is released from the LV or after loosing of orientation due to any failure. During this mode the ADCS suppers the satellite angular velocity that received from the LV, Because of power limitation this process should be completed within specified period.
2.4.2
Standby Mode (SM)
After DM satellite can have arbitrary attitude Automatically so after finishing DM, ADCS transfers to SM in order to make attitude acquisition of satellite (i.e. Orient the satellite BCS to be co-onside with OCS to get stabilization at nadir pointing with low accuracy) and stay in this case whenever there is no imaging tasks assigned to the satellite. In this mode the satellite attitude should be kept even with a low accuracy to avoid loosing the satellite’s attitude, it is a low accuracy mode. In this mode, the most important thing is to save the system resources (i.e. lifetime of ADCS devices) and reduce

Chapter 2 ALEXSAT
the consumed power. ADCS stay in SM about 95% of the whole satellite lifetime
2.4.3
High Accuracy Mode (HAM) or Imaging Mode (IM)
In this mode, ADCS should provide the required control to achieve the pointing of the payload requirements. As an example, for imaging remote sensing satellite using magnetic actuator the satellite must be stabilized at nadir with high accuracy during imaging periods, so this mode called imaging mode (IM)..
2.4.4
Emergency Mode (EM)
In case of any failure in ADCS (e.g. loosing satellite attitude or any failure of ADCS devices ) ADCS automatically transfer to EM .In this mode ADCS switch off all ADCS devices and make diagnostic for ADCS devices according to command from ground and send TM to ground in order to take the suitable decision.
2.4.5
Transferring from one operational mode to another
The organization of transfer from one mode to another is shown in
Figure ( 2-1).ADCS operational cyclogram and conditions for transferring
between modes are as follows:
1.
After separation from LV and starting of satellite operation ADCS enters DM.
2.
When DM is finished, ADCS directly transfers the satellite to SM and stay in SM.
3.
Before imaging time, within specified period (i.e. Period sufficient to stabilize the satellite at the required attitude with the required accuracy),ADCS transfers the satellite to IM.
4.
After finishing of imaging task, ADCS transfers the satellite again to SM
5.
In normal cases, the sequence of items 3-4 are repeated.

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6.
In case of any failure (i.e. failure in ADCS devices or attitude orientation ), ADCS directly transfers the satellite to EM.
DM finishing ADCS failure DM SM IM EM Imaging command Finishing imaging session ADCS failure ADCS failure Fixing of ADCS failure
Figure ( 2-1) Organization of transferring from one operational mode to
another.
2.5
ADCS devices
A satellite in space must point to a given direction as assigned by the mission requirements. Many satellites are Earth orientated while others are inertial space object oriented such as sun or a star of interest. The orientation of the satellite in space is known as its attitude. In order to achieve control and stabilization of the satellite, attitude sensors are used to determine the current attitude and actuators are used to generate required torque to maintain the required attitude. This section gives brief description of the most common used ADCS sensors and actuators.
2.5.1
ADCS Sensors
Sensors generally determine the attitude and pointing direction of satellite with respect to reference objects, this object could be inertial space or a

Chapter 2 ALEXSAT
body of known position. The most commonly used reference objects, Earth, Sun, stars, geomagnetic field and inertial space.
2.5.1.1
Earth’s Horizon sensor
For near-Earth satellites the Earth covers a large proportion of the sphere of view and presents a large area for detection. The presence of the Earth alone does not provide a satisfactory attitude reference hence the detection of the Earth’s horizon is widely used.
Horizon sensor is infrared device that detect the contrast between the
cold of deep space and the heat of the Earth’s see Figure ( 2-2). Horizon sensors
can provide pitch and roll attitude knowledge for Earth-pointing satellite. For
the better accuracy in low Earth orbit (LEO), it is necessary to correct the data
for the Earth oblateness and seasonal changes in the apparent horizon .Earth’s
Horizon sensor is used in AEROS-I,-2, MAGSAT, SEASAT
Figure ( 2-2) principle of Earth horizon sensor
2.5.1.2
Sun sensor
Sun sensor is widely used with satellite mission due to the special features of sun as a space object. One of these features is the brightness of the sun, which makes it easy to be distinguished among other solar and stellar

