Passivity based control of Euler Lagrange systems: mechanical, electrical and electromechanical applications
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
London [u.a.]
Springer
1998
|
| Series: | Communications and control engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXIV, 543 S. graph. Darst. |
| ISBN: | 1852330163 |
Staff View
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| 245 | 1 | 0 | |a Passivity based control of Euler Lagrange systems |b mechanical, electrical and electromechanical applications |c Romeo Ortega ... |
| 246 | 1 | 3 | |a Passivity-based control of Euler Lagrange systems |
| 264 | 1 | |a London [u.a.] |b Springer |c 1998 | |
| 300 | |a XXXIV, 543 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Communications and control engineering | |
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| 650 | 0 | 7 | |a Reglerentwurf |0 (DE-588)4177447-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804126706630393856 |
|---|---|
| adam_text | Contents
Notation xxxi
1 Introduction 1
1 From control engineering to mathematical control theory and back . . 1
2 A route towards applications 3
3 Why Euler-Lagrange systems? 4
4 On the role of interconnection 7
5 Why passivity? 8
6 What is passivity-based control? 10
7 Some historical remarks 12
7.1 Euler-Lagrange systems and nonlinear dynamics 12
7.2 Passivity and feedback stabilization 12
2 Euler-Lagrange systems 15
1 The Euler-Lagrange equations 16
2 Input-output properties 19
2.1 Passivity of EL systems 20
2.2 Passivity of the error dynamics 22
2.3 Other properties and assumptions 24
2.4 Passive subsystems decomposition 25
2.5 An EL structure-preserving interconnection 26
3 Lyapunov stability properties 27
3.1 Fully-damped systems 27
3.2 Underdamped systems 28
4 Examples 30
xiii
xiv CONTENTS
4.1 A rotational/translational proof mass actuator 30
4.2 Levitated ball 32
4.3 Flexible joints robots 34
4.4 The Duffing system 35
4.5 A marine surface vessel 36
5 Concluding remarks 37
I Mechanical Systems 39
3 Set-point regulation 41
1 State feedback control of fully-actuated systems 42
1.1 A basic result: The PD controller 42
1.2 An introductory example 44
1.3 Physical interpretation and literature review 46
2 Output feedback stabilization of underactuated systems 48
2.1 Literature review 48
2.2 Problem formulation 48
2.3 Euler-Lagrange controllers 49
2.4 Examples 51
3 Bounded output feedback regulation 61
3.1 Literature review 61
3.2 Problem formulation 61
3.3 Globally stabilizing saturated EL controllers 63
3.4 Examples 68
4 Set-point regulation under parameter uncertainty 75
4.1 Literature review 76
4.2 Adaptive control 77
4.3 Linear PID control 79
4.4 Nonlinear PID control 82
4.5 Output feedback regulation: The PI2D controller 85
5 Concluding remarks 91
CONTENTS xv
4 Trajectory tracking control 93
1 State feedback control of fully-actuated systems 94
1.1 The PD+ controller 95
1.2 The Slotine and Li controller 96
2 Adaptive trajectory tracking 97
2.1 Adaptive controller of Slotine and Li 97
2.2 A robust adaptive controller 98
3 State feedback of underactuated systems 100
3.1 Model and problem formulation 100
3.2 Literature review 101
3.3 A passivity-based controller 102
3.4 Comparison with backstepping and cascaded designs 104
3.5 A controller without jerk measurements 105
4 Output feedback of fully-actuated systems 108
4.1 Semiglobal tracking control of robot manipulators 109
4.2 Discussion on global tracking 110
5 Simulation results Ill
6 Concluding remarks 113
5 Adaptive disturbance attenuation: Friction compensation 115
1 Adaptive friction compensation 116
1.1 The LuGre friction model 117
1.2 DC motor with friction 119
1.3 Robot manipulator 122
1.4 Simulations 124
2 State-space passifiable systems with disturbances 127
2.1 Background 127
2.2 A theorem for passifiable affine nonlinear systems 129
3 Concluding remarks 131
xvi CONTENTS
II Electrical systems 133
6 Modeling of switched DC—to—DC power converters 135
1 Introduction 135
2 Lagrangian modeling 137
2.1 Modeling of switched networks 137
2.2 A variational argument 138
2.3 General Lagrangian model: Passivity property 140
2.4 Examples 145
3 Hamiltonian modeling 157
3.1 Constitutive elements 158
3.2 LC circuits 160
3.3 Examples 161
4 Average models of PWM regulated converters 168
4.1 General issues about pulse-width-modulation 169
4.2 Examples 171
4.3 Some structural properties 176
5 Conclusions 180
7 Passivity-based control of DC—to—DC power converters 181
1 Introduction 181
2 PBC of stabilizing duty ratio 182
2.1 The Boost converter 183
2.2 The Buck-boost converter 187
2.3 Simulation results 188
3 Passivity based sliding mode stabilization 191
3.1 Introduction 191
3.2 Sliding mode control of the Boost converter 192
3.3 Passivity-based sliding controller 198
4 Adaptive stabilization 206
4.1 Controller design 206
4.2 Simulation results 211
5 Experimental comparison of several nonlinear controllers 213
CONTENTS xvii
5.1 Feedback control laws 213
