Stringent demands on modern guided weapon systems require new approaches to guidance, control, and estimation. There are requirements for pinpoint accuracy, low cost per round, easy upgrade paths, enhanced performance in counter-measure environments, and the ability to track low-observable targets. Advances in Missile Guidance, Control, and Estimation brings together in one volume the latest developments in the three major missile-control components—guidance, control, and estimation—as well as advice on implementation. It also shows how these elements contribute to the overall missile design process. Shares Insights from Well-Known Researchers and Engineers from Israel, Korea, France, Canada, the UK, and the US The book features contributions by renowned experts from government, the defense industry, and academia from the United States, Israel, Korea, Canada, France, and the United Kingdom. It starts from the ground up, developing equations of missile motion. It reviews the kinematics of the engagement and the dynamics of the target and missile before delving into autopilot design, guidance, estimation, and practical implementation issues. Covers Nonlinear Control Techniques as Well as Implementation Issues The book discusses the design of autopilots using new nonlinear theories and analyzes the performance over a flight envelope of Mach number and altitude. It also contains a chapter on the recent integrated-guidance-and-control approach, which exploits the synergy between the autopilot and guidance system design. The book then outlines techniques applied to the missile guidance problem, including classical guidance, sliding mode-based, and differential game-based techniques. A chapter on the use of differential games integrates the guidance law with the estimation of the target maneuver. A chapter on particle filter describes the latest development in filtering algorithms. The final chapters—written by engineers working in the defense industry in the US, Israel, and Canada—consider the design and implementation issues of a command-to-line-of-sight guidance system and autopilots. An Invaluable Resource on the State of the Art of Missile Guidance A guide to advanced topics in missile guidance, control, and estimation, this invaluable book combines state-of-the-art theoretical developments presented in a tutorial form and unique practical insights. It looks at how tracking, guidance, and autopilot algorithms integrate into a missile system and guides control system designers through the challenges of the design process.
Author(s): S.N. Balakrishnan, Antonios Tsourdos, B.A. White
Series: Automation and Control Engineering
Publisher: CRC Press
Year: 2012
Language: English
Pages: xxxviii+688
Tags: Военные дисциплины;Баллистика и динамика выстрела;Боеприпасы;
Advances in Missile Guidance, Control, and Estimation......Page 4
Contents......Page 8
Preface......Page 10
Contributors......Page 12
Introduction......Page 14
Homing Guidance Kinematics......Page 16
Line of Sight Kinematics......Page 18
Airframe Equations of Motion......Page 22
Translational dynamics......Page 25
Rotational dynamics......Page 27
Inertial/body axis transformation......Page 28
Guidance algorithm development......Page 32
Zero-effort miss......Page 33
Challenges......Page 34
MATLAB®/Simulink® Disclaimer......Page 38
1.1 Introduction......Page 40
1.2 Preliminaries......Page 41
1.2.1 Missile Model......Page 42
1.2.2 Taxonomy of Models......Page 44
1.2.3.1 Linearization via Coordinate Transformation......Page 46
1.2.3.2 Input– Output Feedback Linearization......Page 48
1.2.3.3 Input– Output Pseudolinearization......Page 49
1.3 Augmented Lateral Acceleration Autopilot Design......Page 53
1.4.1 Nominal Autopilot Model......Page 58
1.4.2 Robust Performance Design......Page 59
