System Identiﬁcation for Robust and Inferential Control · I Introduction 1 1 Towards Next-Generation Motion Control 3 ... B. Introduction to Large Truncated Toeplitz Matrices

System Identification for Robust and Inferential Controlwith Applications to ILC and Precision Motion Systems

Tom Oomen

System Identification for Robust and

Inferential Controlwith Applications to ILC and Precision

Motion Systems

disc

The research reported in this thesis is part of the research program of the Dutch Instituteof Systems and Control (DISC). The author has successfully completed the educationalprogram of the Graduate School DISC.

This research is supported by Philips Applied Technologies, Eindhoven, The Netherlands.

System Identification for Robust and Inferential Control with Applications to ILC andPrecision Motion Systems by Tom Oomen – Eindhoven: Technische UniversiteitEindhoven, 2010 – Proefschrift.

A catalogue record is available from the Eindhoven University of Technology Library.ISBN: 978-90-386-2189-0.

Reproduction: Ipskamp Drukkers B.V., Enschede, The Netherlands.Cover design: Oranje Vormgevers, Eindhoven, The Netherlands.

Copyright c©2010 by T. A. E. Oomen. All rights reserved.

System Identification for Robust and

Inferential Controlwith Applications to ILC and Precision

Motion Systems

PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Technische Universiteit Eindhoven,

op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn,

voor een commissie aangewezen door het College voor Promoties

in het openbaar te verdedigen

op maandag 19 april 2010 om 16.00 uur

door

Tom Antonius Elisabeth Oomen

geboren te Breda

Dit proefschrift is goedgekeurd door de promotoren:

prof.ir. O.H. Bosgra

en

prof.dr.ir. M. Steinbuch

Contents

I Introduction 1

1 Towards Next-Generation Motion Control 3

1.1 From Micro-Scale to Nano-Scale . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Next-Generation High Precision Motion Systems . . . . . . . . . . . . . 5

1.3 Next-Generation Motion Control . . . . . . . . . . . . . . . . . . . . . 6

1.4 Requirements for System Identification in View of Next-Generation Mo-

tion Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5 Present Limitations of System Identification for Robust and Inferential

Feedback Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6 Present Limitations of Iterative Learning Control . . . . . . . . . . . . 24

1.7 Research Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.8 Research Approach and Contributions . . . . . . . . . . . . . . . . . . 29

II-A System Identification for Robust and Inferential Con-trol - Theory 35

2 Connecting System Identification and Robust Control through a Com-

mon Coordinate Frame 37

2.1 The Interrelation between System Identification, Model Uncertainty,

and Robust Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.3 Robust-Control-Relevant Coprime Factor Identification . . . . . . . . . 42

2.4 Towards Robust-Control-Relevant Model Sets . . . . . . . . . . . . . . 53

2.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

2.6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.A Proof of Proposition 2.3.15 . . . . . . . . . . . . . . . . . . . . . . . . . 67

3 System Identification for Robust Inferential control 73

3.1 Unmeasured Performance Variables in System Identification and Robust

Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

VI Contents


3.3 Optimal Inferential Control . . . . . . . . . . . . . . . . . . . . . . . . 76

3.4 Inferential-Control-Relevant Identification . . . . . . . . . . . . . . . . 84

3.5 Model Uncertainty Structures for Robust Inferential Control . . . . . . 89



4 A Well-Posed Deterministic Model Validation Framework for Robust

Control by Design of Validation Experiments 95

4.1 Model Validation in View of Robust Control . . . . . . . . . . . . . . . 95

4.2 Model Validation Problem . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.3 A Frequency Domain Approach to Finite Time Model Validation . . . . 100

4.4 Disturbance Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.5 Averaging in a Deterministic Framework . . . . . . . . . . . . . . . . . 109

4.6 Model Validation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

4.7 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.8 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122



4.B Estimating Nonparametric Disturbance Models: Finite Time Results . 127

4.C Proof of Proposition 4.6.7 . . . . . . . . . . . . . . . . . . . . . . . . . 128

II-B System Identification for Robust and Inferential Con-trol - Applications 131

5 Next-Generation Industrial Wafer Stage Motion Control via System

Identification and Robust Control 133

5.1 High Performance Wafer Stage Motion Control . . . . . . . . . . . . . . 133

5.2 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.3 System Identification of a Nominal Model . . . . . . . . . . . . . . . . 139

5.4 Constructing Robust-Control-Relevant Uncertain Model Sets through

Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.5 Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5.6 Performance Monitoring via Model Validation . . . . . . . . . . . . . . 156

