Nonlinear Control and Filtering Using Differential Flatness Approaches (eBook)

Dr. G. Rigatos, obtained a diploma (1995) and a Ph.D. (2000) both from the Department of Electrical and Computer Engineering, of the National Technical University of Athens (NTUA), Greece. Currently he holds a Researcher position (Grade B) at the Industrial Systems Institute (Greek Secretariat for Research and Technology), on the topic of “Modelling and Control of Industrial Systems”. In 2001 he was a post-doctoral researcher at the Institut de Recherche en Informatique et Systèmes Aléatoires IRISA, in Rennes France. In 2007 he was an invited professor (maître des conférences) at Université Paris XI (Institut d’ Electronique Fondamentale). In 2012 he held a Lecturer Position at the Department of Engineering, of Harper-Adams University College, in Shropshire, UK on the topic of “Mechatronics and Artificial Intelligence". He has also been an adjunct professor in Greek Universities where he has taught courses on systems and control theory. His research interests include the areas of control and robotics, optimization and fault diagnosis, adaptive systems and computational intelligence. He is a member of the IEEE, IET and IMACS.

Foreword 7
Preface 9
Acknowledgments 15
Contents 16
Acronyms 28
1 Nonlinear Dynamical Systems and Global Linearizing Control Methods 29
1.1 Introduction 29
1.2 Characteristics of the Dynamics of Nonlinear Systems 29
1.3 Computation of Isoclines 34
1.4 Basic Features in the Study of Nonlinear Dynamics 36
1.4.1 The Phase Diagram 36
1.4.2 Stability Analysis of Nonlinear Systems 37
1.4.3 Stability Analysis of Nonlinear Models 39
1.5 Phase Diagrams and Equilibria of Nonlinear Models 40
1.5.1 Phase Diagrams for Linear Dynamical Systems 40
1.5.2 Multiple Equilibria for Nonlinear Dynamical Systems 45
1.5.3 Limit Cycles 47
1.6 Bifurcations in Nonlinear Dynamics 49
1.6.1 Bifurcations of Fixed Points of Nonlinear Models 49
1.6.2 Saddle-Node Bifurcations of Fixed Points in a One-Dimensional System 49
1.6.3 Pitchfork Bifurcation of Fixed Points 50
1.6.4 The Hopf Bifurcation 52
1.7 Predecessors of Differential Flatness Theory 54
1.7.1 The Differential Geometric Approach 54
1.7.2 Elaboration on the Frobenius Theorem 57
1.7.3 Input--Output Linearization 58
1.7.4 Elaborating on Input--Output Linearization 61
1.7.5 Input-State Linearization 65
1.7.6 Stages in the Implementation of Input-State Linearization 71
1.7.7 Input--Output and Input-State Linearization for MIMO Systems 72
1.7.8 Dynamic Extension 73
2 Differential Flatness Theory and Flatness-Based Control 74
2.1 Introduction 74
2.2 Definition of Differentially Flat Systems 75
2.2.1 The Background of Differential Flatness Theory 75
2.2.2 Differential Flatness for Finite Dimensional Systems 76
2.3 Properties of Differentially Flat Systems 84
2.3.1 Equivalence and Differential Flatness 84
2.3.2 Differential Flatness and Trajectory Planning 99
2.3.3 Differential Flatness, Feedback Control and Equivalence 102
2.4 Flatness-Based Control and State Feedback for Systems ƒ 106
2.5 Classification of Types of Differentially Flat Systems 109
2.5.1 Criteria About the Differential Flatness of a System 109
2.5.2 A Sufficient Condition for Showing that a System Is Not Differentially Flat 112
2.5.3 Liouvillian and Nondifferentially Flat Systems 113
2.6 Elaborated Criteria for Checking Differential Flatness 114
2.6.1 Implicit Control Systems on Manifolds of Jets 114
2.6.2 The Lie-Backlünd Equivalence for Implicit Systems 116
2.6.3 Conditions for Differential Flatness of Implicit Systems 117
2.6.4 Example of Elaborated Differential Flatness Criteria to Nonlinear Systems 120
2.7 Distributed Parameter Systems and Their Transformation ƒ 123
