Advanced Control of Aircraft, Spacecraft and Rockets

Ashish Tewari is a Professor in the Department of Aerospace Engineering at the IIT-Kanpur. He specializes in flight mechanics and control, and his research areas include attitude dynamics and control, re-entry flight dynamics and control, non-linear optimal control and active control of flexible flight and structures. He has authored 2 books Atmospheric and Space Flight Dynamics and Modern Control Design with MATLAB and SIMULINK, and over 40 refereed journal and conference papers.

• Series Preface xiii Preface xv1 Introduction 11.1 Notation and Basic Definitions 11.2 Control Systems 31.2.1 Linear Tracking Systems 71.2.2 Linear Time-Invariant Tracking Systems 91.3 Guidance and Control of Flight Vehicles 101.4 Special Tracking Laws 131.4.1 Proportional Navigation Guidance 131.4.2 Cross-Product Steering 161.4.3 Proportional-Integral-Derivative Control 191.5 Digital Tracking System 241.6 Summary 25Exercises 26References 282 Optimal Control Techniques 292.1 Introduction 292.2 Multi-variable Optimization 312.3 Constrained Minimization 332.3.1 Equality Constraints 342.3.2 Inequality Constraints 382.4 Optimal Control of Dynamic Systems 412.4.1 Optimality Conditions 432.5 The Hamiltonian and the Minimum Principle 442.5.1 Hamilton–Jacobi–Bellman Equation 452.5.2 Linear Time-Varying System with Quadratic Performance Index 472.6 Optimal Control with End-Point State Equality Constraints 482.6.1 Euler–Lagrange Equations 502.6.2 Special Cases 502.7 Numerical Solution of Two-Point Boundary Value Problems 522.7.1 Shooting Method 542.7.2 Collocation Method 572.8 Optimal Terminal Control with Interior Time Constraints 612.8.1 Optimal Singular Control 622.9 Tracking Control 632.9.1 Neighboring Extremal Method and Linear Quadratic Control 642.10 Stochastic Processes 692.10.1 Stationary Random Processes 752.10.2 Filtering of Random Noise 772.11 Kalman Filter 772.12 Robust Linear Time-Invariant Control 812.12.1 LQG/LTR Method 822.12.2 H2/H?E?E Design Methods 892.13 Summary 96Exercises 98References 1013 Optimal Navigation and Control of Aircraft 1033.1 Aircraft Navigation Plant 1043.1.1 Wind Speed and Direction 1103.1.2 Navigational Subsystems 1123.2 Optimal Aircraft Navigation 1153.2.1 Optimal Navigation Formulation 1163.2.2 Extremal Solution of the Boundary-Value Problem: Long-Range Flight Example 1193.2.3 Great Circle Navigation 1213.3 Aircraft Attitude Dynamics 1283.3.1 Translational and Rotational Kinetics 1323.3.2 Attitude Relative to the Velocity Vector 1353.4 Aerodynamic Forces and Moments 1363.5 Longitudinal Dynamics 1393.5.1 Longitudinal Dynamics Plant 1423.6 Optimal Multi-variable Longitudinal Control 1453.7 Multi-input Optimal Longitudinal Control 1473.8 Optimal Airspeed Control 1483.8.1 LQG/LTR Design Example 1493.8.2 H?E?E Design Example 1603.8.3 Altitude and Mach Control 1663.9 Lateral-Directional Control Systems 1733.9.1 Lateral-Directional Plant 1733.9.2 Optimal Roll Control 1773.9.3 Multi-variable Lateral-Directional Control: Heading-Hold Autopilot 1803.10 Optimal Control of Inertia-Coupled Aircraft Rotation 1833.11 Summary 189Exercises 192References 1944 Optimal Guidance of Rockets 1954.1 Introduction 1954.2 Optimal Terminal Guidance of Interceptors 1954.3 Non-planar Optimal Tracking System for Interceptors: 3DPN 1994.4 Flight in a Vertical Plane 2084.5 Optimal Terminal Guidance 2114.6 Vertical Launch of a Rocket (Goddard’s Problem) 2164.7 Gravity-Turn Trajectory of Launch Vehicles 2194.7.1 Launch to Circular Orbit: Modulated Acceleration 2204.7.2 Launch to Circular