5.7 Analysis of Position Dependent Dynamical Behavior - A Control Per-

spective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6 Continuously Variable Transmission Control through System Identi-

fication and Robust Control Design 169

6.1 Continuously Variable Transmission Control . . . . . . . . . . . . . . . 169


Contents VII

6.3 Nominal Model Identification . . . . . . . . . . . . . . . . . . . . . . . 175

6.4 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

6.5 Robust Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

7 Dealing with Unmeasured Performance Variables in a Prototype Mo-

tion System via System Identification and Robust Control 191

7.1 Unmeasured Performance Variables in Next-Generation Motion Control 191


7.3 H∞-Optimal Inferential Control . . . . . . . . . . . . . . . . . . . . . . 197

7.4 Nonparametric Identification . . . . . . . . . . . . . . . . . . . . . . . . 200

7.5 Weighting Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . 204

7.6 Parametric Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 206

7.7 Validation-Based Uncertainty Modeling . . . . . . . . . . . . . . . . . . 210

7.8 Nominal Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . 215

7.9 Robust Control Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

7.10 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

III System Identification for Sampled-Data Iterative Learn-ing Control 231

8 Suppressing Intersample Behavior in Iterative Learning Control 233

8.1 Iterative Learning Control for Performance Enhancement in Sampled-

Data Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233


8.3 Multirate Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

8.4 Multirate Iterative Learning Control . . . . . . . . . . . . . . . . . . . 240

8.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243


9 Parametric System Identification in View of Sampled-Data Iterative

Learning Control 251

9.1 Modeling Aspects in Optimal Control of the Intersample Behavior in

Iterative Learning Control . . . . . . . . . . . . . . . . . . . . . . . . . 251


9.3 Low-Order Linear Time-Invariant Models for Multirate Identification

and Optimal Iterative Learning Control . . . . . . . . . . . . . . . . . . 254

9.4 Identification for Multirate Iterative Learning Control . . . . . . . . . . 257

9.5 Optimal Multirate Iterative Learning Control . . . . . . . . . . . . . . 259

9.6 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262



VIII Contents

9.B Proof of Proposition 9.5.3 . . . . . . . . . . . . . . . . . . . . . . . . . 269

IV Closing 271

10 Conclusions and Recommendations 273

10.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

10.2 Recommendations for Future Research Directions . . . . . . . . . . . . 278

Addenda 285

A Numerically Reliable Transfer Function Estimation 285

A.1 Frequency Domain Identification Involving `∞-Norms via Lawson’s al-

gorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

A.2 A Numerically Reliable Approach for Solving Nonlinear Least Squares

Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286

B Robust Controller Synthesis using the Skewed Structured Singular

Value 289

C Dealing with Subsample Delays in System Identification of Sampled-

Data Systems 291

C.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

C.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291

C.3 Pre-existing Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 292

C.4 Subsample Delays in System Identification of Sampled-Data Systems . 293

C.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

C.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299

Bibliography 316

Summary 317

Samenvatting (in Dutch) 319

Dankwoord (in Dutch) 321

Curriculum Vitae 323

Bibliography

Ahn, H.-S., Moore, K. L., and Chen, Y. Monotonic convergent iterative learning con-

troller design based on interval model conversion. IEEE Transactions on Automatic

Control, 51(2):366–371, 2006.

Albertos, P. and Sala, A., editors. Iterative Identification and Control. Springer,

London, United Kingdom, 2002. ISBN 1-85233-509-2.

Albertos, P. and Sala, A. Multivariable Control Systems: An Engineering Approach.

Springer-Verlag, London, United Kingdom, 2004. ISBN 1-85233-738-9.

Amann, N., Owens, D. H., and Rogers, E. Iterative learning control for discrete-time

systems with exponential rate of convergence. IEE Proceedings Control Theory &

Applications, 143(2):217–224, 1996.

Amirthalingam, R. and Lee, J. H. Subspace identification based inferential control

applied to a continuous pulp digester. Journal of Process Control, 9(5):397–406,

1999.

Anderson, B. D. O. From Youla-Kucera to identification, adaptive and nonlinear con-

trol. Automatica, 34(12):1485–1506, 1998.

Arnold, B. Shrinking possibilities. IEEE Spectrum, 46(4):26–28, 50–56, 2009.

Astrom, K. J., Hagander, P., and Sternby, J. Zeros of sampled systems. Automatica,

20(1):31–38, 1984.

Astrom, K. J. and Wittenmark, B. Computed-Controlled Systems: Theory and Design.

