The complexity of artificial satellites has grown very fast in the last 20 years. This complexity applies to any platform and payload technological domain; for what concerns the subject of this book we observe a clear trend in dynamic, functional and computational requirements, from quite static systems of past century to new satellites with increased capabilities in orbital and attitude agility and autonomy, which have become important features of current AOCS systems. This transformation took place thanks to a new generation of more accurate and intelligent sensors and also thanks to the enormous growth of on-board processing capability.

Moreover, as a general trend, payload functional complexity has produced an increase of satellites’ installed solar array power and a need for large antennas and telescopes. These evolutions led to the installation of large flexible appendages on relatively light platforms, making the subject of treating low frequency flexibilities with a relatively high modal mass an important problem in AOC design.

The need for lighter platforms implementing an augmented capacity of orbital transfer has led to search for more efficient plasmic propulsion systems, which require new AOCS concepts, including autonomous navigation and guidance.

The subjects presented in this text have been selected to provide theoretical tools to design modern satellite attitude and orbit control systems.

Before continuing with the description of the content of the book, we shall go through the main satellite applications and explain what are the latest technological advances in AOCS along with possible future trends.

We will consider in this review Earth observation applications optical and radar, telecommunication and navigation, scientific applications and microsatellites.

Fig. 1.1
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Active array synthetic aperture radar satellite

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1.1 Radar Earth Observation

The typical Earth observation satellite flies in low Earth orbit (LEO), typically between 400–1000 km. The launcher injects these satellites directly into their final orbit, therefore the satellite propulsion system is typically limited. The choice of the altitude is a compromise between the need to have a good image resolution, that calls for lower altitudes, and the need to have a short revisit time over the same target. The orbits chosen are often almost polar, dawn/dusk Sun-synchronous, but also low inclination orbits can be selected when the service is provided over low latitude regions.

AOCS requirements depend on the specific instrument (synthetic aperture radar, radar altimeters, scatterometers): we refer here to high quality synthetic aperture radar satellites, as the one shown in Fig. 1.1, which usually require a significant amount of solar array power and integrate quite large antennas . This makes the issue of flexibility effects very important in AOCS design. When these satellites have a completely active antenna their attitude is normally quite stable, apart from periodic repointings and low rate attitude steering (so called yaw steering) to compensate for the Earth’s rotation effects on the doppler shift of the received ground scattered electromagnetic wave. When the antenna does not implement an electronic steering capability, the AOCS design must provide an important attitude agility in its place. This calls for a high bandwidth rate control, fed by gyros with low noise performance figures and flexible modes ’ disturbance rejection filters, control moment gyro (CMG) actuators with important torque and momentum figures, and suitable control laws. When the radar has a very large antenna, thruster pulses for orbit corrections can produce intolerable flexible mode excitations. The AOCS uses star trackers (STT) to determine the attitude and GNSS receivers with a precise orbit determination filter to determine in real time the satellite’s position with very high accuracy. The attitude and orbit knowledge are significant in providing a good image target geo-location.

1.2 Optical Earth Observation

The considerations made for radar satellites in terms of orbital selection apply here as well, except for the fact that the orbits chosen are almost polar, day/night Sun-synchronous, in order to have a long passage with Sun illuminating the targets at midday, which provides a good and stable image quality.

During the day passage satellite points towards desired targets using a very accurate star tracker while the on-board navigation system provides the information of the satellite’s position in order to precisely geolocate the image. These satellites are typically as compact as possible with very small and rigid solar arrays, and the telescope body solidly integrated within the platform (see Fig. 1.2).

Fig. 1.2
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Optical panchromatic satellite

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The AOCS requirements depend on the specific instrument used (hyper-spectral, panchromatic, thermal-infrared); we refer here to high quality panchromatic satellites which typically require important stability and pointing performances to support the high resolution capacity. The main problems related to the design of a high performance AOCS for these applications are a high frequency attitude stability during imaging and a large attitude agility in order to produce many images of the same location. The first issue calls for a high bandwidth rate control fed by gyros with low noise performance figures and flexible mode fast dumping; the agility instead calls for the use of CMG actuators. The appendages are designed to be extremely stiff in order to avoid oscillations after the agile maneuvers. The CMG shall provide very high torques in the range of many Newton-meters, but they shall be also extremely well-balanced in order not to produce micro-vibration levels such to affect the image quality. Other important issues related to AOCS design are: star trackers (STT) working under high speed conditions, multiple STTs’ optical heads and gyros for precise attitude determination (PAD) and very precise orbit determination (POD) to increase the quality of image’s geo-location.