Chapter 2 ALEXSAT
objects. also the Sun-Earth distance makes it appear as nearly a point source (0.25 º). Those factors urge ADCS designer to rely upon sun sensors in high pointing accuracy missions.
Sun sensor measures one or two angles between their mounting base
and incident sunlight. Categories of sensors are ranging from just sun presence
detector, which detects the existence of sun, rather accurate analogue sensor
measuring sun incidence angle, up to high accuracy digital instrument, which
measure the sun direction to accuracy down to one arc-minute. Typical digital
sun sensor is shown Figure ( 2-3).
Sun sensor is accurate and reliable, but require direct line of sight to the sun. Since most low-Earth orbits include eclipse periods, the attitude determination system should provide some way of handling the regular loss of Sun vision. Sun sensor is used in AEROS-1,2 , GEOS-3, MAGSAT, SAGE, SEASAT.
Figure ( 2-3) Sun sensors
2.5.1.3
Star mapper
Star mapper provides the most accurate absolute pointing information
possible for a satellite attitude. It contains Charged-Coupled Device (CCD)
sensors or Active Pixel Sensors (APS) which provides a relatively inexpensive

Chapter 2 ALEXSAT
Figure ( 2-4) Start sensor
The accuracy and autonomy provided by a star camera would be impossible without high-speed microprocessors for image processing and star identification. Star sensor is used in ATS-6, Egyptsat-1, LANDSAT-D·, MAGSAT.
2.5.1.4
Magnetometers
Magnetometers are simple, lightweight sensors that measure both the direction and magnitude of the Earth’s magnetic field. They are reliable but require complex software for interpretation and provide relatively coarse attitude determination as compared to horizon, sun, and star sensors. Navigational information are used with a computer model of the Earth’s magnetic field to approximate the field direction at the satellite’s current

Chapter 2 ALEXSAT
position. Comparison between measured and calculated earth magnetic field is used to provide information about satellite orientation. Employing estimation techniques such as Kalman filter, allows magnetometer to work as standalone device for attitude determination. The Earth’s magnetic field also varies with time and can't be calculated precisely, so a magnetometer is often used with another sensor such as a sun, horizon or star sensor or a gyroscope in order to improve the accuracy. Magnetometer is used in AEROS-1, Egyptsat1, GEOS- 3, SEASA.
Figure ( 2-5) flux-gate magnetometer
2.5.1.5
Inertial Sensor or Gyro
By definition, a gyroscope, is any instrument, which uses a rapidly spinning mass to sense and respond to changes in the inertial orientation of its spin axis. There are types of attitude sensing gyros: mechanical and optical gyro. These sensors measure satellite orientation change.
•
Mechanical Gyroscopes
The angular momentum of a gyro, in the absence of an external torque,
remains constant in magnitude and direction in space. Therefore, any rotation
of the satellite about the gyro's input axis results in a precession of the gimbal

Chapter 2 ALEXSAT
Figure ( 2-6) Three degree-of-freedom gyroscope construction geometry.
•
Optical Gyroscopes
Optical gyros are gyroscopes that utilize a light ring instead of a mechanical rotor as the main component to determine rotational changes. All optical gyros work on the same principle, the Sagnac effect, This effect works on relativistic principles but can be described in "normal" terms. Two light beams are traveling through circular paths of the same length but in opposite directions around in an optical coil. If the optical coil is rotating, one of the light beams will take a longer period of time to travel the circumference of the coil. This time lag is measured and converted into a rotational rate for the coil. Thus, the rotation the gyro is feeling can be measured. The length changes associated with the light beam are of nuclear dimensions and are difficult to measure. However, great accuracy can be achieved through the use of this type of gyroscope. The most common devices of this type is the Ring Laser Gyro

