Hjem

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, V MC 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 D