## Abstract

This chapter provides introductory material to satellite control system (SCS). It is based on the author’s experience, who has been working in areas of SCS development, including designing, testing, operating of real SCS, as well as reviewing and overseeing various SCS projects. It briefly presents SCS generic futures and functional principles: tasks, architecture, basic components and algorithms, operational modes, simulation and testing. The chapter is divided into two parts, namely, Part I: SCS Architecture and Main Components and Part II: SCS Simulation, Control Modes, Power, Interface and Testing. This chapter focuses on Part I. Part II will be presented as a separate chapter in this book.

### Keywords

- satellite control
- attitude and orbit
- determination
- estimation
- sensors
- actuators
- coordinate systems
- reference frame
- state estimation and Kalman filtering
- earth gravity
- magnetic fields

## 1. Introduction

Satellite control system (SCS) is a core, essential subsystem that provides to the satellite capabilities to control its orbit and attitude with a certain performance that is required for satellite mission and proper functioning of satellite payload operation. However, the first mandatory task for SCS is assuring satellite safe functionality; providing sufficient electric power, thermal and communication conditions to be able for nominal functioning during specified life time at different sun lightening conditions (including potential eclipse periods), protecting against life critical failures proving to satellite safe attitude in Safe Hold Mode (SHM). Without SCS or satellite guidance, navigation and control (GN&C) system, any Earth-orbiting satellite could be considered just as artificial space body, demonstrating the * launcher*capability for the satellite launch. As soon as a satellite is assigned to perform a certain space mission, it has to have SCS and a kind of special device (s)-payload (s), performing scientific, commercial or military tasks that are dedicated to this mission. Today, the widespread satellite and SCS design philosophy [1, 2, 3] is based on the concept that satellite is a platform (bus or transportation vehicle) for the very important person (VIP) passenger, which is the payload, and this platform is aimed just to deliver and carry it in space. This approach has been proven as successful or, at least, satisfactory from the commercial point of view. However, the first Soviet satellite “Sputnik” and further Soviet/Russian satellites were built and launched under the different philosophy that satellite is the main “personage” performing a space mission and the payload (unlikely the ballistic rocket war head (s)) is just one of the satellite subsystems that should be integrated into the satellite board under the satellite chief designer guidance, who is responsible for the mission performance. From the author’s point of view, this approach has certain advantages following from the Aerospace System Engineering, integration and distribution functions, and responsibilities between the space mission participants. In this chapter, SCS is presented from this point of view, integrating conventionally separate satellite GN and C subsystems and devices into the joint integrated system, attitude and orbit determination and control system (AODCS). The main principles and features of this system are presented in this chapter.

## 2. Earth-orbiting satellites and the role of the control system

The first human-made Earth-orbiting satellite (Soviet Sputnik), Simplest Satellite (SS-1), was launched on October 4, 1957. This satellite was launched following the development of the Soviet intercontinental ballistic rocket R-7 (8 K71). Nevertheless, it started a new era of space human exploration (Figure 1).

SS-1 technical characteristics are as follows [4, 5]:

Mass 83.6 kg; sealed from two identical hemispheres with a diameter of 0.58 m; life time 3 months; payload, two 1 W transmitters (HF, 20.005 and VHF, 40.002 MHz) with four unidirectional deployable antennas (four 2.4–2.9 m metallic rods); electrical batteries, silver-zinc; sufficient for 2 weeks.

Orbit: perigee 215 km, apogee 939 km, period 96.2 min, eccentricity 0.05, inclination angle 65.10 deg.

Inside, the satellite sphere was filled by nitrogen, and the temperature was kept within 20–23 deg. C with automatic thermoregulation-ventilation system (thermometer-ventilator).

The satellite had no attitude control and was free rotated around its center of mass in orbit, keeping initial angular speed, provided by the separation pulse after the separation from the launch rocket. However, thanks to the four rod antennas that provided unidirectional radio transmission in the two-radio bends, HF and VHF, SS-1 evidently indicated its presence in space for all people over the world. Even amateur radio operators with amateur receivers could receive famous now signals: BIP, BIP, BIP…!! (Figure 2).

