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E-raamat: Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based Approach

  • Formaat: 340 pages
  • Ilmumisaeg: 06-Feb-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429822148
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Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based ApproachSuurem pilt
  • Formaat: 340 pages
  • Ilmumisaeg: 06-Feb-2019
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429822148
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This book discusses all spacecraft attitude control-related topics: spacecraft (including attitude measurements, actuator, and disturbance torques), modeling, spacecraft attitude determination and estimation, and spacecraft attitude controls. Unlike other books addressing these topics, this book focuses on quaternion-based methods because of its many merits. The book lays a brief, but necessary background on rotation sequence representations and frequently used reference frames that form the foundation of spacecraft attitude description. It then discusses the fundamentals of attitude determination using vector measurements, various efficient (including very recently developed) attitude determination algorithms, and the instruments and methods of popular vector measurements. With available attitude measurements, attitude control designs for inertial point and nadir pointing are presented in terms of required torques which are independent of actuators in use. Given the required control torques, some actuators are not able to generate the accurate control torques, therefore, spacecraft attitude control design methods with achievable torques for these actuators (for example, magnetic torque bars and control moment gyros) are provided. Some rigorous controllability results are provided.The book also includes attitude control in some special maneuvers, such as orbital-raising, docking and rendezvous, that are normally not discussed in similar books. Almost all design methods are based on state-spaced modern control approaches, such as linear quadratic optimal control, robust pole assignment control, model predictive control, and gain scheduling control. Applications of these methods to spacecraft attitude control problems are provided. Appendices are provided for readers who are not familiar with these topics.

Arvustused

"This book provides a good and comprehensive overview of spacecraft attitude dynamics, determination and control, including advances in the quaternion-based approach, with application to practical problems such as coupled attitude and orbit control and model predictive optimal control with realistic actuators constraints. In conclusion, the book is a good and useful resource for researchers and research minded engineers wishing to develop a more detailed understanding of some of the latest advances in robust pole placement and model predictive control to spacecraft attitude control. The quaternion based approach is applied to practical attitude estimation and attitude control problems ranging from nadir pointing using reaction wheels or CMGs to momentum dumping using magnetic torquers and coupled attitude and orbit control for spacecraft docking." Nadjim Horri, Coventry University, The Aeronautical Journal, Oct 2020

Preface v
1 Introduction
1(6)
1.1 Organization of the Book
3(3)
1.2 Some Basic Notations and Identities
6(1)
2 Orbit Dynamics and Properties
7(14)
2.1 Orbit Dynamics
7(4)
2.2 Conic Section and Different Orbits
11(3)
2.2.1 Circular Orbits
11(1)
2.2.2 Elliptic Orbits
12(2)
2.2.3 Hyperbolic Orbits
14(1)
2.3 Property of Keplerian Orbits
14(2)
2.4 Keplerian Orbits in Three-dimensional Space
16(5)
2.4.1 Celestial Inertial Coordinate System
17(1)
2.4.2 Orbital Parameters
17(4)
3 Rotational Sequences and Quaternion
21(22)