Chapter 2 ALEXSAT
(RLG) and Fiber Optic Gyros (FOG) .Gyros are used in ATS-6, Egyptsat1,LANDSAT-D·, MAGSAT.
Figure ( 2-7) The QRS11Pro gyro used on Rømer
Typical values for accuracy of ADCS sensors are shown in the following table
Table 2-1 Ranges of ADCS sensors accuracy
Sensor
Accuracy
Earth’s Horizon sensor
0.05 deg. (GEO)
0.1 deg. (LEO)
Sun sensor
0.01 deg.
Star mapper
2 arc. sec.
Magnetometers
1.0 deg. (5,000 Km altitude)
5.0 deg. (200 Km altitude)
Gyro
0.001 deg./hr
2.5.2
ADCS Actuators
ADCS actuators are used to generate the required torque for correction of satellite attitude. The generated torque is operated against the environmental disturbance or to force the satellite to point to a cretin direction according to the

Chapter 2 ALEXSAT
control system requirement. A brief description of the commonly used actuators is presented in this section.
2.5.2.1
Momentum and Reaction Wheel
Momentum wheels and reaction wheels are similar in construction; they are simply motor with a flywheel mounted on the motor shaft, the difference in terminology resulting primarily from the speed at which they operate. A momentum wheel typically operates at constant speed, providing a means of momentum storage, which in turn provides gyroscopic stabilization to the satellite. Reaction wheels generally operate at varying speed, providing means of reacting torque. According to Newton's third law, as a torque is electrically applied on the motor shaft to cause the wheel to accelerate, an equal and opposite torque is generated on the satellite, causing the attitude to change.
Momentum wheels are commonly used singly or in pairs to provide spin
stabilization. Normally, reaction wheel system consists of four wheels. Three
reaction wheels are aligned to the satellite pitch, yaw and roll control axes. The
fourth wheel is skewed symmetrically with respect to the orthogonal control
axes. This commonly used configuration provides full redundancy for roll or
pitch or yaw in case of wheel failure. An image of typical reaction wheel is
shown in Figure ( 2-8)

Chapter 2 ALEXSAT
Figure ( 2-8) The TELDIX Momentum and Reaction
Momentum and reaction wheels have the advantage of providing quick and accurate attitude control. Also, they can be used at any altitude. Their disadvantage is that they can be costly, massive, and require large amounts of power. However, wheels may saturate since the RW is a motor that has maximum speed, since the angular momentum that can be stored in the wheels is limited, so a secondary control system is used to prevent the stored momentum from reaching the maximum limit. The secondary control system can be thrusters system or magnetorquers. Momentum and reaction wheels are used in Egyptsat1, FLTSATCOM, MAGSAT and SEASAT Error! Reference source not found..
2.5.2.2
Magnetic actuators
Magnetic actuators enforce a torque on the satellite by generating a dipole moment, which interacts with the Earth's magnetic field. Generally, there are two types of magnetic actuators, torque coils and magnetic rods or magnetorqure.
1.
Torque Coils

Chapter 2 ALEXSAT
The torque coil is simply a long copper wire, winded up into a coil.
Generally, three coils are used, one coil in each axis as shown in Figure ( 2-9
The generated dipole moment by each coil is calculated by L
ANiLcoil⋅⋅=
( 2.1)
Where, is the current in the coil, N is the number of windings in the coil, and A is the area spanned by the coil. coili
Figure ( 2-9) Torque Coils
2.
Torque Rods
Torque rods operate on the same principle as torque coils, but instead of
a large area coil the windings is spun around a piece of ferromagnetic material
with very high permeability as shown in Figure ( 2-10). Ferromagnetic
materials, have a relative permeability, , of up to 106. the generated dipole
moment is calculated by the following formula
η L
ANiLcoil⋅⋅⋅=η
( 2.2)
Hence, generating specified dipole moment from magnetic rod needs current much lower than that needed to magnetic coil. However, the weight of