1.3 Telecom Satellites

The telecom satellites typically fly in geosynchronous (GEO) orbit, about 36000 km above the Earth. Even if some launchers are able to place medium size satellites directly in such an orbit, the classic procedure is an injection into a highly eccentric orbit called GTO (geosynchronous transfer orbit) followed by a number of satellite maneuvers aimed at reaching the final GEO. These maneuvers form what is called the LEOP (launch and early operational phase) of the telecom satellite. These satellites are equipped with very important propulsion systems which allow them to perform LEOP transfers and following station keeping maneuvers to maintain their location in GEO.

The AOCS must be designed to support LEOP maneuvers which nowadays are made simpler by using a new generation of autonomous star trackers which can provide satellite attitude measurement looking at any direction of the sky. In the past, satellites’ LEOP were much more complex because using Earth sensors and Sun sensors which could work only if pointed towards the Earth and the Sun. When placed on station, telecom satellites deploy an important system of solar arrays and antennas (see in Fig. 1.3 a typical Ka-band telecom antenna system). These antennas must be accurately pointed while they are excited by orbital maneuver pulses, thus Ka-band satellites may need a dedicated antenna pointing controller.

The driving force of telecom satellite business is the commercial competition among the big players of this market. This calls for a strong focus on satellite costs and efficiency which has led in two directions: increased on-station solar array power in order to implement more communication channels and search of lower cost launching systems. The AOCS design must comply with these low cost requirements still maintaining enough flexibility.

In order to reduce launch mass and cost, the trend is to replace the satellites’ propulsion with fully electric low thrust systems. The AOCS will have to perform a very long LEOP, lasting a few months, in order to reach the GEO location. The launchers’ injection orbits could be medium Earth orbits (MEO) or GTO but also LEO cases are under study. In Fig. 1.4 a pictorial view of a LEO to GEO spiral transfer is shown. Other trends in telecom AOCS design are relevant to gyro-less design and autonomous navigation and guidance, to reduce the costs of on-board hardware and ground station support during such a long LEOP.

Fig. 1.3
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Telecom Ka-band multispot satellite

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Fig. 1.4
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Pictorial view of a LEO to GEO transfer by electric propulsion

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1.4 The Navigation Satellites

The navigation satellites are those forming the constellations which allow to accurately measure the position of mobile ground receivers (so called GNSS receivers ): the GPS constellation, the Glonass constellation and the Galileo constellation. These satellites are normally injected directly into their final MEO orbit with medium inclination, and the main requirement of AOCS design is its low cost as in the telecom case. The satellite attitude on station is pointed at the Earth and a rotation around Earth’s direction is implemented in order to point the solar arrays always towards the Sun (yaw steering). One of the main issues of navigation satellites’ design is the launching cost: an important novelty under study for Galileo second generation is to adopt an on-board electric propulsion system in order to give these satellites an important orbit transfer capability and use lower cost launch opportunities.

1.5 Scientific Satellites

Scientific missions give an extremely wide range of possibilities. We can have missions to Mars, to the Moon or L1, L2, L4 Lagrangian points, not to mention planetary missions to our solar system. Many scientific missions are also implemented in LEO for example to measure the physical properties of our planet. The objectives of such missions may be exploration of planets of our Solar System, observation of Sun or deep space observation (Fig. 1.5) in different bandwidths. Each scientific mission may have its peculiar problems; in general AOCS is designed to take images of stars or to point very precisely towards some spot of the Space. Issues like high precision pointing and microvibrations are common in these missions. Microvibrations produced by momentum management systems may be damped using passive or active dampers. These satellites shall be controlled with very accurate star trackers and smooth actuation systems like those using cold gas reaction control thrusters (RCTs). Large flexible appendages are quite common in these missions such as telescopes and antennas , for example, when exploring far locations of our solar system large antennas may be deployed in order to increase the communication antenna gain and ensure a good data rate.

