ADCS - Spacecraft Attitude Determination and Control

Cover
Contents
List of examples
List of figures
Biography
	Michael Paluszek (1954–)
Preface
Acknowledgments
1 Introduction
	1.1 Overview of the book
	1.2 Types of spacecraft
	1.3 Courses based on this book
		1.3.1 A one-semester course
		1.3.2 A half-semester course
		1.3.3 An eight-lecture course
	References
2 History
	2.1 Space story
	2.2 Introduction
	2.3 Pre-1950 – dreaming of space
	2.4 1950s – getting started
	2.5 1960s – the Golden Age: Apollo to the moon
	2.6 1970s – the Space Shuttle era
	2.7 1980s – internationalization
	2.8 1990s – Hubble
	2.9 2000s – commercial space is reborn
	2.10 2010s – the space station and beyond
	2.11 The future
	References
3 Single-axis control
	3.1 Space story
	3.2 Introduction
	3.3 Dynamical systems
	3.4 Control system
	3.5 Kalman filter
	3.6 Simulation
	3.7 Adding a mode
4 ACS system design
	4.1 Introduction
	4.2 Design flow
	4.3 Organization of ACS design teams
	4.4 Requirements analysis
		4.4.1 Direct requirements
		4.4.2 Indirect (or derived) requirements
		4.4.3 Control-system requirements
	4.5 Satellite design
		4.5.1 Selecting a satellite configuration
		4.5.2 Selecting a control strategy
		4.5.3 Selecting actuators
		4.5.4 Thrusters
		4.5.5 Wheels
		4.5.6 Pivoted wheels and control-moment gyros
		4.5.7 Selecting sensors
		4.5.8 Selecting processors
		4.5.9 Selecting delta-V engines
		4.5.10 Selecting the station-keeping engines
		4.5.11 Selecting the interfaces
		4.5.12 Cost
5 Kinematics
	5.1 Space story
	5.2 Introduction
	5.3 Euler angles
	5.4 Transformation matrices
	5.5 Quaternions
		5.5.1 Introduction
		5.5.2 Fundamental properties of the quaternion
		5.5.3 Quaternion nomenclature
		5.5.4 Quaternion operations
		5.5.5 Quaternion transformations
		5.5.6 Quaternion derivative
		5.5.7 Small angles
		5.5.8 Physical interpretation of the quaternion
			5.5.8.1 Single-axis rotation
			5.5.8.2 Multiple-axis rotation
			5.5.8.3 Small rotation
		5.5.9 Incremental quaternion for maneuvers
		5.5.10 Angle and unit vector to a quaternion
		5.5.11 Axis-alignment quaternion
		5.5.12 Small angles
		5.5.13 Quaternion interpolation
6 Attitude dynamics
	6.1 Space story
	6.2 Introduction
	6.3 Inertia matrix
		6.3.1 Definition
		6.3.2 Inertia matrix from components
		6.3.3 Common inertia matrices
	6.4 Rigid body
	6.5 Gyrostat
	6.6 Dual spin
	6.7 Gravity gradient
	6.8 Nutation dynamics
	6.9 Planar slosh model
	6.10 N-body hub with single degree-of-freedom hinges
	6.11 N-body hub with wheels
	6.12 Control-moment gyros
	6.13 Flexible structures
	References
7 Environment
	7.1 Space story
	7.2 Introduction
	7.3 Optical environment
		7.3.1 Solar radiation
		7.3.2 Earth albedo
		7.3.3 Earth radiation
	7.4 Atmosphere
	7.5 Plasma
	7.6 Gravity
		7.6.1 Point mass
		7.6.2 Spherical harmonics
	7.7 Magnetic fields
	7.8 Ionizing radiation
	References
8 Disturbances
	8.1 Space story
	8.2 Introduction
	8.3 External disturbances
		8.3.1 Surface geometry
		8.3.2 Aerodynamic
			8.3.2.1 Simple drag coefficient
			8.3.2.2 Surface-accommodation coefficients
		8.3.3 Electrodynamic force
		8.3.4 Gravity gradient
		8.3.5 Residual dipole
		8.3.6 Radio-frequency forces
		8.3.7 Solar pressure
		8.3.8 Earth-albedo force and torque
		8.3.9 Planetary-radiation force and torque
		8.3.10 Thermal torque
		8.3.11 Thruster plumes
		8.3.12 Outgassing force
		8.3.13 Shadowing
	8.4 Internal disturbances
	8.5 Fourier-series representation
	References
9 Budgets
	9.1 Introduction
	9.2 Pointing budgets
