Description
Book SynopsisFlight Vehicle Dynamics and Control Rama K. Yedavalli, The Ohio State University, USA A comprehensive textbook which presents flight vehicle dynamics and control in a unified framework Flight Vehicle Dynamics and Controlpresents the dynamics and control of various flight vehicles, including aircraft, spacecraft, helicopter, missiles, etc, in a unified framework. It covers the fundamental topics in the dynamics and control of these flight vehicles, highlighting shared points as well as differences in dynamics and control issues, making use of the systems level' viewpoint. The book begins with the derivation of the equations of motion for a general rigid body and then delineates the differences between the dynamics of various flight vehicles in a fundamental way. It then focuses on the dynamic equations with application to these various flight vehicles, concentrating more on aircraft and spacecraft cases. Then the control systems analysis and design is carried out both from transfer f
Table of ContentsPreface xxi
Perspective of the Book xxix
Part I Flight Vehicle Dynamics 1
Roadmap to Part I 2
1 An Overview of the Fundamental Concepts of Modeling of a Dynamic System 5
1.1 Chapter Highlights 5
1.2 Stages of a Dynamic System Investigation and Approximations 5
1.3 Concepts Needed to Derive Equations of Motion 8
1.4 Illustrative Example 15
1.5 Further Insight into Absolute Acceleration 20
1.6 Chapter Summary 20
1.7 Exercises 21
Bibliography 22
2 Basic Nonlinear Equations of Motion in Three Dimensional Space 23
2.1 Chapter Highlights 23
2.2 Derivation of Equations of Motion for a General Rigid Body 23
2.3 Specialization of Equations of Motion to Aero (Atmospheric) Vehicles 32
2.4 Specialization of Equations of Motion to Spacecraft 43
2.5 Flight Vehicle DynamicModels in State Space Representation 52
2.6 Chapter Summary 58
2.7 Exercises 58
Bibliography 60
3 Linearization and Stability of Linear Time Invariant Systems 61
3.1 Chapter Highlights 61
3.2 State Space Representation of Dynamic Systems 61
3.3 Linearizing a Nonlinear State Space Model 63
3.4 Uncontrolled, Natural Dynamic Response and Stability of First and Second Order Linear Dynamic Systems with State Space Representation 66
3.5 Chapter Summary 73
3.6 Exercises 74
Bibliography 75
4 Aircraft Static Stability and Control 77
4.1 Chapter Highlights 77
4.2 Analysis of Equilibrium (Trim) Flight for Aircraft: Static Stability and Control 77
4.3 Static Longitudinal Stability 79
4.4 Stick Fixed Neutral Point and CG Travel Limits 86
4.5 Static Longitudinal Control with Elevator Deflection 92
4.6 Reversible Flight Control Systems: Stick Free, Stick Force Considerations 99
4.7 Static Directional Stability and Control 105
4.8 Engine Out Rudder/Aileron Power Determination: Minimum Control Speed, VMC 107
4.9 Chapter Summary 111
4.10 Exercises 111
Bibliography 114
5 Aircraft Dynamic Stability and Control via Linearized Models 117
5.1 Chapter Highlights 117
5.2 Analysis of Perturbed Flight from Trim: Aircraft Dynamic Stability and Control 117
5.3 Linearized Equations of Motion in Terms of Stability Derivatives For the Steady, Level Equilibrium Condition 122
5.4 State Space Representation for Longitudinal Motion and Modes of Approximation 124
5.5 State Space Representation for Lateral/Directional Motion and Modes of Approximation 131
5.6 Chapter Summary 138
5.7 Exercises 139
Bibliography 140
6 Spacecraft Passive Stabilization and Control 143
6.1 Chapter Highlights 143
6.2 Passive Methods for Satellite Attitude Stabilization and Control 143
6.3 Stability Conditions for Linearized Models of Single Spin Stabilized Satellites 146
6.4 Stability Conditions for a Dual Spin Stabilized Satellite 149
6.5 Chapter Summary 151
6.6 Exercises 152
Bibliography 152
7 Spacecraft Dynamic Stability and Control via Linearized Models 155
7.1 Chapter Highlights 155
7.2 Active Control: Three Axis Stabilization and Control 155
7.3 Linearized Translational Equations of Motion for a Satellite in a Nominal Circular Orbit for Control Design 158
7.4 Linearized Rotational (Attitude) Equations of Motion for a Satellite in a Nominal Circular Orbit for Control Design 160
7.5 Open Loop (Uncontrolled Motion) Behavior of Spacecraft Models 161
7.6 External Torque Analysis: Control Torques Versus Disturbance Torques 161