2.7.1 State-Space Description of a Heat Diffusion Dynamics 123
2.7.2 Differential Flatness of the Nonlinear Heat Diffusion PDE 126
3 Nonlinear Adaptive Control Based on Differential Flatness Theory 129
3.1 Introduction 129
3.2 Flatness-Based Adaptive Neuro-Fuzzy Control for SISO Systems 130
3.2.1 Overview 130
3.3 Flatness-Based Adaptive Fuzzy Control for SISO Dynamical Systems 131
3.3.1 Transformation of SISO Nonlinear Systems into a Canonical Form 131
3.3.2 Adaptive Control Law for SISO Nonlinear Systems 132
3.3.3 Approximators of SISO System Unknown Dynamics 133
3.3.4 Lyapunov Stability Analysis for SISO Dynamical Systems 135
3.3.5 Simulation Tests 137
3.4 Flatness-Based Adaptive Fuzzy Control for MIMO Systems 142
3.4.1 Overview 142
3.4.2 Differential Flatness for MIMO Nonlinear Dynamical Systems 143
3.4.3 Flatness-Based Adaptive Fuzzy Control for MIMO Nonlinear Systems 146
3.4.4 Flatness-Based Control for a MIMO Robotic Manipulator 148
3.4.5 Lyapunov Stability Analysis for MIMO Nonlinear Systems 153
3.4.6 Simulation Tests 159
4 Nonlinear Kalman Filtering Based on Differential Flatness Theory 166
4.1 Introduction 166
4.2 The Derivative-Free Nonlinear Kalman Filter 167
4.2.1 Overview 167
4.2.2 Extended Kalman Filtering for Nonlinear Dynamical Systems 168
4.2.3 Derivative-Free Kalman Filtering to SISO Nonlinear Systems 174
4.2.4 Simulation Tests 177
4.2.5 Derivative-Free Kalman Filtering for MIMO Nonlinear Systems 188
4.2.6 Simulation Tests 191
4.3 The Derivative-Free Distributed Nonlinear Kalman Filter 197
4.3.1 Overview 197
4.3.2 Overview of the Extended Information Filter 198
4.3.3 Distributed Filtering for Sensorless Control 202
4.3.4 Simulation Tests 204
5 Differential Flatness Theory and Industrial Robotics 207
5.1 Overview 207
5.2 Adaptive Fuzzy Control of Underactuated MIMO Robots 209
5.2.1 Overview 209
5.2.2 Dynamic Model of the Closed-Chain 2-DOF Robotic System 210
5.2.3 Linearization of the Closed-Chain 2-DOF Robotic System Using Lie Algebra Theory 216
5.2.4 Differential Flatness of the Underactuated Manipulator 219
5.2.5 Flatness-Based Adaptive Fuzzy Control for the Underactuated Robot 222
5.2.6 Simulation Tests 222
5.3 Observer-Based Adaptive Fuzzy Control of MIMO Robots 223
5.3.1 Overview 223
5.3.2 Estimation of the Robot's State Vector 225
5.3.3 Application of Flatness-Based Adaptive Fuzzy Control 227
5.3.4 Dynamics of the Observation Error 228
5.3.5 Approximation of the System's Unknown Dynamics 229
5.3.6 Lyapunov Stability Analysis 230
5.3.7 The Role of Riccati Equation Coefficients in Observer-Based Adaptive Fuzzy Control 236
5.3.8 Simulation Tests 238
5.4 State Estimation-Based Control of Underactuated Robots 242
5.4.1 Overview 242
5.4.2 Derivative-Free Nonlinear Kalman Filter for the Closed-Chain 2-DOF Robotic System 243
5.4.3 Simulation Tests 246
5.5 Distributed Filtering Under External Disturbances 247
5.5.1 Overview 247
5.5.2 Dynamics and Control of the Robot 249
5.5.3 Simulation Tests 251
5.6 Distributed Nonlinear Filtering Under Measurement Delays 254
5.6.1 Networked Control Under Communication Disturbances 254
5.6.2 Networked Kalman Filtering for an Autonomous System 255
5.6.3 Smoothing Estimation in Case of Delayed Measurements 256
5.6.4 Distributed Filtering-Based Fusion of the Robot's State Estimates 259
5.6.5 Simulation Tests 260
6 Differential Flatness Theory in Mobile Robotics and Autonomous Vehicles 263
6.1 Outline 263
6.2 State Estimation-Based Control of Autonomous Vehicles 265
6.2.1 Localization and Autonomous Navigation of Ground Vehicles 265
6.2.2 Application of Derivative-Free Kalman Filtering to MIMO UGV Models 266
6.2.3 Controller Design for UGVs 268
6.2.4 Derivative-Free Kalman Filtering for UGVs 271
6.2.5 Simulation Tests 272