5.2 Experimental configuration 219
5.3 Experimental results 221
5.4 Conclusions 236
III Electromechanical systems 241
8 Nested—loop passivity—based control: An illustrative example 243
1 Introduction 244
1.1 Model and control problem 245
2 Passivity-based control with total energy-shaping 246
3 Nested-loop passivity-based control 247
3.1 Control structure 248
3.2 Passivity-based controller design 249
4 Output-feedback passivity-based control 253
5 Comparison with feedback linearization and backstepping 254
5.1 Feedback-linearization control 255
5.2 Integrator backstepping control 256
5.3 Comparison of the schemes 257
5.4 Simulation results 259
5.5 Conclusions and further research 262
9 Generalized AC motor 265
1 Introduction 265
1.1 AC motors 265
1.2 Review of previous work 268
1.3 Outline of the rest of this chapter 279
2 Lagrangian model and control problem 280
2.1 The Euler-Lagrange equations for AC machines 281
2.2 Control problem formulation 283
2.3 Remarks to the model 284
2.4 Examples 287
xviii CONTENTS
3 A passivity-based approach for controller design 288
3.1 Passive subsystems feedback decomposition 288
3.2 Design procedure 289
4 A globally stable torque tracking controller 289
4.1 Strict passifiability via damping injection 290
4.2 Current tracking via energy-shaping 292
4.3 From current tracking to torque tracking 294
4.4 PBC for electric machines 297
5 PBC of underactuated electrical machines revisited 302
5.1 Realization of the PBC via BP transformability 302
5.2 A geometric perspective 304
6 Examples 305
7 Conclusions 307
7.1 Summary 307
7.2 Open issues 308
10 Voltage-fed induction motors 311
1 Induction motor model 312
1.1 Dynamic equations 312
1.2 Some control properties of the model 313
1.3 Coordinate transformations 315
1.4 Remarks to the model 318
1.5 Concluding remarks 320
2 Problem formulation 320
3 A nested-loop PBC 321
3.1 A systems inversion perspective of the torque tracking PBC 323
3.2 Observer-less PBC for induction motors 327
3.3 Remarks to the controller 331
3.4 Integral action in stator currents 333
3.5 Adaptation of stator parameters 334
3.6 A fundamental obstacle for rotor resistance adaptation .... 335
3.7 A ^-implementation 337
CONTENTS xix
3.8 Definitions of desired rotor flux norm 338
3.9 Simulation results 340
4 A PBC with total energy-shaping 342
4.1 Factorization of workless forces 343
4.2 Problem formulation 344
4.3 Ideal case with full state feedback 344
4.4 Observer-based PBC for induction motors 346
4.5 Remarks to the controller 348
4.6 A dg-implementation 349
4.7 Simulation results 351
4.8 Concluding remarks 353
5 Field-oriented control and feedback linearization 353
5.1 Rationale of field-oriented control 354
5.2 State estimation or reference values 357
5.3 Shortcomings of FOC 358
5.4 Feedback linearization 361
6 Experimental results 363
6.1 Experimental setup 363
6.2 Outline of experiments 369
6.3 Observer-less control 370
6.4 Observer-based control 375
6.5 Comparison with FOC 376
6.6 Concluding remarks 379
11 Current—fed induction motors 381
1 Model of the current-fed induction motor 383
2 Field orientation and feedback linearization 385
2.1 Direct field-oriented control 385
2.2 Indirect field-oriented control 386
2.3 Observer-based feedback-linearizing control 387
2.4 Remarks to OBFL and FOC 390
3 Passivity-based control of current-fed machines 392
xx CONTENTS
3.1 PBC is downward compatible with FOC 392
3.2 Stability of indirect FOC for known parameters 393
4 Experimental comparison of PBC and feedback linearization 394
4.1 Experimental setup 395
4.2 Selection of flux reference in experiments 398
4.3 Speed tracking performance 399
4.4 Robustness and disturbance attenuation 401
4.5 Conclusion 402
5 Robust stability of PBC 403
5.1 Global boundedness 404
5.2 Coordinate changes and uniqueness of equilibrium 405
5.3 Local asymptotic stability 409
5.4 Global exponential stability 410
6 Off-line tuning of PBC 415
6.1 Problem formulation 416
6.2 Change of coordinates 417
6.3 Local stability 418
6.4 A performance evaluation method based on passivity 420
6.5 Illustrative examples 425
7 Discrete-time implementation of PBC 429
7.1 The exact discrete-time model of the induction motor 431
7.2 Analysis of discrete-time PBC 432
7.3 A new discrete-time control algorithm 433
7.4 Discussion of discrete-time controller 435
7.5 Experimental results 435
8 Conclusions and further research 438
12 Feedback interconnected systems: Robots with AC drives 441
1 Introduction 442
1.1 Cascaded systems 442
1.2 Robots with AC drives 445
2 General problem formulation 446
CONTENTS xxi
3 Assumptions 448
3.1 Realizability of the controller 448
3.2 Other assumptions 450
4 Problem solution 451
4.1 Proof of Theorem 12.7 451
5 Application to robots with AC drives 455
5.1 Model 455
5.2 Global tracking controller 457
6 Simulation results 461
7 Concluding remarks 464
13 Other applications and current research 467
1 Other applications 468
2 Current research 469
