Adaptive and Robust Active Vibration Control (eBook)

Ioan Doré Landau has been Emeritus Research Director at CNRS since September 2003 and continues to collaborate with LAG INPG. His research interests encompass theory and applications in system identification, adaptive control, robust digital control and nonlinear systems. He has (co-)authored over 200 papers. He is the author of several books and holds several patents and was the origin of several software packages in control developed by ADAPTECH. He advised 35 PhD students. He has delivered a number of Plenary Talks at International Conferences. Dr. Landau received the Rufus Oldenburger Medal 2000 from ASME. He was an IEEE-CSS "Distinguished Lecturer" for 2001-2003. He has been an IFAC Fellow since 2007 and received the Life Achievement Award from MCA in 2009.

Series Editors’ Foreword 7
Preface 9
Website 10
Expected Audience 11
About the Content 11
Pathways Through the Book 12
Acknowledgements 14
References[1] Constantinescu, A.: Commande robuste et adaptative d’une suspension active. Thèse de doctorat, Institut National Polytechnique de Grenoble (2001)[2] Alma, M.: Rejet adaptatif de perturbations en contrôle actif de vibrations. Ph.D. thesis, Université de Grenoble (2011)[3] Airimitoaie, T.B.: Robust design and tuning of active vibration control systems. Ph.D. thesis, University of Grenoble, France, and University “Politehnica” of Bucharest, Romania (2012)[4] Castellanos-Silva, A.: Compensation adaptative par feedback pour le contrôle actif de vibrations en présence d’incertitudes sur les paramétres du procédé. Ph.D. thesis, Université de Grenoble (2014)[5] Landau, I.D., Silva, A.C., Airimitoaie, T.B., Buche, G., Noé, M.: Benchmark on adaptive regulation—rejection of unknown/time-varying multiple narrow band disturbances. European Journal of Control 19(4), 237—252 (2013). http://dx.doi.org/10.1016/j.ejcon.2013.05.007#1 14
Contents 15
Acronyms 23
Part I Introduction to Adaptive and Robust Active Vibration Control 25
1 Introduction to Adaptive and Robust Active Vibration Control 26
1.1 Active Vibration Control: Why and How 26
1.2 A Conceptual Feedback Framework 32
1.3 Active Damping 34
1.4 The Robust Regulation Paradigm 34
1.5 The Adaptive Regulation Paradigm 35
1.6 Concluding Remarks 37
1.7 Notes and Reference 38
References 38
2 The Test Benches 41
2.1 An Active Hydraulic Suspension System Using Feedback Compensation 41
2.2 An Active Vibration Control System Using Feedback Compensation Through an Inertial Actuator 44
2.3 An Active Distributed Flexible Mechanical Structure ƒ 46
2.4 Concluding Remarks 49
2.5 Notes and References 50
References 50
Part II Techniques for Active Vibration Control 51
3 Active Vibration Control Systems---Model Representation 52
3.1 System Description 52
3.1.1 Continuous-Time Versus Discrete-Time Dynamical Models 52
3.1.2 Digital Control Systems 53
3.1.3 Discrete-Time System Models for Control 55
3.2 Concluding Remarks 58
3.3 Notes and References 58
References 58
4 Parameter Adaptation Algorithms 59
4.1 Introduction 59
4.2 Structure of the Adjustable Model 60
4.2.1 Case (a): Recursive Configuration for System Identification---Equation Error 60
4.2.2 Case (b): Adaptive Feedforward Compensation---Output Error 62
4.3 Basic Parameter Adaptation Algorithms 64
4.3.1 Basic Gradient Algorithm 64
4.3.2 Improved Gradient Algorithm 67
4.3.3 Recursive Least Squares Algorithm 72
4.3.4 Choice of the Adaptation Gain 77
4.3.5 An Example 81
4.4 Stability of Parameter Adaptation Algorithms 82
4.4.1 Equivalent Feedback Representation of the Adaptive Predictors 83
4.4.2 A General Structure and Stability of PAA 86
4.4.3 Output Error Algorithms---Stability Analysis 90
4.5 Parametric Convergence 92
4.5.1 The Problem 92
4.6 The LMS Family of Parameter Adaptation Algorithms 96
4.7 Concluding Remarks 97
4.8 Notes and References 98
References 98
5 Identification of the Active Vibration Control Systems---The Bases 100
5.1 Introduction 100
5.2 Input--Output Data Acquisition and Preprocessing 102
5.2.1 Input--Output Data Acquisition Under an Experimental Protocol 102
5.2.2 Pseudorandom Binary Sequences (PRBS) 102
5.2.3 Data Preprocessing 104
5.3 Model Order Estimation from Data 105
5.4 Parameter Estimation Algorithms 107
5.4.1 Recursive Extended Least Squares (RELS) 109
5.4.2 Output Error with Extended Prediction Model (XOLOE) 111