6.2.6 Derivative-Free Kalman Filter-Based Navigation of the Autonomous Vehicle 276
6.3 State Estimation-Based Control and Synchronization of Cooperating Vehicles 285
6.3.1 Overview 285
6.3.2 Distributed Kalman Filtering for Unmanned Ground Vehicles 287
6.3.3 Simulation Tests 288
6.4 Distributed Fault Diagnosis for Autonomous Vehicles 289
6.4.1 Integrity Testing in Navigation Sensors of AGVs 289
6.4.2 Sensor Fusion for AGV Navigation 291
6.4.3 Canonical Form for the AGV Model 294
6.4.4 Derivative-Free Extended Information Filtering for UGVs 294
6.4.5 Simulation Tests 295
6.5 Velocity Control of 4-Wheel Vehicles 296
6.5.1 Overview 297
6.5.2 Dynamic Model of the Vehicle 300
6.5.3 Flatness-Based Controller for the 3-DOF Vehicle Model 304
6.5.4 Estimation of Vehicle Disturbance Forces with Kalman Filtering 307
6.5.5 Simulation Tests 310
6.6 Active Vehicle Suspension Control 312
6.6.1 Overview 312
6.6.2 Dynamic Model of Vehicle Suspension 316
6.6.3 Flatness-Based Control for a Suspension Model 320
6.6.4 Compensating for Model Uncertainty with the Use of the Hinfty Kalman Filter 321
6.6.5 Robust State Estimation with the Use of Disturbance Observers 324
6.6.6 Simulation Tests 326
6.7 State Estimation-Based Control of Quadrotors 328
6.7.1 Overview 328
6.7.2 Kinematic Model of the Quadropter 334
6.7.3 Euler-Lagrange Equations for the Quadropter 335
6.7.4 Design of Flatness-Based Controller for the Quadrotor's Model 337
6.7.5 Estimation of the Quadrotor's Disturbance Forces and Torques with Kalman Filtering 339
6.7.6 Simulation Tests 342
6.8 State Estimation-Based Control of the Underactuated Hovercraft 344
6.8.1 Overview 344
6.8.2 Lie Algebra-Based Control of the Underactuated Hovercraft 347
6.8.3 Flatness-Based Control of the Underactuated Vessel 353
6.8.4 Disturbances' Compensation with the Use of the Derivative-Free Nonlinear Kalman Filter 354
6.8.5 Simulation Tests 356
7 Differential Flatness Theory and Electric Power Generation 360
7.1 Outline 360
7.2 State Estimation-Based Control of PMSGs 361
7.2.1 The PMSG Control Problem 361
7.2.2 Dynamic Model of the Permanent Magnet Synchronous Generator 363
7.2.3 Lie Algebra-Based Design of State Estimators for the PMSG 365
7.2.4 Differential Flatness of the PMSG 370
7.2.5 Estimation of PMSG Disturbance Input with Kalman Filtering 372
7.2.6 Simulation Experiments 375
7.3 State Estimation-Based Control of DFIGs 381
7.3.1 Overview 381
7.3.2 The Complete Sixth-Order Model of the Induction Generator 382
7.3.3 Input--Output Linearization of the DFIG Using Lie Algebra 386
7.3.4 Input--Output Linearization of the DFIG Using Differential Flatness Theory 390
7.3.5 Kalman Filter-Based Disturbance Observer for the DFIG Model 394
7.3.6 Simulation Tests 396
7.4 Flatness-Based Control of DFIG in Cascading Loops 400
7.4.1 Overview 400
7.4.2 A New Proof of the Differential Flatness of the DFIG 401
7.4.3 Control of the DFIG in Cascading Loops 403
7.4.4 EKF Implementation for Sensorless Control of the DFIG 406
7.4.5 Simulation Tests 408
7.5 State Estimation-Based Control of Distributed PMSGs 411
7.5.1 Overview 411
7.5.2 Dynamic Model of the Distributed Power Generation Units 413
7.5.3 Lie Algebra-Based Design of a Feedback Controller for the PMSG 414
7.5.4 Differential Flatness of the Distributed PMSG Model 416
7.5.5 Simulation Tests 420
8 Differential Flatness Theory for Electric Motors and Actuators 426
8.1 Introduction 426
8.2 Flatness-Based Adaptive Control of DC Motors 427
8.2.1 Overview 427
8.2.2 Dynamics and Linearization of the DC Motor Model 428
8.3 Flatness-Based Control of Induction Motors in Cascading Loops 432
8.3.1 Overview 432
8.3.2 A Cascading Loops Scheme for Control of Field-Oriented Induction Motors 433
8.3.3 A Flatness-Based Control Approach for Induction Motors 437