Since SS-1, about 8378 satellites were launched to year 2018 [6]. Early satellite launches were extraordinary events and demonstrated tremendous achievement of the launched state, the USSR (4 Oct. 1957, SS-1), the USA (31 Jan. 1958, Explorer 1) and Canada (29 Sep. 1962, Alouette, launched by Thor-Agena, a US two-stage rocket), but with time, satellite launches became ordinary and usually pursue a certain military or civil mission.

Among the civil missions (satellites), the following types can be determined as already conventional: navigation, communication, Earth observation, scientific, geophysics and geodetic, technology demonstration and developers training. These satellites are usually equipped with a kind of payload system(s) (radio/TV transmitter/transducer, radar, telescope or different scientific instrument, etc.) to perform certain dedicated space mission(s). For example, the first Canadian Earth observation satellite RADARSAT-1 (Nov 4, 1995–May 10, 2013; Figure 3) was equipped with a side-looking synthetic aperture radar (SAR) on board the International Space Station (November 1998, ISS; Figure 4) was installed a Canadian robotic arm for its assembling and maintenance.

According to the satellite altitude (h), their orbits can be classified as low-altitude (LEO), 200–2000 km; medium-altitude (MEO), 5000–20,000 km; and high-altitude (HEO), h > 20,000 km; according to eccentricity as: close to circular e < 0.01; elliptical 0.01 < e < 0.3; highly elliptical 0.3 < e < 0.8.

There are satellites with special type of orbit such as polar (i = 90 deg), equatorial geostationary (GEO, i = 0 and h = 35,800 km) and Sun-synchronous provide orbital precession equal to Sun annual rate (i depends on satellite period) (Figure 5).

Miniaturized low-cost satellites are as follows: small satellites (100–500 kg), microsatellite (below 100 kg) and nanosatellite (below 10 kg).

A large diversity of satellites serving for different missions is in space now. A widespread point of vew is that all of them are transportation platforms delivering and carrying in orbit dedicated to the planned space mission payload system, like a VIP passenger. For example, it could be the postman for the postal horse carriage for many years ago. Namely, the satellite with its control system (SCS) provides to the payload all conditions required for the mission performance (orbit, attitude, power, pressure, temperature, radiation protection and communication with ground mission control center (MCC)). That is why from the mission integration point of view, the SCS can be seen as the space segment integration bases that set their development and operation process in corresponding order. In turn, SCS as satellite subsystem also can be reviled and established in satellite onboard equipment architecture, combining the group of subsystems that are dedicated to orbit and attitude determination and control tasks. It could be done rather from the System Engineering than from the commercial practice point of view and would significantly streamline satellite development order and the degree of responsibility of all the developers.

It should be mentioned that such group of aircraft equipment in aviation has been named as GN&C Avionics; hence, for space, it can be named as the * Spacetronics*, and the heritage of system development and integration wherever it is possible should be kept. Essential difference with Avionics for the Spacetronics is that it should work for specified life time in space environment (dedicated orbit) after mechanical start-up impacts (overload, vibration) connected to the launch into the orbit. The verification of this capability is usually gained in special space qualification ground tests that imitate launch impact and space environment with thermo-vacuum and radiation chambers, mechanical load and vibration stands [7, 8].

## 3. Satellite control system architecture and components

### 3.1 SCS architecture

Today, for many satellites, GN&C onboard equipment can be presented by the following subsystems, performing related functions listed below:

Global Positioning System (GPS)—onboard satellite orbit and time determination

Propulsion system—orbit/attitude control system

Attitude Determination and Control System (ADCS)—satellite attitude determination and control

Integration of these subsystems can be named as * attitude and orbit determination and control system or Spacetronic system.*Typically, AODCS includes the following components:

Onboard computer system (OBCS) or dedicated to AODCS electronic cards (plates) in Central Satellite Computer System (e.g., command and data handling computer (C&DH))

Sensors

Actuators

Basic AODCS architecture is presented in Figure 6.