	9.3 Propellant budgets
	9.4 Power budgets
	9.5 Mass budgets
10 Actuators
	10.1 Space story
	10.2 Introduction
	10.3 Types of actuators
	10.4 Reaction-wheel model
		10.4.1 Introduction
		10.4.2 Momentum exchange
		10.4.3 Motor model
		10.4.4 Reaction-wheel state equations with current feedback
		10.4.5 Tachometer
		10.4.6 Friction
		10.4.7 Zero crossings
		10.4.8 Commutation
		10.4.9 Suspensions
	10.5 Control-moment gyro
		10.5.1 Introduction
		10.5.2 Modeling
		10.5.3 Torque distribution
		10.5.4 Single-axis control-moment gyros
	10.6 Thrusters
		10.6.1 Introduction
		10.6.2 Pulsewidth modulation
		10.6.3 Minimum impulse bit
		10.6.4 Time constants
		10.6.5 Fuel system
	10.7 Magnetic torquers
		10.7.1 The magnetic field
		10.7.2 Magnetic torque
			10.7.2.1 Torque production
			10.7.2.2 Magnetic-torquer design
	10.8 Solenoids
		10.8.1 Introduction
		10.8.2 Derivation of the equations of motion for a dual-coil solenoid
		10.8.3 Derivation of the equations of motion for a single-coil solenoid
	10.9 Stepping motor
	10.10 Dampers
	References
11 Sensors
	11.1 Space story
	11.2 Introduction
	11.3 Types of sensors
	11.4 Planetary optical sensors
		11.4.1 Horizon sensors
		11.4.2 Earth and planetary sensors
		11.4.3 Scanning Earth sensor
		11.4.4 Analog Sun sensors
		11.4.5 Digital Sun sensors
	11.5 Gyros
	11.6 Other sensors
		11.6.1 Magnetometers
		11.6.2 Accelerometers
		11.6.3 Potentiometers
		11.6.4 Angle encoders
	11.7 Star cameras
		11.7.1 Pinhole camera
		11.7.2 Optical errors
		11.7.3 Imaging-chip errors
	11.8 GPS
	References
12 Attitude control
	12.1 Space story
	12.2 Introduction
	12.3 Attitude control phases
	12.4 Attitude control system
	12.5 Single-axis control
	12.6 Three-axis control
	12.7 Gravity-gradient control
	12.8 Nutation control
	12.9 Momentum-bias Earth-pointing control
	12.10 Mixed control
	12.11 Magnetic-torquer-only control
		12.11.1 BDot
	12.12 Low-bandwidth small-angle control
	12.13 Lyapunov control
	12.14 Orbit-transfer maneuver
	12.15 Docking
	12.16 Command distribution
		12.16.1 The optimal torque-distribution problem
		12.16.2 Reaction wheels
		12.16.3 Linear programming
	12.17 Attitude profile design
		12.17.1 Alignment method
		12.17.2 Minimizing the separation angle between vectors
		12.17.3 Computing the target-inertial vector
			12.17.3.1 Sun pointing
			12.17.3.2 Nadir pointing
			12.17.3.3 Latitude–longitude pointing
			12.17.3.4 Orbit-normal pointing
			12.17.3.5 LVLH pointing
	12.18 Actuator sizing
		12.18.1 Maneuvers
		12.18.2 Disturbances
	References
13 Momentum control
	13.1 Space story
	13.2 Introduction
	13.3 Momentum growth
	13.4 Control algorithms
	13.5 Control-torque generation
		13.5.1 Thruster control
			13.5.1.1 Direct
			13.5.1.2 Off-pulsing
		13.5.2 Magnetic control
			13.5.2.1 Magnetic field
			13.5.2.2 Instantaneous control
			13.5.2.3 Individual torquer control
			13.5.2.4 Average control
		13.5.3 Solar and aerodynamic pressure
			13.5.3.1 Introduction
			13.5.3.2 Torque-equilibrium attitude
			13.5.3.3 Momentum management with solar wings
			13.5.3.4 Gravity-gradient momentum management
14 Attitude estimation
	14.1 Introduction
	14.2 Star sensor
	14.3 Planet sensor
		14.3.1 Acquisition
		14.3.2 Roll and pitch measurements from a planet sensor
	14.4 Sun sensor
	14.5 Magnetometer
	14.6 GPS
	14.7 Earth/Sun/magnetic field
	14.8 Noise filters
	References
15 Recursive attitude estimation
	15.1 Introduction
	15.2 Batch methods
	15.3 Vector measurements
	15.4 Disturbance estimation
	15.5 Stellar-attitude determination
