Variable-structure systems and sliding-mode control

Preface......Page 7
Acknowledgements......Page 9
Contents......Page 10
Nomenclature......Page 12
Part I New HOSM Algorithms......Page 13
 1.1 Introduction......Page 14
 1.2 Preliminaries: Weighted Homogeneity......Page 16
 1.3 Homogeneity Approach to Output Regulation Under Uncertainty......Page 18
 1.4 Homogeneous Control Templates......Page 20
  1.4.1 Recursion in r......Page 21
  1.4.2 Examples of Recursive Homogeneous Control Design......Page 22
 1.5 Design of a Completely New Control Family......Page 23
  1.5.1 Simulation......Page 24
  1.6.1 Asymptotically Optimal Differentiation......Page 26
  1.6.2 Filtering Differentiators......Page 28
 1.7 Discrete Differentiators......Page 31
  1.7.1 Numeric Differentiation......Page 33
 1.8 Conclusion......Page 35
 References......Page 36
2 Discontinuous Integral Control for Systems with Arbitrary Relative Degree......Page 40
 2.1 Introduction......Page 41
 2.2 Preliminaries: Differential Inclusions and Homogeneity......Page 44
 2.3 Integral Controller: Main Results......Page 46
  2.3.1 HOSM Controllers with Discontinuous Integral Action......Page 49
  2.3.2 Homogeneous and Continuous Approximations of the I-Controllers......Page 51
  2.3.4 Discussion and Properties of the Controllers......Page 53
 2.4 Example......Page 56
 2.5 Convergence Proofs of the Full State Nonpassivity-Based I-Controllers......Page 59
  2.5.2 Auxiliary Functions and Some Important Relations......Page 60
  2.5.3 Derivative of the Lyapunov Function Candidate......Page 62
 2.6 Convergence Proofs for the Passivity-Based I-Controllers......Page 66
  2.6.1 The Lyapunov Function Candidate......Page 67
  2.6.2 A Passivity Interpretation of the I-Controller......Page 69
  2.6.3 A Strong Lyapunov Function and the Robustness Issue......Page 70
 2.7 A Lyapunov Function Approach for the Partial State Integral Controller......Page 71
  2.7.2 Derivative of the LF Candidate......Page 72
  2.7.3 Gain Calculation......Page 75
 2.8 Conclusions......Page 76
 References......Page 78
Part II Properties of Continuous Sliding-Mode Algorithms......Page 81
 3.1 Introduction......Page 82
  3.2.1 Notation......Page 85
  3.2.2 Considered System and Stability Notions......Page 86
  3.2.3 Reaching Time Function......Page 87
  3.2.4 Homogeneity Properties......Page 88
  3.2.5 Quasi-linear System Representation......Page 90
  3.3.1 Unperturbed Reaching Time Function......Page 91
  3.3.2 Reaching Time Estimation......Page 95
  3.3.3 Range of Permitted Perturbations......Page 97
  3.3.4 Asymptotic Properties......Page 99
  3.4.1 Quadratic Lyapunov Function Family......Page 101
  3.4.2 Reaching Time Estimation......Page 102
  3.4.3 Range of Permitted Perturbations......Page 104
  3.4.4 Optimal Lyapunov Function Choice......Page 108
  3.4.5 Asymptotic Properties......Page 112
  3.5.1 Geometric Stability Proof......Page 113
  3.5.2 Reaching Time Estimation......Page 117
  3.5.3 Range of Permitted Perturbations......Page 119
  3.5.4 Asymptotic Properties......Page 120
 3.6 Comparisons......Page 121
  3.6.1 Perturbation Bounds......Page 122
  3.6.2 Reaching Time Estimates......Page 123
 3.7 Conclusion......Page 125
 References......Page 132
 4.1 Introduction......Page 133
 4.2 Problem Statement......Page 135
 4.3 Saturated Continuous Twisting Algorithm......Page 137
  4.3.1 Stability Analysis......Page 138
 4.4 Saturated Feedback Control Using the Twisting Algorithm......Page 147
  4.4.1 Output Feedback Control......Page 149
  4.4.2 Stability Analysis......Page 150
 4.5 Experimental Implementation......Page 151