8.3.4 Implementation of the EKF for the Nonlinear Induction Motor Model 438
8.3.5 Unscented Kalman Filtering for Induction Motor Control 439
8.4 Simulation Results 441
8.5 Flatness-Based Adaptive Control of Electrostatic MEMS Using Output Feedback 443
8.5.1 Introduction 445
8.5.2 Dynamic Model of the Electrostatic Actuator 446
8.5.3 Linearization of the MEMS Model Using Lie Algebra 448
8.5.4 Differential Flatness of the Electrostatic Actuator 450
8.5.5 Adaptive Fuzzy Control of the MEMS Model Using Output Feedback 452
8.5.6 Lyapunov Stability Analysis 457
8.5.7 Simulation Tests 462
9 Differential Flatness Theory in Power Electronics 465
9.1 Introduction 465
9.2 Three-Phase Voltage Source Converters Control 466
9.2.1 Overview 466
9.2.2 Linearization of the Converter's Model Using Lie Algebra 468
9.2.3 Differential Flatness of the Voltage Source Converter 471
9.2.4 Kalman Filter-Based Disturbance Observer for the VSC Model 475
9.2.5 Simulation Tests 477
9.3 Inverters Control 480
9.3.1 Overview 480
9.3.2 Dynamic Model of the Inverter 481
9.3.3 Lie Algebra-Based Control of the Inverter's Model 485
9.3.4 Differential Flatness of the Inverter's Model 488
9.3.5 Flatness-Based Control of the Inverter 490
9.3.6 State and Disturbances Estimation with Nonlinear Kalman Filtering 494
9.3.7 Simulation Tests 495
9.4 Distributed Inverters Synchronization 497
9.4.1 Overview 497
9.4.2 The Synchronization Problem for Parallel Inverters 499
9.5 State and Disturbances Estimation of Parallel Inverters with Nonlinear Kalman Filtering 504
9.6 Simulation Tests 505
10 Differential Flatness Theory for Internal Combustion Engines 513
10.1 Overview 513
10.2 Flatness-Based Control of Valves in Marine Diesel Engines 515
10.2.1 Overview 515
10.2.2 Dynamic Model of the Valve 516
10.2.3 Input--Output Linearization Using Lie Algebra 520
10.2.4 Input--Output Linearization Using Differential Flatness Theory 523
10.2.5 Disturbances Compensation with Derivative-Free Nonlinear Kalman Filter 526
10.2.6 Simulation Tests 528
10.3 Flatness-Based Control of Diesel Combustion Engines 533
10.3.1 Overview 533
10.3.2 Dynamic Model of the Turbocharged Diesel Engine 534
10.3.3 Nonlinear Control of the Diesel Engine Using Lie Algebra 536
10.3.4 A Dynamic Extension-Based Feedback Control Scheme 539
10.3.5 Nonlinear Control of the Diesel Engine Using Differential Flatness Theory 543
10.3.6 Disturbances Compensation Using the Derivative-Free Nonlinear Kalman Filter 547
10.3.7 Simulation Tests 549
10.4 Adaptive Control for Diesel Combustion Engines 550
10.4.1 Overview 550
10.4.2 Observer-Based Adaptive Fuzzy Control for the Diesel Combustion Engine 551
10.4.3 Application of Flatness-Based Adaptive Fuzzy Control to the MIMO Diesel Engine Model 555
10.4.4 Lyapunov Stability Analysis 560
10.4.5 Simulation Tests 565
10.5 Flatness-Based Control and Kalman Filtering for the Spark-Ignited Engine 568
10.5.1 Overview 569
10.5.2 Dynamic Model of the SI Engine 570
10.5.3 Feedback Linearizing Control of the SI Engine Using Lie Algebra 571
10.5.4 Feedback Linearizing Control of the SI Engine Using Differential Flatness Theory 573
10.5.5 Compensation of Disturbances Using the Derivative-Free Nonlinear Kalman Filter 575
10.5.6 Simulation Tests 576
10.6 Flatness-Based Adaptive Fuzzy Control of the Spark-Ignited Engine 579
10.6.1 Overview 580
10.6.2 Flatness-Based Adaptive Fuzzy Control for SI Motors 581
10.6.3 Lyapunov Stability Analysis 584
10.6.4 Simulation Tests 587
10.7 Flatness-Based Control and Kalman Filtering of the Air--Fuel Ratio 588
10.7.1 Overview 588
10.8 Dynamic Model of the Air--Fuel Ratio System 589
10.8.1 The Air and Fuel Flow Models 589
10.8.2 Dynamics of the Air--Fuel Ratio System 591
10.8.3 Differential Flatness of the Air--Fuel Ratio System 592