		15.5.1 Introduction
		15.5.2 Gyro-based attitude determination
		15.5.3 A single-axis Kalman filter with a gyro
		15.5.4 Star identification
	15.6 Kalman filter with roll, pitch, and yaw and a gyro
	15.7 Kalman filter with a quaternion measurement
16 Simulation
	16.1 Space story
	16.2 Introduction
	16.3 Digital simulation
		16.3.1 Numerical errors
		16.3.2 Model truncation
	16.4 Applications of simulation
		16.4.1 A sequence of simulations for ACS development
		16.4.2 Analysis support
			16.4.2.1 Sizing of a reaction wheel
			16.4.2.2 Disturbance modeling
			16.4.2.3 Control design
			16.4.2.4 End-to-end testing
		16.4.3 Performance verification
			16.4.3.1 Single case
			16.4.3.2 Grid test
			16.4.3.3 Numerical gain and phase margins
			16.4.3.4 Monte Carlo
			16.4.3.5 Commands
			16.4.3.6 Edge cases and stress cases
			16.4.3.7 Failure cases
		16.4.4 Interface verification
		16.4.5 Operator training
		16.4.6 Anomaly investigations
	16.5 Artificial damping
	References
17 Testing
	17.1 Space story
	17.2 A testing methodology
	17.3 Reliability
		17.3.1 Requirements flow and testing
		17.3.2 Testing lifecycle for the ACS flight software
	17.4 Flight-vehicle control-system testing
	17.5 Test levels (preflight)
	17.6 Test levels (flight)
	17.7 Simulations
	17.8 Software-development standards
	References
18 Spacecraft operations
	18.1 Space story
	18.2 Introduction
	18.3 Preparing for a mission
	18.4 Elements of flight operations
	18.5 Mission-operations timeline
	18.6 Mission-operations entities
	18.7 Mission-operations preparation
	18.8 Mission-operations organization
	18.9 Mission-control center
	18.10 Mission-operations example
19 Passive control-system design
	19.1 Introduction
	19.2 ISS orbit
	19.3 Gravity gradient
	19.4 Simulations
20 Spinning-satellite control-system design
	20.1 Introduction
	20.2 Spinning-spacecraft operation
	20.3 Transfer orbit
	20.4 Spinning transfer orbit
		20.4.1 Dynamics
		20.4.2 Actuators and sensors
		20.4.3 Changing the spin rate
		20.4.4 Spin-axis reorientation
		20.4.5 Attitude determination
		20.4.6 Delta-V engine firing
	References
21 Geosynchronous-satellite control-system design
	21.1 Space story
	21.2 Introduction
	21.3 Requirements
	21.4 The design process
	21.5 Mission-orbit design
	21.6 The geometry
	21.7 Control-system summary
	21.8 A mission architecture
	21.9 Design steps
	21.10 Spacecraft overview
	21.11 Disturbances
	21.12 Acquisition using the dual-spin turn
		21.12.1 Dynamics
		21.12.2 Actuators and sensors
		21.12.3 Initialization
		21.12.4 Simulation
		21.12.5 Pitch acquisition
	21.13 Dynamics
		21.13.1 Introduction
		21.13.2 Normal operations
		21.13.3 Dual-spin stability
		21.13.4 Station-keeping operations
		21.13.5 Actuators and sensors
		21.13.6 Control-system organization
		21.13.7 Modes
		21.13.8 Earth sensor
		21.13.9 Gyros
		21.13.10 Noise filtering
		21.13.11 Momentum-wheel pitch and tachometer loops
		21.13.12 Low-bandwidth roll/yaw control
		21.13.13 Thruster control
		21.13.14 High-bandwidth roll/yaw and pitch control
		21.13.15 Magnetic-torquer control
		21.13.16 Thruster control
		21.13.17 Actuator saturation
		21.13.18 Thruster resolution
	21.14 Summary
	References
22 Sun-nadir pointing control
	22.1 Space story
	22.2 Introduction
	22.3 Coordinate frames
	22.4 Sun-nadir pointing
	22.5 Components
		22.5.1 Sensors
		22.5.2 Actuators
	22.6 Attitude determination
		22.6.1 Roll
		22.6.2 Pitch
		22.6.3 Sun-sensor eye preprocessing
		22.6.4 Solar-array pitch
		22.6.5 Yaw
	22.7 Control
