Spacecraft Attitude Dynamics and Control

Spacecraft Attitude Dynamics and ControlPage 1

V. A. Chobotov

Spacecraft Attitude Dynamics and Control

V. A. Chobotov

Chapter 1 Kinematics and Dynamics of Angular Motion1

1.1 Spacecraft Attitude Control Systems1

1.1.1 Spin Control1

1.1.2 Dual-Spin Control1

1.1.3 Three-Axis Active Control1

1.1.4 Momentum Bias Control2

1.1.5 Passive (Gravity Gradient) Control2

1.1.6 Attitude Sensors3

1.1.7 Control Actuators3

1.1.8 Control System Comparisons3

1.2 Basic Concepts of Kinematics4

1.2.1 Velocity and Acceleration4

1.2.2 Euler Angles4

1.2.3 Sequential Orthogonal Rotations5

1.2.3.1 Classical Euler Sequence of Rotations6

1.2.3.2 Euler Rates7

1.2.4 Direction Cosines7

1.2.4.1 Kinematical Equations of Poisson8

1.2.5 Quaternions8

1.2.6 Combined Rotations with Quaternions10

1.3 Fundamentals of Dynamics10

1.3.1 Angular Momentum and Kinetic Energy of a Body10

1.3.2 Principal Moments of Inertia and Axes12

1.3.3 Kinetic Energy13

1.3.4 Euler’s Dynamical Equations14

1.3.5 Torque-Free Body of Revolution Example14

1.4 References16

Chapter 2 Spin Stabilization17

2.1 Introduction17

2.2 Control Requirements17

2.3 Response of the Uncontrolled Vehicle17

2.4 Precession of the Satellite19

2.5 Stability of Motion19

2.6 Passive Nutation Control19

2.7 Active Nutation Damping21

2.8 Vehicle Reorientation in Space22

2.9 Spin-Rate Decrease Due to Fuel Expenditure (Jet Damping)23

2.9.1 Approximate Solution24

2.10 Yo-yo Despin24

2.11 Vehicle Response to External Disturbances25

2.11.1 Response to a Torque Impulse26

2.11.2 Response to Body-Fixed Torques26

2.11.2.1 Equations of Motion26

2.11.3 Kinematical Relationships26

2.11.4 Sequence of Motions27

2.12 Separation Analysis29

2.12.1 Ideal Separation for Spinning Bodies29

2.13 Recommended Practice30

2.13.1 Ceneral Practices30

2.13.2 Compact Near-Rigid Body31

2.13.3 Spin Resonance31

2.14 References32

Chapter 3 Dual-Spin Stabilization33

3.1 Introduction33

3.2 Design Considerations for a Dual-Spin Spacecraft33

3.3 Sensing Subsystem33

3.4 Despin Control System33

3.5 Momentum and Reaction Jet Sizing35

3.6 Equations of Motion and Equilibrium36

3.7 Simplified Dual-Spin System Dynamics37

3.7.1 Perfectly Symmetric System37

3.8 Dual-Spin System Stability Considerations38

3.9 Practical Implications39

3.9.1 Thrusting Maneuvers39

3.9.2 Conditions Leading to Nutation Growth39

3.10 Recommended Practice40

3.11 References40

Chapter 4 Three Axis Active Control41

4.1 Pure Jet Systems41

4.2 Typical Sequence of Control Operations41

4.3 Acquisition Approaches41

4.4 On-Orbit Operation42

4.5 Servomechanisms44

4.5.1 Laplace Transforms45

4.5.2 Basic Properties45

4.5.3 Transform Examples46

4.6 The Standard Diagram46

4.6.1 Single Loop Servo with Unity Feedback47

4.6.2 Servo with Nonunity Feedback47

4.7 A Simple Servomechanism48

4.8 Stability49

4.8.1 Poles and Zeros49

4.9 s-Plane Quadratic Transfer Function Response50

4.10 Attitude Control System Example52

4.10.1 Transfer Function Analysis53

4.10.2 Response to Step Disturbance Torque53

4.11 Graphical Methods54

4.11.1 Nyquist Diagram54

4.11.2 Bode Diagram55

4.11.3 Nichols Diagram55

4.12 Time and Frequency Response of a Position Control Servo56

4.13 The Root-Locus Method58

4.14 Structural Resonance Considerations61

4.15 Recommended Practice for Active Control Systems61

4.15.1 General Considerations61

4.15.2 Thrusting Maneuvers64

4.15.3 Structural Flexibility64

4.16 References64