10.8.4 Flatness-Based Control of the Air--Fuel Ratio System 594
10.8.5 Compensation of Uncertainties with the Derivative-Free Nonlinear Kalman Filter 595
10.8.6 Simulation Tests 599
11 Differential Flatness Theory for Chaotic Dynamical Systems 600
11.1 Introduction 600
11.2 Flatness-Based Control of Chaotic Dynamical Systems 601
11.2.1 Overview 601
11.2.2 Differential Flatness of Chaotic Dynamical Systems 602
11.2.3 Flatness-Based Adaptive Fuzzy Control for Chaotic Systems 606
11.2.4 Design of the Feedback Controller 606
11.2.5 Approximators of Unknown System Dynamics 608
11.2.6 Lyapunov Stability Analysis 609
11.2.7 Nonlinear Feedback Control of Chaotic Systems Based on Fuzzy Local Linearization 612
11.2.8 Simulation Tests 614
11.3 Differential Flatness Theory for Chaos-Based Communication Systems 616
11.3.1 Overview 617
11.3.2 Structure of the Chaotic Communication System 619
11.3.3 Differential Flatness Theory 621
11.3.4 Estimation in Chaotic Modulators with Nonlinear Kalman Filter 622
11.3.5 Channel Equalization and Synchronization Using Dual Kalman Filtering 623
11.3.6 Simulation Tests 626
12 Differential Flatness Theory for Distributed Parameter Systems 633
12.1 Introduction 633
12.2 Pointwise Flatness-Based Control of Distributed Parameter Systems 635
12.2.1 Overview 635
12.2.2 Nonlinear 1D Wave-Type Partial Differential Equations 636
12.2.3 Sine-Gordon Nonlinear PDE in the Model of the Josephson Junction 637
12.2.4 Current Equation in a Josepshon Transmission Line 638
12.2.5 State-Space Description of the Nonlinear Wave Dynamics 639
12.2.6 Solution of the Control and Estimation Problem for Nonlinear Wave Dynamics 642
12.2.7 Simulation Tests 645
12.3 Control of Heat Diffusion in Arc Welding Using Differential Flatness Theory and Nonlinear Kalman Filtering 647
12.3.1 Overview 647
12.4 Dynamic Model of the Arc Welding Process 651
12.5 State-Space Description of the Nonlinear Heat Diffusion Dynamics 653
12.6 Solution of the Control and Estimation Problem for Nonlinear Heat Diffusion 655
12.6.1 Solution of the Control Problem 655
12.6.2 Solution of the Estimation Problem 657
12.7 Simulation Tests 659
12.8 Fault Detection and Isolation in Distributed Parameter Systems 660
12.8.1 Overview 660
12.8.2 Estimation of Nonlinear Wave Dynamics 663
12.8.3 Equivalence Between Kalman Filters and Regressor Models 665
12.8.4 Change Detection with the Local Statistical Approach 666
12.8.5 Simulation Tests 671
12.9 Application to Condition Monitoring of Civil and Mechanical Structures 676
12.9.1 Overview 676
12.9.2 Dynamical Model of the Building---Mechanical Structure 677
12.10 Differential Flatness of the Multi-DOF Building's Structure 679
12.10.1 Damage Detection with the Use of Statistical Criteria 682
12.10.2 Disturbances Estimation with the Derivative-Free Nonlinear Kalman Filter 684
12.10.3 Simulation Tests 686
13 Differential Flatness Theory in the Background of Other Control Methods 691
13.1 Differential Flatness Theory in the Background of Backstepping Control 691
13.1.1 Overview 691
13.1.2 Flatness-Based Control Through Transformation into the Canonical Form 693
13.1.3 A New Approach to Flatness-Based Control for Nonlinear Dynamical Systems 694
13.1.4 Closed-Loop Dynamics 697
13.1.5 Comparison to Backstepping Control 699
13.1.6 Simulation Tests 700
13.2 Differential Flatness and Optimal Control 706
13.3 Boundary Control of Nonlinear PDE Dynamics Using ƒ 707
13.3.1 Overview 707
13.3.2 Transformation of the PDE Model into a Set of Nonlinear ODEs 708
13.3.3 Differential Flatness of the Nonlinear PDE Model 711
13.3.4 Computation of a Boundary Conditions-Based Feedback Control Law 713
13.3.5 Closed-Loop Dynamics 715
13.3.6 Simulation Tests 717
References 720
Index 750