		22.7.1 Reaction-wheel loop
		22.7.2 Attitude loop
		22.7.3 Solar-array control
		22.7.4 Momentum control
23 Lander control
	23.1 Space story
	23.2 Landers
	23.3 Landing concept of operations
	23.4 Selenographic coordinates
	23.5 Linear-tangent guidance law
	23.6 Lunar-lander model
	23.7 Optimal descent
	23.8 Descent control
	23.9 Terminal control
	23.10 Altitude hold
	23.11 Bang-bang landing algorithm
	23.12 Simulation results
	References
24 James Webb Space Telescope ACS design
	24.1 Requirements
	24.2 Spacecraft model
	24.3 Disturbances
	24.4 Attitude maneuvers
	24.5 Momentum control
	24.6 Attitude control
	24.7 Torque distribution
	24.8 Attitude determination
	24.9 Simulation
	References
25 CubeSat control system
	25.1 Space story
	25.2 Introduction
	25.3 Requirements
	25.4 Actuator and sensor selection
	25.5 Design
	25.6 Control-system design
	25.7 Attitude determination
	25.8 Simulation
26 Microwave Anisotropy Satellite
	26.1 The WMAP mission
	26.2 ACS overview
	26.3 Control modes
	26.4 Sensing and actuation
	26.5 Control-system design
	26.6 Nested loops
	26.7 Simulation results
	References
27 Solar sails
	27.1 Introduction
	27.2 Gyrostat with a moving mass
	27.3 Thin-membrane model
	27.4 Momentum control
	27.5 Attitude control
	27.6 Architecture
	References
A Math
	A.1 Vectors and matrices
		A.1.1 Notation
		A.1.2 Vector and matrix representations of operations
		A.1.3 Matrix operations
		A.1.4 Special matrices
		A.1.5 Useful matrix–vector identities
	A.2 Numerical integration
		A.2.1 Linearizing a system
		A.2.2 Nonlinear
			A.2.2.1 Numerical integration methods
		A.2.3 Discontinuities
	A.3 Fourier series
		A.3.1 Trigonometric identities
		A.3.2 Sine and cosine Fourier series
	A.4 Spherical geometry
	A.5 The chain rule in calculus
B Probability and statistics
	B.1 Space story
	B.2 Introduction
	B.3 Axiomatic probability
	B.4 Binomial theorem
	B.5 Probability distributions
	B.6 Evaluating measurements
	B.7 Combining errors
	B.8 Multivariate normal distributions
	B.9 Random signals
	B.10 Outliers
	B.11 Noise models
	B.12 Monte Carlo methods
	References
C Time
	C.1 Time scales
	C.2 Earth rotation
	C.3 Julian date
	C.4 Time standards
		C.4.1 Local time
		C.4.2 UTC
		C.4.3 GPS
		C.4.4 Loran-C
		C.4.5 TAI
		C.4.6 Planetary days
	References
D Coordinate systems
	D.1 Earth-centered inertial coordinates
	D.2 Local vertical/local horizontal coordinates
	D.3 Heliocentric coordinates
	D.4 International Space Station coordinates
	D.5 Selenographic frame
	D.6 Areocentric (Mars) coordinates
E Ephemeris
	E.1 Introduction
	E.2 Planetary orbits
	E.3 Asteroid orbits
	E.4 Planetary orientation
	E.5 Asteroid dynamics
	E.6 Stars
	References
F Laplace transforms
	F.1 Using Laplace transforms
	F.2 Useful transforms
G Control theory
	G.1 Introduction
	G.2 Simple control system
	G.3 The general control system
	G.4 Fundamental relationships
	G.5 Tracking errors
	G.6 State-space closed-loop equations
	G.7 Approaches to robust control
		G.7.1 Introduction
		G.7.2 Modeling uncertainty
		G.7.3 Control-structure design
		G.7.4 Nyquist-like techniques
		G.7.5 LQG methods
		G.7.6 H∞ and μ synthesis
	G.8 Single-input–single-output control design
		G.8.1 Introduction
		G.8.2 Elementary loop compensation
			G.8.2.1 First-order compensators
			G.8.2.2 Generalized integrator
			G.8.2.3 Gain compensation of a double-integrator plant
			G.8.2.4 More complex compensation of a double-integrator plant
	G.9 Digital control
		G.9.1 Introduction
		G.9.2 Modified continuous design