Chapter 5 Momentum Exchange Systems65

5.1 Introduction65

5.2 Reaction Wheel Systems65

5.2.1 Response to Attitude Error66

5.2.2 Response to an Impulse66

5.2.3 Control Torque Required67

5.3 Momentum Bias System67

5.3.1 Equations of Motion68

5.3.2 Roll-Yaw Control71

5.3.3 Pitch On-Orbit Wheel Control73

5.4 Control Moment Gyro Systems73

5.4.1 Single CMG Control System Dynamics73

5.4.2 Component Equations74

5.5 References75

Chapter 6 The Environmental Effects77

6.1 Solar Radiation Pressure77

6.1.1 Radiation Force Under Specular Reflection78

6.1.2 Radiation Force Under Diffuse Reflection79

6.1.3 Radiation Force Limiting Cases79

6.1.4 Radiation Torque79

6.1.5 Example — Radiation Torque on a Geosynchronous Satellite80

6.1.6 Momentum Change80

6.2 Gravitational and Inertial Gradients80

6.2.1 Gravitational Field80

6.2.2 Inertial Gradient Field82

6.2.3 Circular Orbit Case82

6.3 Gravity Gradient Torque82

6.4 Geomagnetic Field84

6.4.1 The Near Field Effects84

6.4.2 The Far Field Effects87

6.4.3 The Interplanetary Region87

6.4.3 The Ineraction Region89

6.4.3 The Magnetosphere89

6.4.3 Magnetic Torques89

6.5 References90

Chapter 7 Passive Gravity Gradient Stabilization91

7.1 Introduction91

7.1.1 Booms for Gravity Gradient Systems91

7.1.2 Libration Dampers92

7.2 Equations of Motion93

7.3 Restoring Torques94

7.4 Natural Frequencies94

7.5 Stability Considerations97

7.6 Eccentric Orbit98

7.7 Capture Requirements98

7.7 Steady State Requirements99

7.8 Space Shuttle Gravity Gradient Stabilization — An Example99

7.8.1 Aerodynamic Torque Effects100

7.8.2 Flight Results100

7.9 Tethered Satellite Systems100

7.9.1 Tethered Satellite System Experiment100

7.9.2 Tether Propulsion102

7.10 Recommended Practice for Gravitational Stabilization of
Satellites103

7.11 References104

Chapter 8 Magnetic Stabilization Methods105

8.1 Spin Rate (Momentum) Control105

8.1.1 Precession Control105

8.1.2 Sun Synchronous Spacecraft Example107

8.1.3 Passive Spin Rate Control107

8.2 Control and Minimization of Magnetic Disturbance108

8.2.1 Materials109

8.2.2 Components109

8.2.3 Current Loops109

8.2.4 Dipole Determination110

8.3 Recommended Practice for the Control of the Spacecraft

Magnetic Moment110

8.4 References111

Chapter 9 Stability of Motion113

9.1 Types of Stability Concepts113

9.2 Stability Criteria for Linear Systems113

9.2.1 Routh-Hurwitz Conditions113

9.2.2 Alternate Conditions for Second Order Systems114

9.2.3 Quasilinear Systems115

9.3 Stability in Nonlinear Systems115

9.3.1 Matrix Differential Equations116

9.3.2 Some Definitions116

9.3.3 Stability118

9.3.4 Asymptotic Stability118

9.4 Theory of the Direct Method of Liapunov118

9.4.1 Theorems119

9.4.2 Criteria of Stability for the First Approximation of Perturbed Motion120

9.5 Application to Automatic Control Systems121

9.5.1 Criteria for Asymptotic Stability for Some Nonlinear Systems122

9.6 A General Method for the Construction of Liapunov Functions
for Linear and Nonlinear Systems122

9.6.1 Extension to Nonlinear Systems123

9.7 Synthesis of a Control System by the Direct Method124

9.8 Stability Analysis Example124

9.9 References126

Appendix A Problem Sets127

A.1 Problem Set 1: Kinematics127

A.2 Problem Set 2: Dynamics128

A.3 Problem Set 3: Control Theory132

A.4 Problem Set 4: Gravity Gradient, Stability, and Magnetic

Stabilization134

Appendix B Nomenclature137

B.1 Lower and Uppercase Symbols137

B.2 Greek Symbols137

B.3 Other Symbols137

Index139