Fig. 1.5
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Hubble space telescope exploring the deep space. Credit NASA

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Fig. 1.6
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Two nanosats from the international space station. Credit NASA

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1.6 Microsatellites

Microsatellites are a new way to conceive space missions. In this paradigm microsatellite or nanosatellites constellations or swarms (see Fig. 1.6) in low orbits should perform the same task of a single satellite at a higher orbit. An example can be provided by optical satellites: by using a smaller telescope aperture on a smaller satellite flying at a proportionally lower orbit, we get the same resolution as if flying at a higher orbit with a larger telescope aperture on a larger satellite.

The loss of revisit time of a lower orbit microsatellite, is compensated by launching many of them (3–4). The global cost is in favor of small satellite solutions (see [1]). Microsatellite constellations can be conceived also for other applications like global internet services and local area networking. Some microsatellites in flying formation close to each other can be used as a single instrument by synthesizing their measurements to provide a type of information which is not reachable with a single satellite: this happens in particular in the case of optical applications, radar interferometry, bistatic radar applications and localization of electromagnetic sources. The AOCS of such systems faces important challenges: flying formation navigation and guidance (see [2]), low orbit drag compensation by small plasmic thrusters, agility, highly integrated and low cost electronics, inter-satellite link (ISL). In order to reach a high level of integration and an extremely low cost (a factor 10–100 less with respect classic satellites) microsatellites will use commercial off the shelf (COTS) components. The concept of reliability of a single fault tolerant satellite unit is substituted by the concept of dependability of a constellation of microsats. Such an approach open the avionic design to the use of non-Hi-Reliability parts where the quality of the system is guaranteed by specific analyses and tests performed by the satellite manufacturer.

1.7 Content of the Book

Having shortly reviewed the state of the art AOCS needs in satellites’ market, we provide now a description of the contents of the book: our objective is that the presented subjects should be a useful guide in overcoming these challenges.

This book starts with a description of kinematics and reference frames used to describe satellite dynamics (Chap. 2), flight axes and inertial axes. We define here the variables that will be used to express satellite dynamics.

In the following Chap. 3 we develop the equations of the dynamics of a flexible body in space, our original approach follows the format of Lagrangian mechanics and it is suitable for control applications of large space flexible structures. The reader who is not cultivated in analytical mechanics can consult the Appendix and also the relevant bibliography. The satellite state equations are developed as a generalization of Euler’s equations of motion for a rigid body which is the most used simplified model in satellite attitude control. We include also the study of momentum management devices and gravitational torque effects. The chapter ends with the description of linearized equations which are often used in controller design and a description of typical satellite’s flexible modes : sloshing, solar array, antennas .

Chapter 4 is dedicated to a description of a modern architecture and the functions of an AOC system. The main AOC modes are reviewed presenting possible design solutions and examples, the subject is presented with a simple practical engineering approach and a basic control analysis background is necessary to follow the text.

In Chap. 5 the optimal control theory is presented using an Hamiltonian formalism and the maximum principle. The chapter contains a short presentation of linear optimal control using \(H_{\infty }\) techniques for second order systems.

Chapter 6 is dedicated to attitude control applications: we present the analysis of a flexible system, in particular how to write the non linear equations of its dynamics, how to stabilize the non linear system using Lyapunov method, how to make it linear and then use an LQR controller design technique. The last design example deals with robust control synthesis of a linearized satellite’s dynamics using \(H_{\infty }\) synthesis in presence of flexible modes .

The following Chap. 7 deals with orbit control applications. We describe the classic station-keeping maneuvers, then using the maximum principle, we introduce the theory of orbital transfer maneuver optimization with infinite and finite thrust. We provide realistic design examples for many Earth-centered orbit transfers with low thrust guidance.

This book deals both with orbit control and attitude control. This is not a common approach, because nowadays attitude control engineers and orbital control engineers are two different professionals, with dedicated tools, methodologies and a specific background. We have noticed that, more and more often, these specialists must team together in order to design an efficient AOC system (AOCS). This text is written also for these professionals who feel that it is necessary to have a basic knowledge of the other discipline and how the two are linked together.

After these quite theoretical chapters we provide a description of the main technologies which are of interest for AOCS: propulsion systems and sensors and actuators.

In Chap. 8 we review the main satellite propulsion technologies, both chemical and electrical, and along with the general principles we develop a detailed description of plasmic propulsion systems. In the last Chap. 9 state of the art sensors and actuators are described. Modern sensors like star trackers , Sun and Earth sensors , magnetometers, gyros, GNSS receivers are described in terms of design principles, mathematical models and performances available on the market. The same applies to the actuators: wheels, control moment gyros , magneto-torquers.