OBCS, onboard computer system; TLM, telemetry data and commands; PL, payload; PS, propulsion system; RW, inertia reaction wheels; MTR, magnetic torque rods; GPS, satellite navigation Global Positioning System; MAG, 3-axis magnetometer; SS, 2-axis Sun sensor; HS, horizontal plane sensor; ST, star tracker; RS, angular rate sensor; EP, electric power; TR, temperature regulation; VP, vacuumed protection; RP, radiation protection.

Depending on required reliability and life time, each component can be a single or redundant unit. Unlike airplanes, satellite is an inhabitant space vehicle that is operated from the ground. The operation is usually performed via a bidirectional telemetry radio link (TLM) in S-band (2.0–2.2 GHz). Payload data downlink radio link (unidirectional) is usually performed via X-band (7.25–7.75 GHz;). For both links, usually the same data protocol standards are applied Figure 7.

Two subsystems can be allocated in AODCS architecture, namely, orbit determination and control subsystem (ODCS) and attitude determination and control subsystem (ADCS). Practically both subsystems are dynamically uncoupled; however, orbital control requires the satellite to have a certain attitude (as well as orbital knowledge itself), and attitude control requires orbit knowledge also. Hence, orbit (its knowledge) is essentially continuously required on satellite board where it is propagated by special orbit propagator (OP). Due to orbital perturbations (residual atmospheric drag, gravity and magnetic disturbances and solar pressure), satellite orbit changes over time and OP accumulates errors; its accuracy is degraded.

Before the application of satellite onboard GPS receivers, the satellite position and velocity were periodically determined on ground by the ground tracking radio stations (GS, dish antenna), and calculated on-ground orbital parameters were periodically uploaded to satellite OBCS to correct OP, to provide available accuracy. Now with GPS satellite, orbit can be calculated onboard autonomously, and OP can propagate data only during relatively short GPS outage periods. For some applications, orbital data uploaded from the ground still can be used, at least, for fusion with GPS-based OP.

For newly developed satellites with GPS, orbit maneuvers (correction, deorbiting, collision avoidance, special formation flying and orbit servicing missions) can be executed autonomously onboard at planned time or from ground operators using orbital knowledge and TLM commands to activate satellite orbit control thrusters.

### 3.2 AODCS components

Below AODCS components are presented to show their generic principles that can help for the system understanding and modeling. Generic design requirements are presented in [3]. Some design examples can be found in many sources, for example, [1, 9, 10, 11, 12].

#### 3.2.1 Sensors

AODCS sensors are designed to measure satellite orbital and attitude position and velocity. From the most general point of view, they can be considered as the vector measuring devices (VMD). The device can measure in space a physical vector

Vector module and its orientation can be expressed as functions of its projections

It can be noted that measurement of referenced vectors can be used for the determination of satellite position or angular orientation. A minimum of three vectors is required to determine satellite position and two to determine its attitude. If more vectors are measured providing informational redundancy, then such statistical estimation methods as least square method (LSM) and Kalman filter (KF) can be applied. Satellite velocity and angular rate can be derived by the differentiation of its position and attitude applying a kind of filter recommended by the filtering and estimation theory [13, 14, 15]. It should also be noted that if vector orientation is measured for the position determination, then satellite attitude should be known and vice versa.

Especial autonomous satellite navigation system (sensor) is the inertial navigation system (INS/inertial measurement unit (IMU)). It can be used for the determination of satellite position, velocity, orientation and angular rate simultaneously. INS is based on measuring with linear accelerometers and angular rate sensors (“gyros”) the two vectors: satellite linear active acceleration

#### 3.2.1.1 Determination of satellite position and velocity (GPS)

Today, satellite GPS can provide onboard accurate data about position, velocity and time [19] (Figure 9).