2.1 Power electronics 469
2.2 Power systems 470
2.3 Generation of storage functions for forced EL systems 470
2.4 Performance 471
A Dissipativity and passivity 475
1 Circuit example 476
2 Hi and C ze spaces 477
3 Passivity and finite-gain stability 477
4 Feedback systems 479
5 Internal stability and passivity 480
6 The Kalman-Yakubovich-Popov lemma 481
B Derivation of the Euler-Lagrange equations 483
1 Generalized coordinates and velocities 483
2 Hamilton s principle 487
3 From Hamilton s principle to the EL equations 488
4 EL equations for non-conservative systems 489
5 List of generalized variables 489
xxii CONTENTS
6 Hamiltonian formulation 489
C Background material 493
D Proofs 495
1 Proofs for the PI2D controller 495
1.1 Properties of the storage %(? q, fl) 495
1.2 Lyapunov stability of the PI2D 497
2 Proof of positive definiteness of f(qp) defined in (3.43) 498
3 The BP transformation 500
3.1 Proof of Proposition 9.20 500
3.2 A Lemma on the BP Transformation 502
4 Proof of Eqs. (10.41) and (10.77) 503
4.1 A theorem on positivity of a block matrix 503
4.2 ProofofEq. (10.77) 503
4.3 ProofofEq. (10.41) 506
5 Derivation of Eqs. (10.55) and (10.56) 507
5.1 Derivation of Eq. (10.55) 507
5.2 Derivation of Eq. (10.56) 508
6 Boundedness of all signals for indirect FOC 510
6.1 Proof of Proposition 11.10 510
Bibliography 515
Index 539
|
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| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:21:43Z |
| institution | BVB |
| isbn | 1852330163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008194823 |
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| physical | XXXIV, 543 S. graph. Darst. |
| publishDate | 1998 |
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| series2 | Communications and control engineering |
| spelling | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications Romeo Ortega ... Passivity-based control of Euler Lagrange systems London [u.a.] Springer 1998 XXXIV, 543 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Communications and control engineering Controleleer gtt Lagrange functies gtt Lagrange equations Passivity-based control Passives System (DE-588)4202764-0 gnd rswk-swf Rückkopplung (DE-588)4050851-1 gnd rswk-swf Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd rswk-swf Reglerentwurf (DE-588)4177447-4 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Lagrange-Bewegungsgleichungen (DE-588)4166460-7 s Ljapunov-Stabilitätstheorie (DE-588)4167992-1 s Passives System (DE-588)4202764-0 s Rückkopplung (DE-588)4050851-1 s Reglerentwurf (DE-588)4177447-4 s DE-604 Ortega, Romeo 1954- Sonstige (DE-588)120106574 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008194823&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications Controleleer gtt Lagrange functies gtt Lagrange equations Passivity-based control Passives System (DE-588)4202764-0 gnd Rückkopplung (DE-588)4050851-1 gnd Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd Reglerentwurf (DE-588)4177447-4 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| subject_GND | (DE-588)4202764-0 (DE-588)4050851-1 (DE-588)4166460-7 (DE-588)4177447-4 (DE-588)4126142-2 (DE-588)4167992-1 |
| title | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications |
| title_alt | Passivity-based control of Euler Lagrange systems |
| title_auth | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications |
| title_exact_search | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications |
| title_full | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications Romeo Ortega ... |
| title_fullStr | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications Romeo Ortega ... |
| title_full_unstemmed | Passivity based control of Euler Lagrange systems mechanical, electrical and electromechanical applications Romeo Ortega ... |
| title_short | Passivity based control of Euler Lagrange systems |
| title_sort | passivity based control of euler lagrange systems mechanical electrical and electromechanical applications |
| title_sub | mechanical, electrical and electromechanical applications |
| topic | Controleleer gtt Lagrange functies gtt Lagrange equations Passivity-based control Passives System (DE-588)4202764-0 gnd Rückkopplung (DE-588)4050851-1 gnd Lagrange-Bewegungsgleichungen (DE-588)4166460-7 gnd Reglerentwurf (DE-588)4177447-4 gnd Nichtlineares dynamisches System (DE-588)4126142-2 gnd Ljapunov-Stabilitätstheorie (DE-588)4167992-1 gnd |
| topic_facet | Controleleer Lagrange functies Lagrange equations Passivity-based control Passives System Rückkopplung Lagrange-Bewegungsgleichungen Reglerentwurf Nichtlineares dynamisches System Ljapunov-Stabilitätstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008194823&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ortegaromeo passivitybasedcontrolofeulerlagrangesystemsmechanicalelectricalandelectromechanicalapplications AT ortegaromeo passivitybasedcontrolofeulerlagrangesystems |