  4.5.1 System Model......Page 152
  4.5.2 Control Design......Page 153
 References......Page 155
 5.1 Introduction......Page 157
  5.1.1 SMC with Input Constraints......Page 159
  5.1.2 SMC with State Constraints......Page 164
  5.1.3 SMC with Input and State Constraints......Page 173
  5.1.4 Conclusions......Page 179
 References......Page 180
 6.1 Introduction......Page 184
 6.2 Limit Cycles in Lure System and Loeb's Criterion......Page 185
 6.3 Dynamic Harmonic Balance......Page 188
 6.4 Analysis of Orbital Stability Based on Dynamic Harmonic Balance......Page 192
 6.5 Comparison of the Loeb's Criterion and the Criterion Based on Dynamic Harmonic Balance......Page 197
 6.6 Example of Analysis......Page 200
 6.7 Conclusions......Page 202
 References......Page 203
 7.1 Introduction......Page 204
  7.2.1 Ideal Sliding Modes......Page 206
  7.2.2 Class of Disturbances......Page 207
  7.2.3 Real Sliding Modes......Page 208
  7.3.1 Parameters of Chattering Caused by the First-Order Sliding-Mode Controller......Page 210
  7.3.2 Parameters of Chattering Caused by the Super-Twisting Algorithm......Page 211
 7.4 Suboptimal Design of the Super-Twisting Gains for Systems of Relative Degree One with Fast-Parasitic Dynamics......Page 215
 7.5 Conclusions......Page 216
 References......Page 217
Part III Usage of VSS Controllers for Solving Other Control Problems......Page 219
 8.1 Introduction......Page 220
 8.2 Motivational Example for the Bilinear Model......Page 222
 8.3 Description of the Control Design Problem......Page 223
 8.4 Properties of the Model......Page 224
  8.4.1 Nonnegative Solutions......Page 225
  8.4.2 Boundedness of Solutions......Page 226
 8.5 Sliding-Mode Controller......Page 228
  8.5.1 On the Closed-Loop Solutions......Page 229
  8.5.2 Reaching Phase Analysis......Page 231
  8.5.3 Sliding-Phase Analysis......Page 232
 8.6 Robustness......Page 234
 8.7 Numerical Example......Page 235
  8.8.1 Solutions of Delayed Differential Equations......Page 238
  8.8.2 Volterra Equations......Page 239
 References......Page 240
 9.1 Introduction......Page 242
 9.2 Problem Definition......Page 244
 9.3 First-Order Sliding-Mode Control......Page 246
  9.3.1 Conventional First-Order Sliding Mode (FOSM)......Page 247
  9.3.2 FOSM with Numerical Derivatives (FOSM-D)......Page 249
  9.3.3 Stability and Disturbance Compensation......Page 251
 9.4 Integral Sliding-Mode Control (ISMC)......Page 252
  9.4.2 Control Law......Page 253
  9.4.3 Stability and Comparison to Conventional ISMC......Page 254
  9.4.4 Decoupling of Unmatched Uncertainties......Page 255
 9.5 Higher-Order Sliding-Mode Control (HOSM)......Page 256
  9.5.1 Nested Quasi-continuous HOSM Control (nHOSM)......Page 257
  9.5.2 Nested Backward Compensation of Unmatched Disturbances via HOSM Observation (nFOSM)......Page 258
 9.6 Case Studies......Page 260
  9.6.1 Transformations and Resulting Internal Dynamics......Page 261
  9.6.2 Simulation Results......Page 262
 9.7 Discussion and Concluding Remarks......Page 266
 References......Page 275
Part IV Applications of VSS......Page 278
10 Grid-Connected Shunt Active LCL Control via Continuous SMC and HOSMC Techniques......Page 279
 10.1 Introduction......Page 280
  10.2.2 Transfer Function and State-Space Models of the LCL Filter......Page 281
  10.3.1 Root Locus Controller......Page 284
  10.3.3 Improved RST Control Method (RSTimp)......Page 286
  10.3.4 Control Method Synthesis......Page 288
  10.3.5 Controller Feasibility Study RSTimp in Discrete Time......Page 289
  10.3.6 Synthesis of Controller Feasibility RSTimp in Discrete Time......Page 291