1.4.3 Robust Performance Analysis......Page 65
1.4.4 Discussions......Page 66
References......Page 68
2 Polynomial Approach for Design and Robust Analysis of Lateral Missile Control......Page 72
2.1 Introduction......Page 73
2.2 Polynomial Eigenstructure Assignment......Page 74
2.2.1 Controller Structure......Page 76
2.2.2 G ain Matrix Structure......Page 78
2.2.3 Matching Conditions......Page 79
2.3 Robust Analysis......Page 82
2.3.1 D-Stability for Polynomial Family......Page 83
2.3.2 Multilinear Uncertain Systems......Page 86
2.3.3 Developed Algorithm for D-Stability Robustness......Page 89
2.4.1 Missile Model......Page 91
2.4.2 Missile QLPV Form......Page 93
2.4.3 Performance Objectives......Page 94
2.4.4 Sideslip Velocity Controller......Page 95
2.4.5 Multilinear Parametric Uncertain System......Page 97
2.4.6 R obust D- Stability Analysis Criteria......Page 98
2.4.7 Applying FIT......Page 99
2.4.8 Simulation Results......Page 100
2.5.1 Matching Conditions with Full Feedback......Page 101
2.5.2 Lateral Acceleration Design with Full State Feedback Control......Page 103
2.5.3 Lateral Acceleration Design with Partial State Feedback Control......Page 105
2.5.4 Actuator Dynamics of First Order......Page 106
2.5.5 Actuator Dynamics of Second Order......Page 109
2.6 Discussions and Conclusions......Page 112
References......Page 113
3 Control Design and Gain Scheduling Using Observer-Based Structures......Page 116
3.1 Introduction......Page 117
3.2 O bserver- Based Realization of a Given Controller......Page 119
3.2.1 Augmented- Order Compensators......Page 124
3.2.2 Discussion......Page 127
3.2.3 In Brief......Page 130
3.2.4 Reduced- Order Compensator Case......Page 131
3.3 Illustrations......Page 133
3.3.1 Illustration 1: Plant State Monitoring......Page 135
3.3.2 Illustration 2: Controller Switching......Page 136
3.3.3 Illustration 3: Smooth Gain Scheduling......Page 137
3.4 Cross Standard Form......Page 139
3.4.1 Definitions......Page 140
3.4.2 Low-Order Controller Case (nK ≤ n)......Page 141
3.4.2.1 Uniqueness Condition......Page 143
3.4.2.2 Existence of CSF......Page 145
3.4.4 I llustration......Page 146
3.4.4.1 Improving K0 with Frequency- Domain Specification......Page 148
3.5 Discrete- Time Case......Page 149
3.5.1 Discrete- Time Predictor Form......Page 150
3.5.2 Discrete- Time Estimator Form......Page 151
3.5.3 Discrete- Time CSF......Page 152
3.6.1 Description......Page 153
3.6.2 Objectives......Page 154
3.6.3 Launch Vehicle Control Design......Page 155
3.6.3.1.1 State Feedback on Rigid Model......Page 156
3.6.3.1.2 Augmented State with Wind Dynamics......Page 157
3.6.3.1.3 Kalman’s Filter with LTR Tuning......Page 158
3.6.3.2 Second Synthesis: H∞ Synthesis Using CSF for Frequency-Domain Specifications......Page 159
3.6.4 G ain Scheduling......Page 161
3.7 Conclusions......Page 164
References......Page 165
4.1 Introduction......Page 168
4.2 Nonlinear Air–Air Missile Model......Page 172
4.3 Missile Autopilot Control Loop Design......Page 174
4.3.1 Outer Loop Control Design......Page 175
4.3.1.1 Upper Bound on Estimation Error......Page 177
4.3.1.2 Upper Bound of Neural Network Weights......Page 178
4.3.2 Inner Loop Control Design......Page 179
4.3.3 BTT/ STT Command Logic......Page 181
4.4 Simulation Studies......Page 182
4.4.1 Performance at Various Altitude Conditions......Page 188
Acknowledgment......Page 193
References......Page 194
5.1 Introduction......Page 196
5.2.1 Equations of Motion......Page 199
5.2.2 Cost Function......Page 201
5.2.3 Body-Based IGC Results......Page 202
5.2.3.1 Weight Sensitivity......Page 203
5.2.3.2 Discussion of Missile Physics......Page 205
5.3.1 Missile IGC Design in Vertical Plane......Page 206
5.3.1.1 Results......Page 208
5.3.2.1 Intercept Geometry......Page 211
5.3.2.2 Approximate Solutions......Page 213