3.1 Some Frequently used Frames
22(2)
3.1.1 Body-fixed Frame
22(1)
3.1.2 The Earth Centered Inertial (ECI) Frame
22(1)
3.1.3 Local Vertical Local Horizontal Frame
23(1)
3.1.4 South-east Zenith (SEZ) Frame
23(1)
3.1.5 North-east Nadir (NED) Frame
23(1)
3.1.6 The Earth-centered Earth-fixed (ECEF) Frame
23(1)
3.1.7 The Orbit (Perifocal PQW) Frame
24(1)
3.1.8 The Spacecraft Coordinate (RSW) Frame
24(1)
3.2 Rotation Sequences and Mathematical Representations
24(7)
3.2.1 Representing a Fixed Point in a Rotational Frame
24(2)
3.2.2 Representing a Rotational Point in a Fixed Frame
26(1)
3.2.3 Rotations in Three-dimensional Space
27(2)
3.2.4 Rotation from One Frame to Another Frame
29(1)
3.2.5 Rate of Change of the Direction Cosine Matrix
30(1)
3.2.6 Rate of Change of Vectors in Rotational Frame
30(1)
3.3 Transformation between Coordinate Systems
31(4)
3.3.1 Transformation from ECI (XYZ) to PQW Coordinate
31(1)
3.3.2 Transformation from ECI (XYZ) to RSW Coordinate
32(1)
3.3.3 Transformation from Six Classical Parameters to (v, r)
32(2)
3.3.4 Transformation from (v, r) to Six Classical Parameters
34(1)
3.4 Quaternion and Its Properties
35(8)
3.4.1 Equality and Addition
36(1)
3.4.2 Multiplication and the Identity
36(1)
3.4.3 Complex Conjugate, Norm, and Inverse
37(1)
3.4.4 Rotation by Quaternion Operator
38(3)
3.4.5 Matrix Form of Quaternion Production
41(1)
3.4.6 Derivative of the Quaternion
41(2)
4 Spacecraft Dynamics and Modeling
43(10)
4.1 The General Spacecraft System Equations
45(2)
4.1.1 The Dynamics Equation
45(1)
4.1.2 The Kinematics Equation
45(2)
4.2 The Inertial Pointing Spacecraft Model
47(1)
4.2.1 The Nonlinear Inertial Pointing Spacecraft Model
47(1)
4.2.2 The Linearized Inertial Pointing Spacecraft Models
47(1)
4.3 Nadir Pointing Momentum Biased Spacecraft Model
48(5)
4.3.1 The Nonlinear Nadir Pointing Spacecraft Model
48(1)
4.3.2 The Linearized Nadir Pointing Spacecraft Model
49(4)
5 Space Environment and Disturbance Torques
53(12)
5.1 Gravitational Torques
54(2)
5.2 Atmosphere-induced Torques
56(2)
5.3 Magnetic Field-induced Torques
58(5)
5.4 Solar Radiation Torques
63(1)
5.5 Internal Torques
64(1)
6 Spacecraft Attitude Determination
65(18)
6.1 Wahba's Problem
66(1)
6.2 Davenport's Formula
67(1)
6.3 Attitude Determination Using QUEST and FOMA
68(1)
6.4 Analytic Solution of Two Vector Measurements
69(5)
6.4.1 The Minimum-angle Rotation Quaternion
69(1)
6.4.2 The General Rotation Quaternion
70(2)
6.4.3 Attitude Determination Using Two Vector Measurements
72(2)
6.5 Analytic Formula for General Case
74(4)
6.5.1 Analytic Formula
75(2)
6.5.2 Numerical Test
77(1)
6.6 Riemann-Newton Method
78(2)
6.7 Rotation Rate Determination Using Vector Measurements
80(3)
7 Astronomical Vector Measurements
83(6)
7.1 Stars' Vectors
83(1)
7.2 Earth's Magnetic Field Vectors
84(1)
7.2.1 Ephemeris Earth's Magnetic Field Vector
84(1)
7.2.2 Measured Earth's Magnetic Field Vector
85(1)
7.3 Sun Vector
85(4)
7.3.1 Ephemeris Sun Vector
85(2)
7.3.2 Sun Vector Measurement
87(2)
8 Spacecraft Attitude Estimation
89(8)
8.1 Extended Kalman Filter Using Reduced Quaternion Model
90(4)
8.2 Kalman Filter Using Reduced Quaternion Model
94(2)
8.3 A Short Comment
96(1)
9 Spacecraft Attitude Control
97(22)
9.1 LQR Design for Nadir Pointing Spacecraft
98(1)
9.2 The LQR Design for Inertial Pointing Spacecraft
99(8)
9.2.1 The Analytic Solution
99(1)
9.2.2 The Global Stability of the Design
100(2)
9.2.3 The Closed-loop Poles
102(4)
9.2.4 The Simulation Result
106(1)
9.3 The LQR Design is a Robust Pole Assignment
107(12)
9.3.1 Robustness of the Closed-loop Poles
107(1)
9.3.2 The Robust Pole Assignment
108(5)
9.3.3 Disturbance Rejection of Robust Pole Assignment
113(1)
9.3.4 A Design Example
114(5)
10 Spacecraft Actuators
119(6)
10.1 Reaction Wheel and Momentum Wheel
119(1)
10.2 Control Moment Gyros
120(1)