  10.4.2 SMC Design......Page 292
  10.4.3 SMC with an Artificial Increase of Relative Degree......Page 294
  10.4.4 C-HOSMC Design......Page 296
 10.5 Simulation Results......Page 297
  10.5.2 Simscap-Sim_Power_System Simulation Results......Page 298
  10.6.2 Electrical Data/Description of the Site......Page 302
  10.6.3 Modeling of the Industrial Site Network......Page 304
  10.6.4 Modeling Validation......Page 305
  10.6.5 Simscap-Sim_Power_System Simulation of the SAF Within the Industrial Site......Page 306
 10.7 Conclusion......Page 309
 References......Page 311
11 On the Robust Distributed Secondary Control of Islanded Inverter-Based Microgrids......Page 313
 11.1 Introduction......Page 314
 11.2 Microgrid Modeling......Page 318
  11.2.1 Secondary Control Objectives for Islanded Microgrids......Page 322
  11.3.1 Voltage Secondary Controller Design......Page 323
  11.3.2 Frequency Secondary Controller Design......Page 327
  11.4.1 Voltage Secondary Controller Design......Page 330
  11.4.2 Frequency Secondary Controller Design......Page 333
 11.5 Simulations and Discussion of Results......Page 337
  11.5.1 MG Model Parameters and Details......Page 338
  11.5.2 Simulations Case Studies Outline......Page 342
  11.5.3 Numerical Simulation Results......Page 349
 11.6 Conclusions......Page 356
 References......Page 358
12 Local and Wide-Area Sliding-Mode Observers in Power Systems......Page 362
 12.1 Introduction......Page 363
  12.2.1 Angles Definitions......Page 365
  12.2.2 Swing Equations......Page 366
 12.3 A Super-Twisting-Like Sliding-Mode Observer for Frequency Reconstruction for Synchronous Generators......Page 368
  12.3.1 Super-Twisting-Like Sliding-Mode Observer Design......Page 369
  12.3.2 Real Data-Based Super-Twisting-Like Observer Validation......Page 371
 12.4 Sliding-Mode Observer for a Single Synchronous Generator with Transient Voltage Dynamics......Page 375
  12.4.1 Observer Design......Page 376
  12.4.2 Simulation-Based Observer Validation......Page 378
  12.5.1 Power Grid System Description......Page 380
  12.5.2 Algebraic Observers Design......Page 385
  12.5.3 Super-Twisting-Like Sliding-Mode Observers for the Generators......Page 387
  12.5.4 Numerical Test Cases......Page 389
 References......Page 392
 13.1 Introduction......Page 395
 13.2 Sliding-Mode-Based Platooning......Page 396
  13.2.1 String Stability......Page 398
  13.2.2 Sliding-Mode Controller Design for Nonzero Initial Spacing Errors......Page 399
  13.2.3 First-Order Actuator Dynamics......Page 403
  13.2.4 Higher-Order Actuator Dynamics......Page 406
  13.2.5 Robustness with Respect to Lateral Deviation......Page 412
  13.3.1 Description of the Testbed......Page 418
  13.3.2 Results......Page 425
 13.4 Conclusion and Future Work......Page 431
 References......Page 432
 14.1 Introduction......Page 434
  14.1.1 Traditional Guidance and Control......Page 435
  14.1.2 Integrated Guidance and Control......Page 436
  14.1.3 Single-Loop Guidance and Control......Page 437
  14.2.1 Engagement Kinematics......Page 439
  14.2.2 Missile Dynamics......Page 441
  14.2.3 Integrated State-Space Model......Page 443
  14.2.4 Intercept Strategy......Page 444
  14.2.6 The Difficulty of Single-Loop G&C......Page 446
  14.3.1 Fundamentals of Sliding-Mode Control......Page 447
  14.3.2 High-Order Sliding-Mode Control......Page 448
  14.3.3 High-Order Sliding-Mode Differentiators......Page 449
  14.4.1 Integrated Single-Loop G&C Using HOSMC......Page 450
  14.4.2 Case Studies......Page 451
  14.4.3 Conclusion......Page 460
 References......Page 462