Sliding modes after the first decade of the 21st century : state of the art ; [collection of the plenary and semiplenary talks in the joint 11th IEEE Workshop on Variable Structure Systems (VSS2010) and the principal meeting for the international project

**The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is coordinated by the IEEE Technical Committee on Variable Structure Systems (VSS) and Sliding Modes (SM). The presented results include the reports of the research groups collaborating in a framework of the Unión European Union – México project of Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICyT) 93302 titled "Automatization and Monitoring of Energy Production Processes via Sliding Mode Control". The book starts with the overview of the sliding mode control concepts and algorithms that were developed and discussed in the last two decades The research papers are combined in three sections: Part I: VSS and SM Algorithms and their Analysis Part II: SMC Design Part III: Applications of VSS and SMC The book will be of interests of engineers, researchers and graduate students working in the area of the control systems design. Novel mathematical theories and engineering concepts of control systems are rigorously discussed and supported by numerous applications to practical tasks.** Cover......Page 1 Front matter......Page 2 Sliding Mode Control Up until 1990......Page 22 Twisting Algorithm......Page 23 The Super-Twisting Algorithm......Page 24 Recapitulations......Page 26 Discussion on the Definition of r-th Order Sliding Motions......Page 27 Arbitrary Order Sliding Mode Controllers......Page 28 Black-Box Control [92]......Page 30 Terminal Sliding Mode Control......Page 31 Lyapunov Based Approach......Page 34 Chattering Problem and HOSM......Page 35 Chattering Analysis in the Frequency Domain......Page 36 Singularly Perturbed Analysis of Homogeneous Sliding Modes in the Presence of Fast Actuators......Page 41 Energy Based Approach [3]......Page 44 HOSM Observation and Identification......Page 45 HOSM Observation and Unknown Inputs Identification......Page 46 Time Invariant Parameter Identification......Page 49 Recapitulation......Page 51 Integral Sliding Mode Control......Page 52 HOSM Output Based Control......Page 54 ASMC with Known Bounds for the Disturbance......Page 56 HOSM Based Unmatched Uncertainties Compensation......Page 57 Model Based Application of HOSM......Page 58 Exact Unmatched Uncertainties Compensation Based on HOSM Observation......Page 59 Conclusions......Page 60 Open Problems......Page 61 Oscillatory Nature of Relay Delayed Systems......Page 62 Prediction Method......Page 64 Methods of Oscillation Control......Page 65 Distributed Parameter Systems......Page 66 References......Page 68 Introduction......Page 77 Preliminaries......Page 80 Standard SISO Regulation Problem and the Idea of Its Solution......Page 81 Homogeneity, Finite-Time Stability and Accuracy......Page 82 Second Order Sliding Mode Controllers......Page 85 Arbitrary Order Sliding Mode Controllers......Page 87 Arbitrary Order Robust Exact Differentiation......Page 90 Output-Feedback Control......Page 91 Control Magnitude Adjustment......Page 93 Parameter Adjustment......Page 94 Chattering Analysis......Page 95 Robustness Issues......Page 99 Control Simulation......Page 100 Signal Processing: Real-Time Differentiation......Page 104 Image Processing......Page 106 References......Page 108 Introduction......Page 111 Ideal and Real Sliding Modes: Poincare Maps and Frequency-Domain Approach......Page 112 Analysis of Convergence – Quasi-Static DF Approach......Page 114 Frequency-Domain Characteristics and Convergence Rate......Page 120 Extension to Higher-Order Plants......Page 124 Extention to Other Types of Controllers......Page 127 Conclusions......Page 129 References......Page 130 Introduction......Page 131 Problem Statement and Main Results......Page 134 Stability Analysis without Perturbations: An ALE Approach......Page 137 Convergence Time......Page 138 The Class of Perturbations......Page 139 Robust Stability Analysis: A Riccati Inequality Approach......Page 140 Practical Stability......Page 141 Frequency Domain Interpretation: The Circle Criterium......Page 142 A Non Quadratic Strong Lyapunov Function for the GSOA......Page 144 Uniformity in the Convergence......Page 145 The GSOA with Variable Gains......Page 146 Conclusions......Page 147 Appendix......Page 148 Proof of Theorem 4.1......Page 150 Proof of Proposition 4.1......Page 152 Proof of Theorem 4.3......Page 153 Proof of Theorem 4.4......Page 156 Proof of Proposition 4.2......Page 159 Proof of Proposition 4.3......Page 161 Proof of Theorem 4.5......Page 164 References......Page 165 A New Design of Sliding Mode Control Systems......Page 168 Introduction......Page 169 Problem Formulation......Page 171 Convergence Analysis......Page 174 A Simulation Example......Page 178 Conclusions......Page 182 References......Page 183 Introduction......Page 185 Preliminaries on Fractional Calculus......Page 187 Second-Order