Chapter 2 ALEXSAT
magnetic rod increases drastically because of the metal core in the rods. Another inconvenience of the torque rods is the hysteresis effect associated with ferromagnetic core which add nonlinearity to the control loop. Advantages and disadvantages of using magnetic actuator will be discussed in details in Error! Reference source not found.. Magnetic actuators are used with Egyptsat1, MAGSAT, TIROS-IX, LANDSAT-D and AEROS-1, 2Error! Reference source not found. .
Figure ( 2-10) Torque rods
2.5.2.3
Thruster
Thruster works on the principle of Newton's third law, according to which "for every action, there is an equal and opposite reaction". Referring to this principle, if gas is propelled out of a nozzle, the satellite will accelerate in opposite direction. However, if the nozzles are not pointed directly away from the center of mass this will lead to cause rotational of satellite as well. In addition, if two thrusters in opposite direction but not co-lined rotation only will be generated. The source of the used gas defines the type of thruster . Cold gass thrusters use high pressure storage tank. Hot gas thrusters use the combustion of either monopropellant or bipropellant.
Six thrusters are needed to be mounted in pairs to generate the torque needed for three-axis control. Thruster as actuator is highly accurate and generate higher torque than RW and magnetic rods. On the other hand, the structure used with the thrusters is large and heavy. Besides, run out of either

Chapter 2 ALEXSAT
gas or propellant will lead to stop functioning of thrusters. Thrusters are used in ATS-3,6 , FLTSATCOM, GOES-I and SKYNETError! Reference source not found. .
Figure ( 2-11) Torque generated thruster mounted to satellite
2.6
Disturbance Environment
In an Earth orbit, the space environment imposes several external torques that the ADCS system must tolerate. According to orbit altitude, three or four sources of disturbing torques are affecting the space craftError! Reference source not found. . These torques are; gravity gradient, magnetic field effect, solar radiation pressure, and aerodynamic forces. Those disturbances are affected by the satellite’s geometry, orientation, and mass properties in addition to satellite orbital altitude.
2.6.1
Gravity Gradient Disturbance
Any object with nonzero dimensions orbiting Earth will be subjected to
a “gravity-gradient” torque. In short, the portions of the satellite that are closer
to the Earth are subjected to a slightly larger force than those parts farther away
Error! Reference source not found. . This creates a force imbalance that has
a tendency to orient the satellite towards the center of Earth in order to
compensate this imbalance. According to [Error! Reference source not
found. the gravity gradient torque can be determined by equation ( 2.3) . The
worst case torque arises at Θ =90o By Ahmad Farrag 2011 faraagahmad@hotmail.com

Chapter 2 ALEXSAT
)2sin( 233Θ−=iiZZggJJRT μ
( 2.3)
Where,
Tgg: is the resulting gravitational torque [Nm
μ: is the gravitational constant of the earth [m³/s² (μ = 3.896*1014m³/s²)
Jii :is the moment of inertia tensor for the satellite in i axis.(in body coordinate system) [kgm² (i=x,y,z)
Θ Is the maximum deviation angel from the local vertical [rad
R: is the distance between satellite center of mass and earth center of mass [km
The previous formula for calculation of gravity gradient is used to give course estimation of gravity gradient disturbance torque but an accurate formula given in Error! Reference source not found. is used in calculation of satellite mathematical model
2.6.2
Magnetic Field Disturbance
Magnetic field torques are generated by interactions between the satellite magnetic dipole and the Earth’s magnetic field. This satellite magnetic dipole is the summation of two components; first component is the induced magnetic dipole, which is caused by current running through the satellite wiring harness and second component is the residual dipole moment, which is caused due to magnetic properties of the satellite components. The satellite magnetic dipole exhibits transient and periodic fluctuations due to power switching between different subsystems. These effects can be minimized by proper placement of the wiring harness. The magnetic torque is calculated by following formula
BDTm×=
( 2.4)
Where
D= the vector of total satellite magnetic dipole.
B= local geomagnetic field vector.

Chapter 2 ALEXSAT
In the worst case, the vectors are perpendicular to each other and the cross product turns into a product of scalar values.
2.6.3
Solar Radiation Pressure Disturbance
Solar radiation pressure is a result of the transfer of momentum from
photons of light to the surface of the satellite. The result of this pressure across
the satellite surface is a force that acts through the center of pressure, , of the
satellite. In most cases, the center of pressure is not co-onside with the center of
mass of the satellite, thus a torque will be generated around the center of
mass see Figure ( 2-12). For Earth-orbiting satellite, where the distance from
the satellite to the Earth is small compared to the Earth-Sun distance, the mean
solar flux acting on the satellite is considered a constant (regardless of orbital
radius or position).
psccm
The solar radiation torque is calculated using the following equation [Error! Reference source not found. .
( 2.5) )()cos()1(gpssSpcciqAcSoT−⋅⋅+⋅⋅=
Where
So is solar constant [W/m² = 1428 W/m² (max)
c is speed of light [m/s = 3*108 m/s
A is the cross sectional area subjected to solar radiation pressure [m²
q is reflectance factor (0: perfectly absorbing, 1: perfectly reflecting)
si is the angle of sun light incidence [rad
cps is the center of pressure [m
cg is the center of gravity [m
Referring to the previous assumptions, the solar pressure disturbance torque is the only one that is not dependent of the orbit altitude. However, it is dependent of the sun incidence angle i. The worst case torque arises at i = 0°.