5.5 Validation of the Identified Models 113
5.5.1 Whiteness Test 113
5.6 Concluding Remarks 115
5.7 Notes and References 116
References 116
6 Identification of the Test Benches in Open-Loop Operation 117
6.1 Identification of the Active Hydraulic Suspension in Open-Loop Operation 117
6.1.1 Identification of the Secondary Path 118
6.1.2 Identification of the Primary Path 123
6.2 Identification of the AVC System Using Feedback Compensation Through an Inertial Actuator 124
6.2.1 Identification of the Secondary Path 124
6.2.2 Identification of the Primary Path 130
6.3 Identification of the Active Distributed Flexible Mechanical Structure Using Feedforward--Feedback Compensation 131
6.4 Concluding Remarks 137
6.5 Notes and References 137
References 137
7 Digital Control Strategies for Active Vibration Control---The Bases 139
7.1 The Digital Controller 139
7.2 Pole Placement 141
7.2.1 Choice of HR and HS---Examples 142
7.2.2 Internal Model Principle (IMP) 144
7.2.3 Youla--Ku?era Parametrization 145
7.2.4 Robustness Margins 147
7.2.5 Model Uncertainties and Robust Stability 150
7.2.6 Templates for the Sensitivity Functions 152
7.2.7 Properties of the Sensitivity Functions 152
7.2.8 Input Sensitivity Function 155
7.2.9 Shaping the Sensitivity Functions for Active Vibration Control 157
7.3 Real-Time Example: Narrow-Band Disturbance Attenuation on the Active Vibration Control System Using an Inertial Actuator 161
7.4 Pole Placement with Sensitivity Function Shaping by Convex Optimisation 164
7.5 Concluding Remarks 167
7.6 Notes and References 167
References 168
8 Identification in Closed-Loop Operation 170
8.1 Introduction 170
8.2 Closed-Loop Output Error Identification Methods 171
8.2.1 The Closed-Loop Output Error Algorithm 175
8.2.2 Filtered and Adaptive Filtered Closed-Loop Output Error Algorithms (F-CLOE, AF-CLOE) 176
8.2.3 Extended Closed-Loop Output Error Algorithm (X-CLOE) 177
8.2.4 Taking into Account Known Fixed Parts in the Model 178
8.2.5 Properties of the Estimated Model 179
8.2.6 Validation of Models Identified in Closed-Loop Operation 180
8.3 A Real-Time Example: Identification in Closed-Loop and Controller Redesign for the Active Control System Using an Inertial Actuator 182
8.4 Concluding Remarks 186
8.5 Notes and References 186
References 187
9 Reduction of the Controller Complexity 188
9.1 Introduction 188
9.2 Criteria for Direct Controller Reduction 190
9.3 Estimation of Reduced Order Controllers by Identification in Closed-Loop 192
9.3.1 Closed-Loop Input Matching (CLIM) 192
9.3.2 Closed-Loop Output Matching (CLOM) 195
9.3.3 Taking into Account the Fixed Parts of the Nominal Controller 195
9.4 Real-Time Example: Reduction of Controller Complexity 197
9.5 Concluding Remarks 200
9.6 Notes and References 201
References 201
Part III Active Damping 202
10 Active Damping 203
10.1 Introduction 203
10.2 Performance Specifications 204
10.3 Controller Design by Shaping the Sensitivity Functions Using ƒ 208
10.4 Identification in Closed-Loop of the Active Suspension ƒ 211
10.5 Redesign of the Controller Based on the Model Identified in Closed Loop 212
10.6 Controller Complexity Reduction 214
10.6.1 CLOM Algorithm with Simulated Data 216
10.6.2 Real-Time Performance Tests for Nominal and Reduced Order Controllers 218
10.7 Design of the Controller by Shaping the Sensitivity Function with Band-Stop Filters 219
10.8 Concluding Remarks 224
10.9 Notes and References 225
References 226
Part IV Feedback Attenuation of Narrow-Band Disturbances 227
11 Robust Controller Design for Feedback Attenuation of Narrow-Band Disturbances 228
11.1 Introduction 228
11.2 System Description 229
11.3 Robust Control Design 231
11.4 Experimental Results 234
11.4.1 Two Time-Varying Tonal Disturbances 235
11.4.2 Attenuation of Vibrational Interference 237
11.5 Concluding Remarks 238
11.6 Notes and References 238
References 239
12 Direct Adaptive Feedback Attenuation of Narrow-Band Disturbances 240
12.1 Introduction 240
12.2 Direct Adaptive Feedback Attenuation of Unknown and Time-Varying ƒ 241
12.2.1 Introduction 241
12.2.2 Direct Adaptive Regulation Using Youla--Ku?era Parametrization 245
12.2.3 Robustness Considerations 247
12.3 Performance Evaluation Indicators for Narrow-Band Disturbance Attenuation 248
12.4 Experimental Results: Adaptive Versus Robust 251