			G.9.2.1 Introduction
			G.9.2.2 The sampler
			G.9.2.3 The delay
			G.9.2.4 The zero-order hold
			G.9.2.5 Pulsewidth modulation
	G.10 Continuous-to-discrete transformations
		G.10.1 The difference equation
		G.10.2 Transforming from the s plane to the z plane
		G.10.3 Transformation of a differentiator
		G.10.4 State estimator
	G.11 Flexible-structure control
		G.11.1 Introduction
		G.11.2 Two coupled inertias
		G.11.3 Double integrator
		G.11.4 Control algorithms
		G.11.5 Lead compensation of the minimum-phase system
		G.11.6 Noncollocated sensor and actuator
	G.12 Model-following control
	G.13 Double-integrator control
		G.13.1 Introduction
		G.13.2 Linear control
		G.13.3 Phase-plane controller
		G.13.4 Control limiting
		G.13.5 Cross-axis coupling
	G.14 Lyapunov control
		G.14.1 Background
		G.14.2 Theory
		G.14.3 Nonlinear rate damper
	G.15 First- and second-order systems
	G.16 Inner and outer loops
H Estimation theory
	H.1 Estimation theory
		H.1.1 Conversion from continuous to discrete time
	H.2 The Kalman-filter algorithm
	H.3 Bayesian derivation
	H.4 Extended Kalman filter
	H.5 Unscented Kalman filter
	H.6 UKF state-prediction step
	H.7 Kalman-filter example
		H.7.1 Dynamical and measurement model
		H.7.2 Linear Kalman filter
		H.7.3 Extended Kalman filter
		H.7.4 Unscented Kalman filter
	References
I Orbit theory
	I.1 Space story
	I.2 Introduction
	I.3 Representations of orbits
		I.3.1 Orbital geometry
		I.3.2 Cartesian coordinates
		I.3.3 Keplerian elements
		I.3.4 Equinoctial elements
	I.4 Propagating orbits
		I.4.1 Introduction
		I.4.2 Kepler propagation
		I.4.3 Numerical integration
	I.5 Gravitational acceleration
		I.5.1 Point masses
		I.5.2 Planetary asymmetries
	I.6 Linearized orbit equations
J Optics
	J.1 Optical sensors
		J.1.1 Optical nomenclature
		J.1.2 Telescope types
		J.1.3 Geometry of imaging
		J.1.4 Telescope performance
			J.1.4.1 Geometric
			J.1.4.2 Errors
		J.1.5 Pinhole camera
	J.2 Radiometry
		J.2.1 Mathematical basis for position and attitude determination using a camera
		J.2.2 Basic radiometry
		J.2.3 Radiosity
		J.2.4 Radiometric sources
		J.2.5 Noise and performance factors
			J.2.5.1 Fill factor
			J.2.5.2 Illumination side
		J.2.6 Dynamic range
		J.2.7 Blooming
		J.2.8 Quantum efficiency
			J.2.8.1 Dark current
			J.2.8.2 Fixed-pattern noise
			J.2.8.3 Readout noise
			J.2.8.4 Radiation hardness
		J.2.9 Imaging-chip theory
			J.2.9.1 Dark current
			J.2.9.2 Cosmic rays
			J.2.9.3 Thermal noise
			J.2.9.4 Transfer efficiency
			J.2.9.5 Reset noise
			J.2.9.6 Photon noise
			J.2.9.7 Quantization noise
			J.2.9.8 Total noise
			J.2.9.9 Blooming
			J.2.9.10 Linearity
			J.2.9.11 Amplifier noise
		J.2.10 Data reduction
	References
K Star-camera algorithms
	K.1 Space story
	K.2 Introduction
	K.3 Center-of-mass star centroiding
		K.3.1 Background noise
		K.3.2 Creating a star blob
		K.3.3 Center-of-mass
	K.4 Star identification
		K.4.1 Catalog processing
		K.4.2 Sorting star pairs with k-vector
	K.5 Fine centroiding
	References
L Magnetic-hysteresis damping
	L.1 Magnetic-hysteresis damper model
	L.2 Energy-dissipation analysis
	References
M Machine intelligence
	M.1 Space story
	M.2 Introduction
	M.3 Branches of machine intelligence
	M.4 Stored command lists
	M.5 Deep Space 1
	M.6 Neural networks
	M.7 Static Earth sensors
	M.8 Expert systems
	M.9 Reinforcement learning
		M.9.1 Introduction
		M.9.2 Optimal attitude trajectory
		M.9.3 Single-axis optimal attitude trajectory
	References
N Glossary of acronyms
Index