Accuracy: position, 15 m (

GPS receiver is a radio range measuring device that measures distance from the desired satellite to navigation satellite constellation (NAVSTAR, USA; GLONASS, Russia; and GALILEO, Europe) and computes its position and velocity. GPS measures the distance R (

A minimum of three navigation satellites should be simultaneously traced by the receiver to determine position and velocity. Then satellite position is the cross-point of three spherical surfaces of the position equation

where ^{th} tracked navigation satellite,

#### 3.2.1.2 Determination of satellite attitude and angular rate

#### 3.2.1.2.1 TRIAD method (MAG, SS, HS)

The TRIAD method [10] is applied when two different vectors are measured. They usually can be any of the three pairs combined with the following three vectors: Earth magnetic induction vector

Let us assume that two different physical nature not collinear vectors

These unit vectors expressed at a given time by measured values in measured frame or body frame and reference values in a reference frame define two rotation matrixes,

where vectors

Rotation matrix

Three Euler angles of rotation, roll (

where

If a pair from the three vectors (B, S, r-write as vectors) is measured, then following VMD in the pair can be used: SS (Figure 10), HS (Figure 11) and MAG (Figure 12).

#### 3.2.1.2.2 LSM method for star tracker (ST)

If more than two vectors are measured and available for attitude determination, then LSM-BATCH method [10] can be applied to use informational redundancy for increasing the stochastic estimation accuracy. This method basically can be applied for any set of VMD but is specifically convenient for the star tracker (ST), when some number (

Let us consider the transformation of the referenced vector

where

If the ST is in the tracking mode keeping in its FOV some

where

Then subtracting from (8)

where

Transforming in (10) matrix product and taking into account random measurement errors, this equation can be represented in the following form:

where

Then this equation can be considered as a “standard” linear algebraic equation:

where,

If

where

#### 3.2.1.2.3 Determination of the angular rate

Satellite angular rate

Measured angular velocity vector

where

Often, specifically for attitude stabilization (keeping or aka pointing) mode, satellite angular rate is estimated by using the so-called body rate estimator and is not measured directly by the RS. Indeed, using for attitude keeping mode small angles and linear approximation, we can simplify satellite attitude dynamics model [9] to three single-axis state equations and present it with the stochastic influences as follows:

where

The linear KF can be applied to synthesize the estimator for the optimal estimation of the vector angle

where

Matrix KF (16) is separated in three independent scalar channels for

It can be shown that in the considering case, the steady-state (

where * filterability index*. Eq. (16) can be represented in the transfer function (Laplace operator) form as a second-order differential equation unit:

where

or in other words, the time constant is in inverse proportionality to the filterability index (in ¼ degree) and the specific damping coefficient is conventional for such a second-order unit 0.707 for each of the three channels.

#### 3.2.1.2.4 Multisensory sensor unit (MSU)

As it can be seen from the consideration above, the use of directly measuring devices (e.g., ST and RS) for attitude and body rate determination has a disadvantage. The random noises are at the devices output, and they have to be filtered in the closed control loop of satellite attitude control that puts some constraints to choose the control law coefficients. However, using indirect body rate measurement, the state estimator (filter) unavoidably introduces additional phase delay in the control loop because of the consecutive inclusion of this filter in the control loop. To use the RS (gyro) and the integrator for body rate and attitude determination autonomously for a long time is not possible because of the accumulated attitude errors caused by the integration of the gyro drift. The following scheme (that is common in Aviation) can be considered as free from the disadvantages above. Let us assume that satellite attitude is determined in two ways: continuous integration of RS angular velocity (IMU) and using VMD, for example, ST. Then this ST is used to correct the attitude derived by the integration of RS output. The idea of MSU is shown in Figure 16.