Chapter 2 ALEXSAT
2.6.4
Aerodynamic Disturbance
Aerodynamic torques are due to atmospheric drag acting on the satellite
as shown in Figure ( 2-12. Aerodynamic torques can be quite significant,
especially at low altitudes (less than 500). At higher altitudes the aerodynamic
torque is almost negligible. These torques is difficult to be calculate because
changing of some parameters, such as cross sectional area of satellite subjected
to the aerodynamic drag during tilting. In addition, atmospheric density varies
significantly with solar activity. The generated torque due to aerodynamic
effects is calculated by ( 2.6) .
()gpaCDadccvAcT−⋅⋅⋅⋅⋅=221ρ
( 2.6)
Where
ρ is the density [kg/m³
cD is the coefficient of drag
A is the cross sectional area subjected to atmospheric drag [m²
vc is the orbital velocity [m/s
cps is the center of pressure [m
cg is the center of gravity [m
Figure ( 2-12) Sunlight and drag effect
2.7
Attitude Control techniques
There are different techniques to apply control torque for disturbance compensation and to maintain the required orientation . For these purposes, two types of control techniques are often employed , passive and active control

Chapter 2 ALEXSAT
Error! Reference source not found. Error! Reference source not found. . Since Attitude control system, is highly mission dependent, so the decision to use a passive or an active control technique or a combination of them depends on mission pointing and stabilization requirements.
2.7.1
Passive Control
For missions with rather coarse orientation requirements, passive control techniques are used for attitude control. The main advantageous of these techniques are saving resources concerning both mass and power and the associated cost. In addition, they provide longer lifetime for the space mission. However, a poor pointing accuracy is obtained. The most common passive control techniques are passive magnetic system (i.e. Permanent magnate), gravity gradient and spin stabilization Error! Reference source not found. .
2.7.1.1
Passive magnetic
In this method, the concept of magnetic compass is applied, that is, the
satellite is equipped with permanent magnet that will keep the alignment
between certain axis of the satellite with geomagnetic field vector .As a result,
the south pole of the magnet will be drawn towards the magnetic north pole of
the Earth, and vice versa. This will lead to a slight tumbling motion with two
revolutions per orbit and no possibilities of controlling spin around the magnets
axis as shown in Figure ( 2-13) so continues nadir pointing will not be possible.
Permanent magnet technique is used in AZUR-1 Error! Reference source not
found. .

Chapter 2 ALEXSAT
Figure ( 2-13) passive magnetic control orientation profile.
2.7.1.2
Gravity-gradient stability
Gravity-gradient stability uses the mass characteristics of the satellite to
maintain the nadir pointing towards Earth (as described in 2.6.1). The
magnitude of gravity-gradient torque decreases with the cube of the orbit
radius, and symmetric around the nadir vector, thus not influencing the yaw of
satellite. Therefore, the gravity gradient stability is used in simple satellite in
LEO without yaw orientation requirements Error! Reference source not
found. .
Yet, stability in the gravity gradient case depends upon the the configuration of the mass characteristics of the space craft. The following condition is necessary for gravity-gradient stability [Error! Reference source not found. :
JzzJxxJyy & Jzz Jxx Jyy +<>>
( 2.7)
Where Jii :is the moment of inertia tensor for the satellite in i axis.(in body coordinate system) (i=x,y,z)