Prentice-Hall, Englewood Cliffs, New Jersey, United States, second edition, 1990.

Balas, G., Chiang, R., Packard, A., and Safonov, M. Robust Control Toolbox 3: User’s

Guide. The Mathworks, Natick, Massachusetts, United States, 2007.

Balas, G. J. and Doyle, J. C. Identification of flexible structures for robust control.

IEEE Transactions on Control Systems Technology, 10(4):51–58, 1990.

Balas, G. J. and Doyle, J. C. Control of lightly damped, flexible modes in the controller

crossover region. Journal of Guidance, Control, and Dynamics, 17(2):370–377, 1994a.

Balas, G. J. and Doyle, J. C. Robustness and performance trade-offs in control design

for flexible structures. IEEE Transactions on Control Systems Technology, 2(4):352–

361, 1994b.

302 Bibliography

Ball, J. A., Gohberg, I., and Rodman, L. Interpolation of Rational Matrix Functions,

volume 45 of Operator Theory: Advances and Applications. Birkhauser, Berlin,

Germany, 1990.

Bamieh, B. Intersample and finite wordlength effects in sampled-data problems. IEEE

Transactions on Automatic Control, 48(4):639–643, 2003.

Bamieh, B., Pearson, J. B., Francis, B. A., and Tannenbaum, A. A lifting technique

for linear periodic systems with applications to sampled-data control. Systems &

Control Letters, 17(2):79–88, 1991.

Bamieh, B. A. and Pearson, J. B. A general framework for linear periodic systems

with applications to H∞ sampled-data control. IEEE Transactions on Automatic

Control, 37(4):418–435, 1992.

van Barel, M. and Bultheel, A. Orthonormal polynomial vectors and least squares

approximation for a discrete inner product. Electronic Transactions on Numerical

Analysis, 3:1–23, 1995.

Bayard, D. S. Statistical plant set estimation using Schroeder-phased multisinusoidal

input design. Applied Mathematics and Computation, 58(2-3):169–198, 1993.

Bayard, D. S. and Chiang, R. Y. Identification, uncertainty characterization and robust

control synthesis applied to large flexible structures control. International Journal

of Robust and Nonlinear Control, 8(2):97–112, 1998.

Bayard, D. S. and Hadaegh, F. Y. Multivariable plant set estimation using multisinu-

soidal input designs. In IFAC Symposium on System Identification, pages 509–513.

Copenhagen, Denmark, 1994.

Bien, Z. and Xu, J.-X. Iterative Learning Control: Analysis, Design, Integration and

Applications. Kluwer Academic Publishers, Norwell, Massachusetts, United States,

1998. ISBN 0-7923-8213-7.

Boerlage, M., de Jager, B., and Steinbuch, M. Control relevant blind identifica-

tion of disturbances with application to a multivariable active vibration isolation

platform. IEEE Transactions on Control Systems Technology, To Appear (DOI:

10.1109/TCST.2009.2015457), 2010a.

Boerlage, M., Middleton, R., Steinbuch, M., and de Jager, B. Rejection of fixed direc-

tion disturbances in multivariable electromechanical motion systems. Mechatronics,

20(1):45–52, 2010b.

Bohn, C. and Unbehauen, H. Minmax and least squares multivariable transfer function

curve fitting: Error criteria, algorithms and comparisons. In Proceedings of the 1998

American Control Conference, pages 3189–3193. Philadelphia, Pennsylvania, United

States, 1998.

Bombois, X., Scorletti, G., Gevers, M., Van den Hof, P. M. J., and Hildebrand, R.

Least costly identification experiment for control. Automatica, 42(10):1651–1662,

2006.

Bottcher, A. and Silbermann, B. Introduction to Large Truncated Toeplitz Matrices.

Springer-Verlag, New York, New York, United States, 1999. ISBN 0-387-98570-0.

Bibliography 303

Boulet, B. and Francis, B. A. Consistency of experimental frequency-response data

with coprime factor plant models. In Proceedings of the 13th American Control

Conference, pages 2738–2739. Baltimore, Maryland, United States, 1994.

Boulet, B. and Francis, B. A. Consistency of open-loop experimental frequency-

response data with coprime factor plant models. IEEE Transactions on Automatic

Control, 43(12):1680–1691, 1998.

Brewer, J. W. Kronecker products and matrix calculus in system theory. IEEE Trans-

actions on Circuits and Systems, 25(9):772–781, 1978.

Brillinger, D. R. Time Series: Data Analysis and Theory. Holt, Rinehart and Winston,

New York, New York, United States, 1975.