7.7 Chapter Summary 162
7.8 Exercises 162
Bibliography 163
Part II Fight Vehicle Control via Classical Transfer Function Based Methods 165
Roadmap to Part II 166
8 Transfer Function Based Linear Control Systems 169
8.1 Chapter Highlights 169
8.2 Poles and Zeroes in Transfer Functions and Their Role in the Stability and Time Response of Systems 174
8.3 Transfer Functions for Aircraft Dynamics Application 179
8.4 Transfer Functions for Spacecraft Dynamics Application 183
8.5 Chapter Summary 184
8.6 Exercises 184
Bibliography 186
9 Block Diagram Representation of Control Systems 187
9.1 Chapter Highlights 187
9.2 Standard Block Diagram of a Typical Control System 187
9.3 Time Domain Performance Specifications in Control Systems 192
9.4 Typical Controller Structures in SISO Control Systems 196
9.5 Chapter Summary 200
9.6 Exercises 201
Bibliography 202
10 Stability Testing of Polynomials 203
10.1 Chapter Highlights 203
10.2 Coefficient Tests for Stability: Routh–Hurwitz Criterion 204
10.3 Left Column Zeros of the Array 208
10.4 Imaginary Axis Roots 208
10.5 Adjustable Systems 209
10.6 Chapter Summary 210
10.7 Exercises 210
Bibliography 211
11 Root Locus Technique for Control Systems Analysis and Design 213
11.1 Chapter Highlights 213
11.2 Introduction 213
11.3 Properties of the Root Locus 214
11.4 Sketching the Root Locus 218
11.5 Refining the Sketch 219
11.6 Control Design using the Root Locus Technique 223
11.7 Using MATLAB to Draw the Root Locus 225
11.8 Chapter Summary 226
11.9 Exercises 227
Bibliography 229
12 Frequency Response Analysis and Design 231
12.1 Chapter Highlights 231
12.2 Introduction 231
12.3 Frequency Response Specifications 232
12.4 Advantages of Working with the Frequency Response in Terms of Bode Plots 235
12.5 Examples on Frequency Response 238
12.6 Stability: Gain and Phase Margins 240
12.7 Notes on Lead and Lag Compensation via Bode Plots 246
12.8 Chapter Summary 248
12.9 Exercises 248
Bibliography 250
13 Applications of Classical Control Methods to Aircraft Control 251
13.1 Chapter Highlights 251
13.2 Aircraft Flight Control Systems (AFCS) 252
13.3 Longitudinal Control Systems 252
13.4 Control Theory Application to Automatic Landing Control System Design 259
13.5 Lateral/Directional Autopilots 265
13.6 Chapter Summary 267
Bibliography 267
14 Application of Classical Control Methods to Spacecraft Control 269
14.1 Chapter Highlights 269
14.2 Control of an Earth Observation Satellite Using a Momentum Wheel and Offset Thrusters: Case Study 269
14.3 Chapter Summary 281
Bibliography 281
Part III Flight Vehicle Control via Modern State Space Based Methods 283
Roadmap to Part III 284
15 Time Domain, State Space Control Theory 287
15.1 Chapter Highlights 287
15.2 Introduction to State Space Control Theory 287
15.3 State Space Representation in Companion Form: Continuous Time Systems 291
15.4 State Space Representation of Discrete Time (Difference) Equations 292
15.5 State Space Representation of Simultaneous Differential Equations 294
15.6 State Space Equations from Transfer Functions 296
15.7 Linear Transformations of State Space Representations 297
15.8 Linearization of Nonlinear State Space Systems 300
15.9 Chapter Summary 304
15.10 Exercises 305
Bibliography 306
16 Dynamic Response of Linear State Space Systems (Including Discrete Time Systems and Sampled Data Systems) 307
16.1 Chapter Highlights 307
16.2 Introduction to Dynamic Response: Continuous Time Systems 307
16.3 Solutions of Linear Constant Coefficient Differential Equations in State Space Form 309
16.4 Determination of State Transition Matrices Using the Cayley–Hamilton Theorem 310
16.5 Response of a Constant Coefficient (Time Invariant) Discrete Time State Space System 314
16.6 Discretizing a Continuous Time System: Sampled Data Systems 317
16.7 Chapter Summary 319
16.8 Exercises 320
Bibliography 321
17 Stability of Dynamic Systems with State Space Representation with Emphasis on Linear Systems 323
17.1 Chapter Highlights 323
17.2 Stability of Dynamic Systems via Lyapunov Stability Concepts 323
17.3 Stability Conditions for Linear Time Invariant Systems with State Space Representation 328
17.4 Stability Conditions for Quasi-linear (Periodic) Systems 337
17.5 Stability of Linear, Possibly Time Varying, Systems 338
