Preface 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...