Bristow, D. A., Tharayil, M., and Alleyne, A. G. A survey of iterative learning con-

trol: A learning-based method for high-performance tracking control. IEEE Control

Systems Magazine, 26(3):96–114, 2006.

Brown, J. W. and Churchill, R. V. Complex Variables and Applications. McGraw-Hill,

New York, New York, United States, sixth edition, 1996.

Bultheel, A., van Barel, M., Rolain, Y., and Pintelon, R. Numerically robust trans-

fer function modeling from noisy frequency domain data. IEEE Transactions on

Automatic Control, 50(11):1835–1839, 2005.

de Callafon, R. A., de Roover, D., and Van den Hof, P. M. J. Multivariable least

squares frequency domain identification using polynomial matrix descriptions. In

Proceedings of the 35th Conference on Decision and Control, pages 2030–2035. Kobe,

Japan, 1996.

de Callafon, R. A. and Van den Hof, P. M. J. Suboptimal feedback control by a scheme

of iterative identification and control design. Mathematical Modelling of Systems,

3(1):77–101, 1997.

de Callafon, R. A. and Van den Hof, P. M. J. Multivariable feedback relevant system

identification of a wafer stepper system. IEEE Transactions on Control Systems

Technology, 9(2):381–390, 2001.

Capon, J. and Goodman, N. R. Probability distributions for estimators of the

frequency-wavenumber spectrum. Proceedings of the IEEE, 58(10):1785–1786, 1970.

Chen, J. Frequency-domain tests for validation of linear fractional uncertain models.

IEEE Transactions on Automatic Control, 42(6):748–760, 1997.

Chen, J. and Gu, G. Control-Oriented System Identification: An H∞ Approach. John

Wiley & Sons, New York, New York, United States, 2000.

Chen, T. and Francis, B. Optimal Sampled-Data Control Systems. Springer, London,

United Kingdom, 1995.

Chien, C.-J. On the iterative learning control of sampled-data systems. In Z. Bien

and J.-X. Xu, editors, Iterative Learning Control: Analysis, Design, Integration and


1998. ISBN 0-7923-8213-7.

Christen, U., Weilenmann, M. F., and Geering, H. P. Design of H2 and H∞ con-

304 Bibliography

trollers with two degrees of freedom. In Proceedings of the 1994 American Control

Conference, pages 2391–2395. Baltimore, Maryland, United States, 1994.

Chu, C.-C. On discrete inner-outer and spectral factorizations. In Proceedings of the

7th American Control Conference, pages 1699–1700. Atlanta, Georgia, United States,

1988.

Chu, C.-C. and Doyle, J. C. On inner-outer and spectral factorizations. In Proceed-

ings of the 23rd Conference on Decision and Control, pages 1764–1765. Las Vegas,

Nevada, United States, 1984.

Compter, J. C. Electro-dynamic planar motor. Precision Engineering, 28(2):171–180,

2004.

Crowder, M. and de Callafon, R. A. Coprime factor perturbation models for closed-loop

model validation techniques. In 13th IFAC Symposium on System Identification,

pages 543–548. Rotterdam, The Netherlands, 2003.

Date, P. and Vinnicombe, G. Algorithms for worst case identification in H∞ and in

the ν-gap metric. Automatica, 40(6):995–1002, 2004.

Davis, R. A. Model Validation for Robust Control. Ph.D. thesis, University of Cam-

bridge, Cambridge, United Kingdom, 1995.

Dehghani, A., Lanzon, A., and Anderson, B. D. O. A two-degree-of-freedom H∞

control design method for robust model matching. International Journal of Robust

and Nonlinear Control, 16(10):467–483, 2006.

Denie, D. S. M. Accuracy Assessment in Frequency Response-Based Identification of

a Flexible Mechatronic Stage. Master’s thesis, Eindhoven University of Technology,

Eindhoven, The Netherlands, 2008. Report DCT 2008.064, APT536-08-2396.

Dijkstra, B. G. and Bosgra, O. H. Extrapolation of optimal lifted system ILC solu-

tion, with application to a waferstage. In Proceedings of the 2002 American Control

Conference, pages 2595–2600. Anchorage, Alaska, United States, 2002.

Ding, F. and Chen, T. Modeling and identification of multirate systems. Acta Auto-

matica Sinica, 31(1):105–122, 2005.

Donkers, T., van de Wijdeven, J., and Bosgra, O. Robustness against model uncertain-

ties of norm optimal iterative learning control. In Proceedings of the 2008 American

Control Conference, pages 4561–4566. Seattle, Washington, United States, 2008.