12.4.1 Central Controller for Youla--Ku?era Parametrization 251
12.4.2 Two Single-Mode Vibration Control 251
12.4.3 Vibrational Interference 254
12.5 Adaptive Attenuation of an Unknown Narrow-Band Disturbance on the Active Hydraulic Suspension 256
12.6 Adaptive Attenuation of an Unknown Narrow-Band Disturbance on the Active Vibration Control System Using an Inertial Actuator 259
12.6.1 Design of the Central Controller 260
12.6.2 Real-Time Results 262
12.7 Other Experimental Results 264
12.8 Concluding Remarks 264
12.9 Notes and References 265
References 266
13 Adaptive Attenuation of Multiple Sparse Unknown and Time-Varying Narrow-Band Disturbances 269
13.1 Introduction 269
13.2 The Linear Control Challenge 269
13.2.1 Attenuation of Multiple Narrow-Band Disturbances Using Band-Stop Filters 271
13.2.2 IMP with Tuned Notch Filters 275
13.2.3 IMP Design Using Auxiliary Low Damped Complex Poles 276
13.3 Interlaced Adaptive Regulation Using Youla--Ku?era IIR Parametrization 277
13.3.1 Estimation of AQ 279
13.3.2 Estimation of BQ(q-1) 281
13.4 Indirect Adaptive Regulation Using Band-Stop Filters 285
13.4.1 Basic Scheme for Indirect Adaptive Regulation 286
13.4.2 Reducing the Computational Load of the Design Using the Youla--Ku?era Parametrization 287
13.4.3 Frequency Estimation Using Adaptive Notch Filters 288
13.4.4 Stability Analysis of the Indirect Adaptive Scheme 291
13.5 Experimental Results: Attenuation of Three Tonal Disturbances with Variable Frequencies 291
13.6 Experimental Results: Comparative Evaluation of Adaptive Regulation Schemes for Attenuation of Multiple Narrow-Band Disturbances 292
13.6.1 Introduction 292
13.6.2 Global Evaluation Criteria 297
13.7 Concluding Remarks 304
13.8 Notes and References 304
References 305
Part V Feedforward-Feedback Attenuation of Broad-Band Disturbances 307
14 Design of Linear Feedforward Compensation of Broad-band Disturbances from Data 308
14.1 Introduction 308
14.2 Indirect Approach for the Design of the Feedforward Compensator from Data 311
14.3 Direct Approach for the Design of the Feedforward Compensator from Data 311
14.4 Direct Estimation of the Feedforward Compensator and Real-Time Tests 315
14.5 Concluding Remark 321
14.6 Notes and References 321
References 322
15 Adaptive Feedforward Compensation of Disturbances 324
15.1 Introduction 324
15.2 Basic Equations and Notations 327
15.3 Development of the Algorithms 329
15.4 Analysis of the Algorithms 332
15.4.1 The Perfect Matching Case 332
15.4.2 The Case of Non-perfect Matching 334
15.4.3 Relaxing the Positive Real Condition 336
15.5 Adaptive Attenuation of Broad-band Disturbances---Experimental Results 337
15.5.1 Broad-band Disturbance Rejection Using Matrix Adaptation Gain 338
15.5.2 Broad-band Disturbance Rejection Using Scalar Adaptation Gain 342
15.6 Adaptive Feedforward Compensation with Filtering of the Residual Error 349
15.7 Adaptive Feedforward + Fixed Feedback Compensation of Broad-band Disturbances 351
15.7.1 Development of the Algorithms 353
15.7.2 Analysis of the Algorithms 355
15.8 Adaptive Feedforward + Fixed Feedback Attenuation of Broad-band Disturbances---Experimental Results 356
15.9 Concluding Remarks 358
15.10 Notes and References 358
References 359
16 Youla--Ku?era Parametrized Adaptive Feedforward Compensators 363
16.1 Introduction 363
16.2 Basic Equations and Notations 364
16.3 Development of the Algorithms 366
16.4 Analysis of the Algorithms 369
16.4.1 The Perfect Matching Case 369
16.4.2 The Case of Non-perfect Matching 370
16.4.3 Relaxing the Positive Real Condition 371
16.4.4 Summary of the Algorithms 371
16.5 Experimental Results 373
16.5.1 The Central Controllers and Comparison Objectives 373
16.5.2 Broad-band Disturbance Rejection Using Matrix Adaptation Gain 373
16.5.3 Broad-band Disturbance Rejection Using Scalar Adaptation Gain 376
16.6 Comparison of the Algorithms 378
16.7 Concluding Remarks 380
16.8 Notes and References 380
References 380
Appendix A Generalized Stability Margin and Normalized Distance Between Two Transfer Functions 382
Appendix B Implementation of the Adaptation Gain Updating---The U-D Factorization 386
Appendix C Interlaced Adaptive Regulation: Equations Development and Stability Analysis 388
Appendix D Error Equations for Adaptive Feedforward Compensation 392
Appendix E ``Integral + Proportional'' Parameter Adaptation Algorithm 399
Index 404