5.3.3.1 Results......Page 214
5.4 Sliding Mode Integrated Guidance and Control......Page 216
5.4.1 Effect of Target Acceleration on PIP Heading Error......Page 217
5.4.2 α-Plane SMIGC Control Law......Page 219
5.4.3 β-Plane SMIGC Control Law......Page 223
5.5 SMIGC Results and Analysis......Page 225
References......Page 230
6 Higher-Order Sliding Modes for Missile Guidance and Control......Page 234
6.1.2 Why Sliding Mode Control?......Page 235
6.2 Fundamentals of Traditional SMC......Page 238
6.3 Fundamentals of HOSM/SOSM Control......Page 241
6.3.1 Twisting Controller......Page 242
6.3.3 SOSM Control Based on Nonlinear Dynamic Sliding Manifold......Page 243
6.3.4 Quasi-Continuous Control Algorithm......Page 244
6.3.5 Supertwisting Controller......Page 245
6.3.5.1 Comparison of Supertwisting and Traditional SMC......Page 246
6.3.6.1 Nonlinear Disturbance Observer/Differentiator......Page 248
6.3.6.2 Disturbance Cancellation......Page 249
6.4 Discussion on Properties of Traditional and Higher- Order SMC......Page 250
6.5.1 I nterception Geometry......Page 251
6.5.2 Missile Model......Page 252
6.5.3 I nterception Strategy......Page 254
6.6 Control Architecture......Page 256
6.6.1 Outer (Guidance) Loop SSOSM Controller Design......Page 257
6.6.2 SSOSM Guidance Simulation Results......Page 258
6.7.1 I nversion......Page 260
6.7.2 Second- Order NDSM- Based Flight Path Angle Autopilot......Page 262
6.7.4 SOSM Supertwist- Based Angle- of- Attack Autopilot......Page 263
6.7.5 I ntegrated SOSM Guidance- Autopilot Simulation Results......Page 264
6.7.6 Higher- Order SMC Quaternion Autopilot......Page 268
6.7.7 Simulation Results for Integrated SOSM Guidance-Quaternion Autopilot......Page 272
Nomenclature......Page 275
References......Page 277
Appendix: Evaluation of the Lipschitz Constant for Outer (Guidance) Loop......Page 279
7.1 Introduction......Page 280
7.2 Miss Distance in PNG......Page 282
7.2.1 Deterministic Disturbances......Page 284
7.2.2 Stochastic Inputs......Page 285
7.2.3 Deterministic Target Maneuvers with Random Starting Times......Page 286
7.3 Class of All PNG- Based Systems Yielding ZMD......Page 287
7.4 Case of Saturating Missile Acceleration......Page 289
7.5 ZMD Guidance as Estimation Problem......Page 292
7.6 Illustrative Example......Page 299
7.6.1 Guidance Law Synthesis......Page 300
7.6.3 Guidance Law Performance......Page 303
7.7 Summary and Conclusions......Page 306
Nomenclature......Page 307
References......Page 308
8.1 Introduction......Page 312
8.2 Homing Guidance Acquisition Geometry......Page 313
8.3 Differential Geometry Kinematics......Page 319
8.4.1 Direct Intercept Geometry of Nonmaneuvering Target......Page 322
8.4.2 Guidance Algorithm for Direct Intercept......Page 324
8.4.3 Direct Intercept Engagement Simulation......Page 329
8.4.4 Maneuvering Intercept Geometry of Maneuvering Target......Page 332
8.4.5 Guidance Algorithm for Maneuvering Intercept......Page 336
8.4.6 Maneuver Intercept Engagement Simulation......Page 338
8.5 Geometry Control......Page 340
References......Page 342
9 Differential Game-Based Interceptor Missile Guidance......Page 346
9.1.1 Vector Equations for Interceptor Missile Guidance......Page 347
9.1.2 Pursuit–Evasion Game Formulation......Page 349
9.1.3 Modeling Assumptions......Page 350
9.1.4 Linearized Interception Model......Page 351
9.2.1 Generalized Game Formulation......Page 353
9.2.2 Terminal Projection Transformation......Page 355
9.2.3 Hard or Soft Control Constraints......Page 356
9.3.1 Ideal Pursuer and Evader Dynamics......Page 357
9.3.2 Ideal Evader and First-Order Pursuer Dynamics......Page 361
9.3.3 First-Order Evader and Pursuer Dynamics......Page 363
9.3.4 Dual Maneuver Devices......Page 365
9.3.5 Time-Varying Parameters......Page 369
9.4.1 General Solution of LQ Differential Games......Page 372