10.3 Magnetic Torque Rods
121(2)
10.4 Thrusters
123(2)
11 Spacecraft Control Using Magnetic Torques
125(54)
11.1 The Linear Time-varying Model
127(3)
11.2 Spacecraft Controllability Using Magnetic Torques
130(7)
11.3 LQR Design Based on Periodic Riccati Equation
137(11)
11.3.1 Preliminary Results
138(2)
11.3.2 Solution of the Algebraic Riccati Equation
140(1)
11.3.3 Solution of the Periodic Riccati Algebraic Equation
141(5)
11.3.4 Simulation Test
146(2)
11.4 Attitude and Desaturation Combined Control
148(17)
11.4.1 Spacecraft Model for Attitude and Reaction Wheel Desaturation Control
151(3)
11.4.2 Linearized Model for Attitude and Reaction Wheel Desaturation Control
154(5)
11.4.3 The LQR Design
159(1)
11.4.3.1 Case 1: im = 0
159(1)
11.4.3.2 Case 2: im ≠ 0
160(1)
11.4.4 Simulation Test and Implementation Consideration
161(1)
11.4.4.1 Comparison with the Design without Reaction Wheels
161(2)
11.4.4.2 Control of the Nonlinear System
163(2)
11.4.4.3 Implementation to Real System
165(1)
11.5 LQR Design Based on a Novel Lifting Method
165(14)
11.5.1 Periodic LQR Design Based on Linear Periodic System
166(2)
11.5.2 Periodic LQR Design Based on Linear Time-invariant System
168(6)
11.5.3 Implementation and Numerical Simulation
174(1)
11.5.3.1 Implementation Consideration
174(2)
11.5.3.2 Simulation Test for the Problem in Section 11.3
176(1)
11.5.3.3 Simulation Test for the Problem in Section 11.4
176(3)
12 Attitude Maneuver and Orbit-Raising
179(12)
12.1 Attitude Maneuver
179(2)
12.2 Orbit-raising
181(4)
12.3 Comparing Quaternion and Euler Angle Designs
185(6)
13 Attitude MPC Control
191(44)
13.1 Some Technical Lemmas
193(1)
13.2 Constrained MPC and Convex QP with Box Constraints
194(4)
13.3 Central Path of Convex QP with Box Constraints
198(1)
13.4 An Algorithm for Convex QP with Box Constraints
199(10)
13.5 Convergence Analysis
209(5)
13.6 Implementation Issues
214(5)
13.6.1 Termination Criterion
214(1)
13.6.2 Initial (x0, y0, z0, λ0, γ0) N2(θ)
214(1)
13.6.3 Step Size
215(3)
13.6.4 The Practical Implementation
218(1)
13.7 A Design Example
219(2)
13.8 Proofs of Technical lemmas
221(14)
14 Spacecraft Control Using CMG
235(14)
14.1 Spacecraft Model Using Variable-speed CMG
237(4)
14.2 Spacecraft Attitude Control Using VSCMG
241(3)
14.2.1 Gain Scheduling Control
241(1)
14.2.2 Model Predictive Control
242(1)
14.2.3 Robust Pole Assignment
243(1)
14.3 Simulation Test
244(5)
15 Spacecraft Rendezvous and Docking
249(18)
15.1 Introduction
249(2)
15.2 Spacecraft Model for Rendezvous
251(10)
15.2.1 The Model for Translation Dynamics
251(6)
15.2.2 The Model for Attitude Dynamics
257(2)
15.2.3 A Complete Model for Rendezvous and Docking
259(2)
15.3 Model Predictive Control System Design
261(2)
15.4 Simulation Test
263(4)
Appendices
Appendix A First Order Optimally Conditions
267(4)
A.1 Problem Introduction
267(1)
A.2 Karush-Kuhn-Tucker Conditions
268(3)
Appendix B Optimal Control
271(8)
B.1 General Discrete-time Optimal Control Problem
271(1)
B.2 Solution of Discrete-time LQR Control Problem
272(2)
B.3 LQR Control for Discrete-time LTI System
274(5)
Appendix C Robust Pole Assignment
279(20)
C.1 Eigenvalue Sensitivity to the Perturbation
279(5)
C.2 Robust Pole Assignment Algorithms
284(11)
C.3 Misrikhanov and Ryabchenko Algorithm
295(4)
References 299(22)
Index 321
Yaguang Yang received his B.S. (1982) and M.S. (1985) degrees from Huazhong University of Science and Technology, China. From 1985 to 1990, he was a lecturer at Zhejiang University in China. In 1996 he received a PhD degree from the Department of Electrical and Computer Engineering at the University of Maryland, College Park. He designed and implemented control systems at UKIRT, CIENA, ITT, and Orbital Sciences Corporation. He is currently with the US Nuclear Regulatory Commission.
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