In integrated IMU attitude (IMU = RS + integrator) as in Figure 14 above (three identical channels),

where

where KF coefficients

#### 3.2.2 Actuators

#### 3.2.2.1 Propulsion system (PS)

Satellite propulsion system [9, 10] is usually designed for satellite orbital and/or angular control. In the first case, PS is commanded from the ground OC by TLM commands in some cases when satellite orbit has to be changed (orbit correction, deorbiting, collision avoidance), in the second controlled automatically from onboard AODCS. It consists of such typical elements as orbital and attitude thrusters (number and installation scheme depending on certain application), propulsion tank with associated pipes, valves, regulators, and electronics. General principles of PS act independently of the type (ion thrusters (0.01–0.1 N), liquid propellant and solid motor (100–10,000 N), cold gas (1-3 N)).

Figure 15 illustrates the satellite control with PS thruster principles. The principle of the formation of the propulsion jet force can be presented by the following equation of variable mass body dynamics that from Russian sources, for example, [23], is known as Prof. I. Meshchersky’s equation:

where

In Section 3.2.2.1.2, it is always

The expelled propulsion mass

where

Discrete pulse modulation control is usually used to minimize the consumption of the propellant for attitude control [9]. Examples of the gas thruster and the tank are presented in Figures 20 and 21.

#### 3.2.2.2 Magnetic torque rods (MTR)

* Magnetorquers*are essentially sets of electromagnets. A conductive wire is wrapped around a ferromagnetic core which is magnetized when excited by the electric current caused by the control voltage applied to the coil. The disadvantage of this design is the presence of a residual magnetic dipole that remains even when the coil is turned off because of the hysteresis in the magnetization curve of the core. It is therefore necessary to demagnetize the core with a proper demagnetizing procedure. Normally, the presence of the core (generally consisting of ferromagnetic) increases the mass of the system. The control voltage is controlled by AODCS control output (Figures 18–20). The magnetic dipole generated by the magnetorquer is expressed by the formula:

where * n*is the number of turns of the wire,

where

Typically, three coils are used; the three-coil assembly usually takes the form of three perpendicular coils, because this setup equalizes the rotational symmetry of the fields which can be generated; no matter how the external field and the craft are placed with respect to each other, approximately the same torque can always be generated simply by using different amounts of current on the three different coils (Figure 22).

It can be seen from Eq. (26) that MTR cannot generate the magnetic torque in the direction that is parallel to Earth magnetic field

However, the following approach can be used to find required vector

Another MTR control method is the so-called B-dot control [25].

where

As the result of (29) control, the satellite will reduce its body rate and is finally slow rotated along Earth’s geomagnetic field line (vector

If the redundancy is required, it is provided by additional (redundant) coil with the same core (Figure 23).

#### 3.2.2.3 Reaction/reaction-momentum wheels (RW/RMW)

Reaction wheels (RW), aka momentum exchange devices [9] or reaction-momentum wheels (RMW), have massive rotated rotor with big axial moment of inertia with respect to the axis of rotation. They are electrically controlled by the electric motors and the rotor is installed on the rotating motor shaft. The controlled voltage, applied to the control winding of the motor, controls its rotor angular speed. The product of the rotor angular acceleration

RW can generate control inertia torques * the saturation speed*. At that state

In general case, RW can be run around in some nominal angular speed

where * absolute*angular momentum vector (column matrix),

*angular momentum vector,*relative

Then differentiating (31) in rotating with angular velocity satellite axis

where

where

Eq. (33) can be represented in the following form:

where

The torque

where

In the operator Laplace s-form (transfer function), Eq. (36) can be rewritten as follows:

where

It should be noted that sometimes the RW control loop is more sophisticated. Special integrators could be connected into the loop to memorize and compensate the dry friction torques acting in bearings. Some small nominal rotating speed can be set for all three RMW to eliminate the dry friction torque having a pike when the wheel speed is zero

However, more representative case is when

Indeed, if we put in (32) that

where _{.}Eq. (38) is known as three degrees of freedom of a free gyroscope precession [21] and represents the gyro-stabilization effect: that gyroscope vector

#### 3.2.3 AODCS OBCS

Independently of sytem arhitecture; it is separate dedicated to AODCS computer, or a special AODCS card within central satellite C&DH computer, it is the integration element of AODCS [1, 11]. AODCS system may consist of the computer (computer card) itself (OBC) and auxiliary intercommunication electronic units (electronic cards) AEU carrying DC/DC electric power conversion and I/O (analog and digital) interface and commutation functions.

