# Flight Dynamics and Control of Aero and Space Vehicles

Aerospace Series (PEP)

1. Edition December 2019

560 Pages, Hardcover*Textbook*

**978-1-118-93445-6**

Flight 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 Control presents 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 function, classical control, as well as modern, state space control points of view. Illustrative examples of application to atmospheric and space vehicles are presented, emphasizing the 'systems level' viewpoint of control design.

Key features:

* Provides a comprehensive treatment of dynamics and control of various flight vehicles in a single volume.

* Contains worked out examples (including MATLAB examples) and end of chapter homework problems.

* Suitable as a single textbook for a sequence of undergraduate courses on flight vehicle dynamics and control.

* Accompanied by a website that includes additional problems and a solutions manual.

The book is essential reading for undergraduate students in mechanical and aerospace engineering, engineers working on flight vehicle control, and researchers from other engineering backgrounds working on related topics.

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

Inseok Hwang, PhD, Professor, Aeronautics and Astronautics

School of Aeronautics and Astronautics, Purdue University

"The book is a "must have" for students as well as practicing engineers. I think that the book is unique and it is a complete guideline for two undergraduate courses. It is extremely well written, and it shows the high level scientific background of its author."

Mario Innocenti, PhD, Full Professor of Aerospace Dynamics and Control

Department of Information Engineering, University of Pisa