Sliding Mode Controllers for Multivariable Linear FOS......Page 189 Sliding Manifold Design......Page 190 Control-Input Design......Page 193 Implementation Issues......Page 194 Simulation Results......Page 196 Disturbance Observer for FOS......Page 197 Discrete-Mode Identification for Switched FOS......Page 200 Disturbance Estimation Test......Page 205 Discrete State Estimation Test......Page 206 Experimental Fault Detection of a Hydraulic Plant......Page 208 References......Page 210 Discussion about Sliding Mode Algorithms, Zeno Phenomena and Observability......Page 214 Discussion on Zeno and Sliding Mode Behavior......Page 215 Zeno Types......Page 216 Mathematical Recalls of H-K Integral......Page 217 Extended Observability Form......Page 220 Discussion on the Observability of the Second Basic Observability Form......Page 221 Observability for the Extended Observability Form......Page 224 The Two Tanks Example......Page 226 References......Page 232 Introduction......Page 235 A General Framework for Design......Page 238 Existence Problem......Page 239 Reachability Problem......Page 244 Liquid Monopropellant Rocket Motor Control......Page 250 References......Page 254 Introduction......Page 257 An Average GPI Controller Design Devoid of Observers......Page 259 A Switched Control Interpretation of the Average Design......Page 261 A GPI Observer Based Approach......Page 262 Definitions and Main Results......Page 266 An Application Example with Simulations......Page 269 An Observer-Free Approach......Page 270 A GPI Observer Based Approach......Page 271 A “Buck” Converter Example with Experimental Results......Page 273 The Buck Converter Model......Page 274 The GPI Sliding Mode Controller......Page 275 Experimental Results......Page 276 Conclusions......Page 279 References......Page 280 Output Feedback Sliding Mode Control Approaches Using Observers and/or Differentiators......Page 281 Introduction......Page 282 Problem Statement......Page 283 Basic Assumptions......Page 284 Output Feedback Model Matching Control......Page 285 Norm State Observer and Norm Bound for Equivalent Disturbance......Page 286 Output Feedback Sliding Mode Controller......Page 287 Variable Structure Lead Filter......Page 288 High-Gain Observers......Page 290 Hybrid Estimation Scheme......Page 294 Peaking Phenomena Avoidance......Page 296 Chattering Alleviation......Page 297 Binary Model Reference Adaptive Control......Page 298 Experimental Results......Page 299 Concluding Remarks......Page 301 References......Page 302 Sliding Modes for Fault Detection and Fault Tolerant Control......Page 305 Introduction......Page 306 Sliding Mode Observers for Fault Detection......Page 307 A Cascade Based Robust Fault Reconstruction Scheme......Page 309 Summary of Fault Reconstruction Algorithm......Page 310 Design Example......Page 315 Reconstruction of Incipient Sensor Faults......Page 317 Simulation Results......Page 322 Unmatched Parametric Uncertainty......Page 323 Fault Tolerant Control......Page 325 Design Procedures......Page 326 Benchmark Simulation Results......Page 329 Conclusions......Page 332 References......Page 333 Applying Sliding Mode Technique to Optimal Filter and Controller Design......Page 336 Introduction......Page 337 Problem Statement......Page 338 Mean-Square Filter Design......Page 339 Example 1......Page 340 Appendix 1......Page 341 Example 2......Page 343 Appendix 2......Page 344 Problem Statement......Page 346 Separation Principle. I......Page 348 Optimal Controller Problem Solution. I......Page 350 Example 3......Page 351 Separation Principle. II......Page 353 Optimal Controller Problem Solution. II......Page 354 Example 4......Page 355 Conclusions......Page 358 References......Page 359 Output Tracking and Observation in Nonminimum Phase Systems via Classical and Higher Order Sliding Modes......Page 361 Introduction......Page 362 System Description......Page 363 The Extended Method of Stable System Center......Page 365 Sliding Variable and Sliding Mode Control......Page 371 The Nonminimum Phase System Output Tracking Error Dynamics in the Sliding Mode......Page 372 Luenberger Observer Design......Page 373 Case Study 1: Output Voltage Tracking in Nonminimum Phase DC/DC Electric Power Converter......Page 374 Model of the Boost DC/DC Converter......Page 375 Sliding Mode Controller Design......Page 377 Sliding Mode Parameter Observer......Page 378 Numerical Simulations......Page 379 Case Study 2: SISO Output Tracking in Systems with Time Delay in Control Feedback......Page 381 Preliminaries......Page 382 Pad ́e Approximation......Page 383 Design of a Sliding Mode Controller for Causal Output Tracking......Page 384 Numerical Example......Page 386 References......Page 388 Introduction......Page 391 Multirate Output Feedback......Page 394 Nonlinear Sliding Surface......Page 396 Control Laws......Page 400 Control Law Based on Reaching Law Approach......Page 401 Control Law with Disturbance Observer......Page 403 Extension to Input-Delay Systems......Page 404 Magnetic Tape