OBC can be divided into two parts: the hardware (HW, power convertor, processor, input/output [I/O] convertors, non-volatile and volatile memory) and the software (SW, operation system [OS] and vital or functional software [VS/FS]) (Figure 26).

What makes the satellite OBC essentially different for the airplane OBC is that its SW can be uploaded and updated from the ground and during operation and scheduled maintenance. OS OBC includes generic computer programs: program of I/O interface, time schedule (dispatcher), embedded test, timer and standard mathematic functions. Satellite SW often is considered as satellite * SW subsystem*that is verified during development (with mathematical high-fidelity Matlab/Simulink simulators and semi-natural processor-in-the-loop (PIL) simulators). SW subsystem should be tested to meet SW requirements [26, 27]. The flight version of the SW subsystem is supported with operation real-time satellite simulators (RSS) [1, 11] located in operation center. It should be mentioned that only final AODCS (OBC (HW + SW), sensors, and actuators)

*[2] that should be performed in the Space Qualification Laboratory [7] during satellite Space Qualification and Acceptance campaign can really minimize the risk of launching a not ready satellite and prevent against AODCS refinishing in orbit during commissioning and operation.*functional test

VS can be separated in two parts, ODCS SW and ADCS SW. For both parts, I/O interface with sensors and actuators is determined in special interface control document(s) (ICD), describing type, certain connectors, and electrical parameters of the exchanging data. These data before using them for functional tasks are pre-processed in OBC with special algorithms.

#### 3.2.3.1 Satellite sensors/actuators data preprocessing

This group of algorithms performs the following common tasks:

Convert data into required physical parameters and units, taking into account certain sensor input–output scale function.

Transform data in certain device frame and compensate device misalignment, bias and scale function errors if it is possible, monitor device state, establishing “on/off,” “work/control,” “data bad/good” flags.

Transfer to C&DH TLM data about sensor/actuator state and their data.

Perform some other auxiliary functions if they are required.

Main functional tasks ODCS SW and ADCS SW can be listed as below.

#### 3.2.3.2 ODCS SW

#### 3.2.3.2.1 Satellite orbit propagation (OP)

To understand the idea of propagation of satellite orbit in Earth gravity field to the simplest, Keplerian motion propagator based on spherical Earth gravity field model might be used [9]; however more realistic results can be obtained with more accurate propagator, taking into account the second zonal harmonic

where

These equations can propagate satellite position and velocity (

where

#### 3.2.3.2.2 Orbital thrusters control

If orbit maneuver is required, then it can be commanded by AODCS SW autonomously, or special control commands TLM (uploaded command tables) are sending to satellite AODCS, and in predetermined time they are executed activating at scheduled time for the calculated period

#### 3.2.3.3 ADCS SW

#### 3.2.3.3.1 Satellite attitude and angular velocity estimation algorithms

This group of algorithms was presented above in 3.2.1.2 and can be used here.

For example, let us consider single-axis stabilized satellite that should keep one axis (e.g.,

In Figure 28,

The following formula represents the mathematical transformation of the Sun vector from the reference into the body frame:

where

Then from (41), (42) can derive the following formulas:

From (43), desired angles and can be derived that can be used for satellite attitude control.

#### 3.2.3.3.2 Angular velocities (body rates)

Let us also assume that the satellite does not have angular velocity sensors RS and its angular velocities should be derived from the measured angles

where

#### 3.2.3.3.3 Satellite control algorithms

If not the optimization criterion to characterize the control quality [13] is required, then conventional negative feedback closed control loop with linear PID (proportional, integral, and damping) control law [9] that provides a good performance for many practical satellite control applications can be used to satisfy the requirements. They are typical for any automatic control system requirements: such as transfer process decay time and overshooting, residual static error caused by the permanent external disturbance, etc. Today, attitude control system performance can be verified mainly on ground with simulation. If we try to evaluate it in flight, then only onboard attitude sensors TLM data can be used for postprocessing, and it should be taken into account that mainly sensors that detect high-frequency noise (perceived errors) will be observable and low-frequency components (sensor biases) are compensated in the closed control attitude stabilization loop. Simple example of single-axis satellite attitude stabilization control loop is presented below. It is a simplified linear model; however, it presents the stabilization principle and essential features. Let us assume that a simple, positional, and damping control law is used to stabilize satellite axis