Chapter 2 ALEXSAT
As a result, the gravity gradient stability can be achieved by
manipulation of lay out of the satellite's components to grantee the above
mentioned condition ( 2.7). Other solution is to add a sufficient mass on a
deployed boom to reach the stability condition. This will increase the moment
of inertia in the directions transverse to the boom, and the satellite will be
stable with the mass pointed toward or away from the earth. Gravity gradient
stability is suffering from continuous oscillation about nadir due to lack of
damping. Hence, gravity-gradient stabilization should be supported with
damping system to reduce the small oscillation around the nadir vector.
Gravity-gradient stabilization technique is used in DODGE, GEOS-3, and
RAE-2 Error! Reference source not found. .
2.7.1.3
Spin stabilization
Spin stabilization technique applies the gyroscopic stability to passively resist the effect of disturbance torques about the spinning axis. Spin-stabilized satellites spins about their major or minor axes, so angular momentum vector remains approximately fixed with respect to inertial space. [Error! Reference source not found. . Spinning satellite is classified according to spinning object to single or dual spin. The stability criteria and the corresponding spinning axis is predicted according to the following analysis.
2.7.1.3.1.
Single Spin
In single spin satellites, the whole satellite spins about the angular
momentum vector as shown in Figure ( 2-14) This method of stabilization is
simple and has a high reliability. The cost is generally low, and it has a long
system life. However, Spin-stabilized satellite are subject to nutation and
precession, but have a gyroscopic resistance which provides stability about the
transverse axis.
On the other side, spinning satellite will have poor maneuverability. Beside, it will not be suitable for systems that need to be Earth pointing, such as payload scanners and communication antennas. Single spin stabilization

Chapter 2 ALEXSAT
technique is used in AEROS-I,2, ALOUETIE-I,2and ARIEL-I Error! Reference source not found. .
Figure ( 2-14) spin stabilization
2.7.1.3.2.
Dual Spin
In satellite with dual spin, a major portion of the satellite is spun, while the payload section is despun. This technique is favorable because fixed inertial orientation is possible on the despun portion. This method of stabilization has a few disadvantages, however. This system is much more complex, which leads to an increase in cost and a decrease in reliability. In addition, the stability is sensitive to mass imbalances. Duel spin stabilization technique is used in ANS, ATS-6, SEASAT and SMM Error! Reference source not found. .
2.7.2
Active control techniques
For complex mission requirements, satellite requires continues autonomous control about the three axes during the mission. In general, active control systems employ momentum exchange wheels, magnetic control devices, and thrusters. Advantages of these systems are high pointing accuracy, and a not constrained to inertial pointing like spin stabilization technique. However, the hardware is often expensive, and complicated, leading to a higher weight and power consumption.

Chapter 2 ALEXSAT
2.7.2.1
Momentum exchange Wheels
Three-axis stabilization through momentum exchange wheels applies
reaction wheels, momentum wheels, and control moment gyros. This is to
provide three axis stabilization. Advantages and disadvantages of this wheel
system are discussed in 2.5.2.1. Three-axis stabilization technique using wheels
is used in Egyptsat1, FLTSATCOM, MAGSAT and SEASAT Error!
Reference source not found. .
2.7.2.2
Magnetic actuators
Magnetic actuators devices use the interaction of the satellite magnetic
dipole moment and the Earth’s magnetic field to provide a control torque.
Magnetic control torques work better in low Earth orbits than higher orbits,
such as geostationary, because as the distance from the Earth increases, the
geomagnetic strength decreases. Advantage and disadvantage of magnetic
actuators is discussed in 2.5.2.2 Three-axis stabilization technique using
magnetic actuators is used in Egyptsat1, MAGSAT, TIROS-IX, LANDSAT-D
and AEROS-1, 2Error! Reference source not found. .
2.7.2.3
Thrusters
Mass propulsive devices, such as thrusters, can be used for three-axis
stabilization. These often consist of six or more thrusters located on the satellite
body. The strength of the obtainable torque is dependent on the thrust level as
well as the torque-arm length about the axis of rotation. Advantage and
disadvantage of thrusters is discussed in 2.5.2.3 2.5.2.2. Three axis stabilization
technique using thrusters is used in ATS-3,6 , FLTSATCOM, GOES-I,
SKYNETError! Reference source not found. .

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