17.6 Bounded Input–Bounded State Stability (BIBS) and Bounded Input–Bounded Output Stability (BIBO) 344
17.7 Chapter Summary 345
17.8 Exercises 345
Bibliography 346
18 Controllability, Stabilizability, Observability, and Detectability 349
18.1 Chapter Highlights 349
18.2 Controllability of Linear State Space Systems 349
18.3 State Controllability Test via Modal Decomposition 351
18.4 Normality or Normal Linear Systems 352
18.5 Stabilizability of Uncontrollable Linear State Space Systems 353
18.6 Observability of Linear State Space Systems 355
18.7 State Observability Test via Modal Decomposition 357
18.8 Detectability of Unobservable Linear State Space Systems 358
18.9 Implications and Importance of Controllability and Observability 361
18.10 A Display of all Three Structural Properties via Modal Decomposition 365
18.11 Chapter Summary 365
18.12 Exercises 366
Bibliography 368
19 Shaping of Dynamic Response by Control Design: Pole (Eigenvalue) Placement Technique 369
19.1 Chapter Highlights 369
19.2 Shaping of Dynamic Response of State Space Systems using Control Design 369
19.3 Single Input Full State Feedback Case: Ackermann’s Formula for Gain 373
19.4 Pole (Eigenvalue) Assignment using Full State Feedback: MIMO Case 375
19.5 Chapter Summary 379
19.6 Exercises 379
Bibliography 381
20 Linear Quadratic Regulator (LQR) Optimal Control 383
20.1 Chapter Highlights 383
20.2 Formulation of the Optimum Control Problem 383
20.3 Quadratic Integrals and Matrix Differential Equations 385
20.4 The Optimum Gain Matrix 387
20.5 The Steady State Solution 388
20.6 Disturbances and Reference Inputs 389
20.7 Trade-Off Curve Between State Regulation Cost and Control Effort 392
20.8 Chapter Summary 395
20.9 Exercises 395
Bibliography 396
21 Control Design Using Observers 397
21.1 Chapter Highlights 397
21.2 Observers or Estimators and Their Use in Feedback Control Systems 397
21.3 Other Controller Structures: Dynamic Compensators of Varying Dimensions 405
21.4 Spillover Instabilities in Linear State Space Dynamic Systems 408
21.5 Chapter Summary 410
21.6 Exercises 410
Bibliography 410
22 State Space Control Design: Applications to Aircraft Control 413
22.1 Chapter Highlights 413
22.2 LQR Controller Design for Aircraft Control Application 413
22.3 Pole Placement Design for Aircraft Control Application 414
22.4 Chapter Summary 421
22.5 Exercises 421
Bibliography 421
23 State Space Control Design: Applications to Spacecraft Control 423
23.1 Chapter Highlights 423
23.2 Control Design for Multiple Satellite Formation Flying 423
23.3 Chapter Summary 427
23.4 Exercises 428
Bibliography 428
Part IV Other Related Flight Vehicles 429
Roadmap to Part IV 430
24 Tutorial on Aircraft Flight Control by Boeing 433
24.1 Tutorial Highlights 433
24.2 System Overview 433
24.3 System Electrical Power 436
24.4 Control Laws and System Functionality 438
24.5 Tutorial Summary 441
Bibliography 442
25 Tutorial on Satellite Control Systems 443
25.1 Tutorial Highlights 443
25.2 Spacecraft/Satellite Building Blocks 443
25.3 Attitude Actuators 445
25.4 Considerations in Using Momentum Exchange Devices and Reaction Jet Thrusters for Active Control 445
25.5 Tutorial Summary 449
Bibliography 449
26 Tutorial on Other Flight Vehicles 451
26.1 Tutorial on Helicopter (Rotorcraft) Flight Control Systems 451
26.2 Tutorial on Quadcopter Dynamics and Control 462
26.3 Tutorial on Missile Dynamics and Control 465
26.4 Tutorial on Hypersonic Vehicle Dynamics and Control 468
Bibliography 470
Appendices 471
Appendix A Data for Flight Vehicles 472
A.1 Data for Several Aircraft 472
A.2 Data for Selected Satellites 476
Appendix B Brief Review of Laplace Transform Theory 479
B.1 Introduction 479
B.2 Basics of Laplace Transforms 479
B.3 Inverse Laplace Transformation using the Partial Fraction Expansion Method 482
B.4 Exercises 483
Appendix C A Brief Review of Matrix Theory and Linear Algebra 487
C.1 Matrix Operations, Properties, and Forms 487
C.2 Linear Independence and Rank 489
C.3 Eigenvalues and Eigenvectors 490
C.4 Definiteness of Matrices 492
C.5 Singular Values 493
C.6 Vector Norms 497
C.7 Simultaneous Linear Equations 499
C.8 Exercises 501
Bibliography 503
Appendix D Useful MATLAB Commands 505
D.1 Author Supplied Matlab Routine for Formation of Fuller Matrices 505
D.2 Available Standard Matlab Commands 507
Index 509