9.4.3 Ideal Evader and First-Order Pursuer Dynamics......Page 375
9.4.4 First-Order Evader and Pursuer Dynamics......Page 376
9.4.5 Dual Maneuver Devices......Page 377
9.4.6 Time-Varying Parameters......Page 378
9.5 Conclusion......Page 379
References......Page 380
10 Optimal Guidance Laws with Impact Angle Control......Page 382
10.1 LQ Optimal Control Problem and Its Solution......Page 383
10.2 Optimal Impact Angle Control Law for Lag-Free Missile (OGL)......Page 385
10.2.1 Derivation of OGL......Page 386
10.2.2 Time-to-Go Calculation for Impact Angle Control Laws......Page 394
10.2.3 Implementing OGL: First Variant......Page 397
10.2.4 OGL for Moving Target: Second Variant......Page 403
10.3 OGL for First-Order Lag Missile (OGL/1)......Page 410
10.4 Energy Optimal Waypoint Guidance......Page 415
10.4.1 Equivalence of Optimal Control Problems......Page 416
10.4.2 Waypoint Guidance Scheme Based on OGL......Page 420
10.4.3 Numerical Examples......Page 428
10.5 Summary......Page 432
References......Page 433
11 Integrated Design of Estimator and Guidance Law......Page 436
11.1.1 Role of Estimator in Guidance System......Page 437
11.1.2.1 Background......Page 438
11.1.2.2 Illustrative Example......Page 439
11.1.3 Estimation in Interception Endgames......Page 442
11.2.1 Modeling Considerations......Page 443
11.2.2 Model Identification......Page 444
11.3.1 Deterministic Estimation Models......Page 445
11.3.2.1 Analytical Solution......Page 446
11.3.2.2 Simulation Results......Page 451
11.3.3 Refined Deterministic Estimation Models......Page 453
11.4.1 Stochastic Optimal Control Guidance Laws......Page 454
11.4.1.1 Problem Formulation......Page 455
11.4.1.3 Linear Stochastic Guidance Law......Page 456
11.4.1.4 Nonlinear Stochastic Guidance Law......Page 459
11.4.2 Fusion of Estimation and Guidance......Page 461
11.5.1 Engineering Approach......Page 462
11.5.2.1 Estimation......Page 463
11.5.2.2 Guidance Law Modifications......Page 464
11.5.3.1 Estimation......Page 466
11.5.3.2 Guidance Law......Page 467
11.6 Conclusions......Page 468
References......Page 469
11.A.1 Simulation Data......Page 471
11.A.2 Simulation Results......Page 473
12 Introduction to Particle Filters for Tracking and Guidance......Page 476
12.1.1 Aims......Page 477
12.1.3 Bayesian Estimation......Page 478
12.2.1 Problem Definition: Dynamic Estimation......Page 479
12.2.2 Formal Bayesian Filter......Page 480
12.2.3 Algorithm of Basic Particle Filter......Page 481
12.2.5 Alternative Resampling Scheme......Page 483
12.2.6 Impoverishment of Sample Set......Page 484
12.2.8 Sample Representation of Posterior pdf......Page 485
12.2.9 Discussion......Page 486
12.3 More General Particle Filters......Page 487
12.4.1 Computational Cost for Basic Filter......Page 489
12.4.2 How Many Samples?......Page 490
12.5.2.1 Dynamics Models......Page 491
12.5.2.3 Sensor Model......Page 492
12.5.2.4 General Form of Measurement/ Classification Likelihood......Page 493
12.5.2.5 Expression for Likelihood with Gaussian Measurements and Uniform Clutter......Page 494
12.5.2.6 Cost Functions for Guidance Problem......Page 496
12.5.3.1 Object Paths......Page 497
12.5.3.2 Sensor Measurements......Page 498
12.5.3.3 Filter Models......Page 500
12.5.3.5 Filter Estimates......Page 501
12.5.3.6 Guidance Analysis......Page 503
12.6.2 Tracking with Nonstandard Sensors......Page 504
12.6.5 Econometrics and Financial Time Series......Page 505
12.7 Conclusions......Page 506
References......Page 507
Appendix: Worked Example—Pendulum Estimation......Page 511
Discussion......Page 515
13.1 Introduction......Page 516
13.2.1 Operators in DT Domain......Page 520
13.2.2 Relationships between DT and CT Systems......Page 521
13.2.3 Principal Discretization Methods......Page 522
13.2.3.3 Pole–Zero Matching......Page 523