where

where

where

Let us take a ball-shaped satellite with the inertia matrix as follows:

where

Let us divide all terms in Eq. (50) by the coefficient

where

As it follows from Eq. (52), steady-state error in attitude stabilization can be calculated with the formula:

where

For Eq. (52), * the optimal*damping coefficient is

Let us evaluate satellite time constant

and MTR has the following parameters: maximal magnetic moment

For the data above, it has the value of

as for a homogeneous sphere. Substituting into Eq. (55) the data above, we can calculate that for SS-1

Now damping coefficient can be calculated with the following formula:

It has the following value:

Finally,

When

Eqs. (51) and (52) were simulated using Simulink (see Figure 29).

Blocks in the pink color present the satellite model, the dark green color is for control law blocks, the cyan blocks are registration oscilloscopes, and the display and the orange color are the disturbances. The red manual switch allows to implement the differentiating filter, transforming the scheme from the approximation (52) to the accurate presentation (51). Disturbing external torque

Simulation of ACS (Figure 29) is presented in Figures 30–34. Units: vertical axis (deg), horizontal axis: (s).

Decay time:

As it can be seen, measured noise is filtered effectively in the control loop, and stabilization error is equal to the sensor bias with opposite sign.

In Figure 34, we can see that the measured (perceived) errors that TLM data provide to ground after the decay time do not present sensor bias and present only measured noise. It is because satellite stabilization error with opposite sign compensates the bias. In general, it can also be seen that the simulation of the approximate second-order model (52) is very close to the accurate model (51). Hence, at least for the analytical representation, (52) can be successfully used.

## 4. Conclusion

Part I of this chapter presents an overview of practical satellite control system, satellite guidance, navigation and control equipment. The work presented here is based on the author’s point of view of integration of this GN&C equipment in the integrated AODCS system (satellite GN&C Spacetronics System). Main work principles, architecture, and components of the satellite control system were briefly highlighted.

The chapter can serve to a wide pool of space system specialists as an introduction to satellite control system development.

## Acknowledgments

The author wishes to express his sincere gratitude to the Canadian Space Agency, where he had the opportunity to learn and possess the knowledge and experience related to the writing of this chapter. As well, he is very thankful to many of his colleagues from Canadian Magellan Aerospace Company (Bristol Aerospace Division) with whom he discussed and analyzed satellite AODCS design projects and issues that helped him to work out the system analysis and its principal concepts presented in this chapter. Additionally, he cannot forget that his experience and background in Aerospace Technology were also accumulated from the former USSR (Moscow Aviation Institute, Moscow Aviapribor Corporation, Moscow Experimental Design Bureau Mars, Institute in Problems in Mechanic of RAN) and Israel (IAI, Lahav Division and Tashan Engineering Center), where he could observe and learn from diverse and wealthy engineering and scientific schools led by great scientists and designers such as Prof. BA. Riabov, Prof. V.P. Seleznev, V.A. Yakovlev, G. I. Chesnokov, V.V. Smirnov, Dr. A. Syrov, Acad. F. Chernousko, A. Sadot and Dr. I. Soroka.

This chapter was written as a solo author since his friend and regular coauthor Prof. George Vukovich from York University of Toronto passed away 2 years ago. For many years, Prof. Vukovich served as Director of his Department of Spacecraft Engineering in CSA. He will always keep good memories of Prof. Vukovich who helped and encouraged him continue his scientific and engineering work.

The author also acknowledges the copyrights of all publishers of the illustrations that were extracted from the open sources in the Internet.