Orbit: Constant Acceleration 2274.8 Launch of Ballistic Missiles 2284.8.1 Gravity-Turn with Modulated Forward Acceleration 2324.8.2 Modulated Forward and Normal Acceleration 2334.9 Planar Tracking Guidance System 2374.9.1 Stability, Controllability, and Observability 2414.9.2 Nominal Plant for Tracking Gravity-Turn Trajectory 2434.10 Robust and Adaptive Guidance 2474.11 Guidance with State Feedback 2504.11.1 Guidance with Normal Acceleration Input 2504.12 Observer-Based Guidance of Gravity-Turn Launch Vehicle 2544.12.1 Altitude-Based Observer with Normal Acceleration Input 2554.12.2 Bi-output Observer with Normal Acceleration Input 2604.13 Mass and Atmospheric Drag Modeling 2664.14 Summary 274Exercises 275References 2755 Attitude Control of Rockets 2775.1 Introduction 2775.2 Attitude Control Plant 2775.3 Closed-Loop Attitude Control 2815.4 Roll Control System 2815.5 Pitch Control of Rockets 2825.5.1 Pitch Program 2825.5.2 Pitch Guidance and Control System 2835.5.3 Adaptive Pitch Control System 2885.6 Yaw Control of Rockets 2945.7 Summary 295Exercises 295Reference 2966 Spacecraft Guidance Systems 2976.1 Introduction 2976.2 Orbital Mechanics 2976.2.1 Orbit Equation 2986.2.2 Perifocal and Celestial Frames 2996.2.3 Time Equation 3016.2.4 Lagrange’s Coefficients 3046.3 Spacecraft Terminal Guidance 3056.3.1 Minimum Energy Orbital Transfer 3076.3.2 Lambert’s Theorem 3116.3.3 Lambert’s Problem 3136.3.4 Lambert Guidance of Rockets 3226.3.5 Optimal Terminal Guidance of Re-entry Vehicles 3276.4 General Orbital Plant for Tracking Guidance 3346.5 Planar Orbital Regulation 3396.6 Optimal Non-planar Orbital Regulation 3456.7 Summary 352Exercises 352References 3557 Optimal Spacecraft Attitude Control 3577.1 Introduction 3577.2 Terminal Control of Spacecraft Attitude 3577.2.1 Optimal Single-Axis Rotation of Spacecraft 3587.3 Multi-axis Rotational Maneuvers of Spacecraft 3647.4 Spacecraft Control Torques 3757.4.1 Rocket Thrusters 3757.4.2 Reaction Wheels, Momentum Wheels and Control Moment Gyros 3777.4.3 Magnetic Field Torque 3787.5 Satellite Dynamics Plant for Tracking Control 3797.6 Environmental Torques 3807.6.1 Gravity-Gradient Torque 3827.7 Multi-variable Tracking Control of Spacecraft Attitude 3837.7.1 Active Attitude Control of Spacecraft by Reaction Wheels 3857.8 Summary 389Exercises 389References 390Appendix A: Linear Systems 391A.1 Definition 391A.2 Linearization 392A.3 Solution to Linear State Equations 392A.3.1 Homogeneous Solution 393A.3.2 General Solution 393A.4 Linear Time-Invariant System 394A.5 Linear Time-Invariant Stability Criteria 395A.6 Controllability of Linear Time-Invariant Systems 395A.7 Observability of Linear Time-Invariant Systems 395A.8 Transfer Matrix 396A.9 Singular Value Decomposition 396A.10 Linear Time-Invariant Control Design 397A.10.1 Regulator Design by Eigenstructure Assignment 397A.10.2 Regulator Design by Linear Optimal Control 398A.10.3 Linear Observers and Output Feedback Compensators 398References 400Appendix B: Stability 401B.1 Preliminaries 401B.2 Stability in the Sense of Lagrange 402B.3 Stability in the Sense of Lyapunov 404B.3.1 Asymptotic Stability 406B.3.2 Global Asymptotic Stability 406B.3.3 Lyapunov’s Theorem 407B.3.4 Krasovski’s Theorem 408B.3.5 Lyapunov Stability of Linear Systems 408References 408Appendix C: Control of Underactuated Flight Systems 409C.1 Adaptive Rocket Guidance with Forward Acceleration Input 409C.2 Thrust Saturation and Rate Limits (Increased Underactuation) 415C.3 Single- and Bi-output Observers with Forward Acceleration Input 417References 432Index 433