Position Tracking......Page 405 Comparison with Different Linear Sliding Surfaces......Page 410 Nonlinear Sliding Surface with Disturbance......Page 411 References......Page 413 Introduction......Page 416 Problem Formulation......Page 419 Design of a Higher Order Sliding Mode Controller......Page 421 Control Issues......Page 424 Problem Formulation and Navigation Strategy......Page 425 Path Planning......Page 428 Path Tracking......Page 433 Experimental Results......Page 438 Conclusion......Page 441 References......Page 442 Introduction......Page 445 Sliding Mode Control of a Wound Rotor Synchronous Generator......Page 446 System Description......Page 447 Direct Sliding Mode Controller......Page 448 Sliding Mode Control with an Outer-PI Loop......Page 451 Dynamic Sliding Mode Controller......Page 452 Simulations......Page 453 Implementing ON/OFF Controllers by Field Parallel Gate Arrays (FPGA)......Page 457 Chattering Reduction......Page 458 A m−Phases Parallel Buck Converter......Page 461 Conclusions......Page 463 References......Page 469 Introduction......Page 470 Problem Statement......Page 471 Adaptive Sliding Mode Control......Page 474 A Unified Approach......Page 477 Control Solutions and Design of Functions F......Page 479 Second Order Sliding Mode Control by Static Output Feedback [17]......Page 483 Control of Electropneumatic Actuator......Page 485 Control of Induction Motor [23]......Page 491 Conclusion......Page 495 References......Page 496 Introduction......Page 498 Application Domains of Sliding Mode......Page 499 Synchronous Machine......Page 500 One Axes Model......Page 502 Sliding-Mode Controller Design......Page 503 Multi-machine Mathematical Model......Page 506 Dynamical Model of a Twin Rotor System......Page 511 Teleoperation System......Page 515 Controller Design......Page 517 Super Twisting Observer Design......Page 518 Simulation Results......Page 519 References......Page 520 Introduction......Page 522 Power Processing Systems......Page 524 Generalized Canonical Element......Page 525 Synthesis of DC Transformers......Page 526 Power Gyrator......Page 532 Loss-Free Resistors......Page 533 Impedance Matching......Page 534 DC-AC Conversion......Page 539 Power Distribution......Page 541 Power Factor Correction......Page 542 Conclusions......Page 543 References......Page 544 Introduction......Page 546 Problem Formulation......Page 547 Solution to the Problem 1: Robust Motion Control for Robot Manipulators......Page 548 Design of the Proposed Second Order Sliding Mode Controller......Page 549 Experimental Results on Motion Control......Page 551 The Considered Industrial Robot......Page 552 The Experiments......Page 553 Comparison with the Super Twisting Second Order Sliding Mode Algorithm......Page 558 The Proposed Diagnostic Scheme......Page 560 Actuator Faults Detection Strategy......Page 561 Sensor Faults Detection Strategy......Page 562 Residual Generation......Page 564 Fault Isolation for Single Faults......Page 565 Experimental Test in Presence of Actuator Faults......Page 566 Experimental Tests in Presence of Sensor Faults......Page 567 Conclusions......Page 568 References......Page 569 Introduction......Page 573 Plant Model......Page 574 The Flux Linkage ψf d Control Loop......Page 575 The Speed ωm Control Loop......Page 576 Plant Model......Page 577 The Idea of Block Integral SM Controllers......Page 578 Block Integral SM Speed Stabilizer......Page 580 SM Voltage Regulator......Page 582 Induction Motor with Magnetic Saturation Control......Page 583 Mathematical Model of Induction Motor with Saturation......Page 584 Plant Model......Page 585 Control Algorithm......Page 588 Induction Motor Hybrid Control......Page 592 Discrete–Time Controller......Page 593 Identification......Page 595 Controller Design......Page 597 References......Page 598 Back matter......Page 600 The book presents the newest results of the major world research groups working in the area of Variable Structure Systems and Sliding Mode Control (VSS/SMC). The research activity of these groups is coordinated by the IEEE Technical Committee on Variable Structure Systems (VSS) and Sliding Modes (SM). The presented results include the reports of the research groups collaborating in a framework of the Unión European Union - México project of Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICyT) 93302 titled "Automatization and Monitoring of Energy Production Processes via Sliding Mode Control". The book starts with the overview of the sliding mode control concepts and algorithms that were developed and discussed in the last two decades The research papers are combined in three sections: Part I: VSS and SM Algorithms and their Analysis Part II: SMC Design Part III: Applications of VSS and SMC The book will be of interests of engineers, researchers and graduate students working in the area of the control systems design. Novel mathematical theories and engeneering concepts of control systems are rigorously discussed and supported by numerous applications to practical tasks