13.2.4 Multirate Systems......Page 524
13.3 Guidance Synthesis via Successive Optimizations......Page 528
13.3.1 System Kinematics and Dynamics......Page 529
13.3.2 Guidance Law Synthesis......Page 532
13.4.1 Optimal DR......Page 539
13.4.2 Polynomial Approach to Dual-Rate DR......Page 541
13.5.1 Digital Guidance Laws......Page 546
13.5.2 Digital Autopilots......Page 554
13.5.2.1 Optimal Redesign......Page 555
13.5.2.2 Redesign with Polynomial Method......Page 557
13.6 Conclusions and Future Directions......Page 560
References......Page 561
14 Design of CLOS Guidance System......Page 566
14.1 Overview......Page 567
14.2 System Operation......Page 568
14.3.2 Sensor......Page 569
14.3.6 Guidance Law......Page 570
14.4.1 Kinematic Model......Page 571
14.4.2 Missile Model......Page 573
14.4.3 Missile Uncertainty Model......Page 577
14.4.5 Sensor Platform Model......Page 578
14.4.6 Sensor Model......Page 579
14.4.6.1 Measurement Error Approximations......Page 580
14.4.6.2 Measurement Model......Page 581
14.5.1 Design Configuration......Page 582
14.5.3 The System Model......Page 583
14.5.5 Optimal Control Solution......Page 588
14.5.6 Design Parameters......Page 589
14.5.7 Design Method......Page 590
14.5.8 Solution of Riccati Equation......Page 591
14.5.9 Summary of Design......Page 593
14.6.1 Generic 3D Estimator......Page 595
14.6.2 Target Estimator......Page 598
14.6.3 Missile State Estimator......Page 601
14.7.1 Guidance Gain Calculation......Page 603
14.7.2 Transformation from Estimator States to System Model States......Page 606
14.7.3 Transformation of Missile Acceleration Commands to Missile Body Coordinates......Page 607
14.7.5 Sensor Frame versus Missile Body Frame Calculations......Page 610
14.7.6 Guidance System Block Diagram......Page 611
14.8.2 Simulation Description......Page 613
14.8.3 Scenario Description......Page 614
14.9 Summary......Page 619
List of Symbols......Page 620
References......Page 623
15 Practical Considerations in Robust Control of Missiles......Page 626
15.1 Introduction......Page 627
15.2.1 Dynamic Models......Page 629
15.2.1.1 Aerodynamics......Page 632
15.2.1.2 Propulsion System Forces and Moments......Page 634
15.2.1.3 Angle-of-Attack and Sideslip Dynamics......Page 636
15.2.1.4 Acceleration Dynamics......Page 637
15.2.2 Autopilot Design Models......Page 639
15.2.2.1 Pitch Autopilot Design Model......Page 640
15.2.2.2 Roll–Yaw Autopilot Design Model......Page 641
15.2.3 Sensor Measurements......Page 642
15.2.3.1 Shaping Zero Dynamics......Page 643
15.2.4.1 Fin Actuator Model......Page 644
15.2.4.3 TVC Actuator Model......Page 645
15.2.5 Flexible Body Dynamics......Page 646
15.2.6 Control Power Analysis......Page 647
15.3.1 Transfer Functions and Transfer Function Matrices......Page 649
15.3.1.1 Example......Page 651
15.3.2 Multivariable Stability Margins......Page 654
15.3.2.1.1 Rayleigh’s Quotient......Page 655
15.3.2.2 Multivariable Nyquist Theory......Page 659
15.3.2.3 Stability Margins for MIMO Systems......Page 664
15.3.3.1 Analysis Models for Uncertain Systems......Page 671
15.3.3.2 Singular Value Robustness Tests......Page 673
15.3.3.3 Real Stability Margin......Page 674
15.4 Optimal Flight Control Design......Page 675
15.4.1 Robust Servomechanism Linear Quadratic Regulator......Page 676
15.4.2 Design Summary for RSLQR......Page 679
15.4.3 Guaranteed Margins from LQR......Page 682
15.5 Adaptive Control Augmentation of Baseline Control......Page 684
15.6 Robustness Analysis of Optimal Baseline Control......Page 688
15.6.1 Robustness Analysis Model......Page 690
15.6.2 Real Margin Analysis......Page 692
15.6.2.1 Comment......Page 694
15.7 Robust Stability Analysis Using Nonlinear Simulation......Page 695
15.8 Summary and Conclusions......Page 698
References......Page 700
Index......Page 702