Douma, S. G. and Van den Hof, P. M. J. Relations between uncertainty structures in

identification for robust control. Automatica, 41:439–457, 2005.

Douma, S. G., Van den Hof, P. M. J., and Bosgra, O. H. Controller tuning freedom

under plant identification uncertainty: Double Youla beats gap in robust stability.

Automatica, 39(2):325–333, 2003.

Doyle, F. J., III. Nonlinear inferential control for process applications. Journal of

Process Control, 8(5-6):339–353, 1998.

Doyle, J. Analysis of feedback systems with structured uncertainties. IEE Proceedings

Control Theory & Applications Part D, 129(6):242–250, 1982.

Doyle, J. Advances in Multivariable Control. ONR/Honeywell Workshop, 1984.

Bibliography 305

Doyle, J., Francis, B., and Tannenbaum, A. Feedback Control Theory. Macmillan

Publishing, New York, New York, United States, 1992.

Doyle, J. C., Glover, K., Khargonekar, P. P., and Francis, B. A. State-space solutions

to standardH2 andH∞ control problems. IEEE Transactions on Automatic Control,

34(8):831–947, 1989.

Doyle, J. C. and Stein, G. Multivariable feedback design: Concepts for a classi-

cal/modern synthesis. IEEE Transactions on Automatic Control, 26(1):4–16, 1981.

Dullerud, G. E. Control of Uncertain Sampled-Data Systems. Birkhauser, Boston,

Massachusetts, United States, 1996. ISBN 0-8176-3851-2.

Edmunds, J. and Kouvaritakis, B. Extensions of the frame alignment technique and

their use in the characteristic locus design method. International Journal of Control,

29(5):787–796, 1979.

Elfring, J. System Identification and Multivariable Control of a Hydraulically Actuated

Pushbelt CVT. Master’s thesis, Eindhoven University of Technology, Eindhoven, The

Netherlands, 2009. DCT 2009.078.

Fan, M. K. H. and Tits, A. L. A measure of worst-case H∞ performance and of largest

unacceptable uncertainty. Systems & Control Letters, 18(6):409–421, 1992.

Forssell, U. and Ljung, L. Closed-loop identification revisited. Automatica, 35(7):1215–

1241, 1999.

Francis, B. A. A Course in H∞ Control Theory, volume 88 of Lecture Notes in Control

and Information Sciences. Springer-Verlag, Berlin, Germany, 1987.

Franklin, G. F., Powell, J. D., and Workman, M. L. Digital Control of Dynamic

Systems. Addison-Wesley, Menlo Park, California, United States, third edition, 1998.

Friedman, J. H. and Khargonekar, P. P. Application of identification in H∞ to lightly

damped systems: Two case studies. IEEE Transactions on Control Systems Tech-

nology, 3(3):279–289, 1995.

Frueh, J. A. and Phan, M. Q. Linear quadratic optimal learning control (LQL). In-

ternational Journal of Control, 73(10):832–839, 2000.

Garnier, H. and Wang, L., editors. Identification of Continuous-Time Models from

Sampled Data. Advances in Industrial Control. Springer-Verlag, London, United

Kingdom, 2009. ISBN 9781848001602.

Gawronski, W. K. Advanced Structural Dynamics and Active Control of Structures.

Springer, New York, New York, United States, 2004. ISBN 0-387-40649-2.

Georgiou, T. T., Karlsson, J., and Shahrouz Takyar, M. Metrics for power spectra: An

axiomatic approach. IEEE Transactions on Signal Processing, 57(3):859–867, 2009.

Georgiou, T. T., Shankwitz, C. R., and Smith, M. C. Identification of linear systems:

A graph point of view. In Proceedings of the 1992 American Control Conference,

pages 307–312. Chicago, Illinois, United States, 1992.

Georgiou, T. T. and Smith, M. C. Optimal robustness in the gap metric. IEEE


Gevers, M. Towards a joint design of identification and control ? In H. L. Trentelman

306 Bibliography

and J. C. Willems, editors, Essays on Control : Perspectives in the Theory and its

Applications, chapter 5, pages 111–151. Birkhauser, Boston, Massachusetts, United

States, 1993. ISBN 0-8176-3670-6.

Gevers, M. Identification for control: From the early achievements to the revival of

experiment design. European Journal of Control, 11(4-5):1–18, 2005.

Gevers, M., Bombois, X., Codrons, B., Scorletti, G., and Anderson, B. D. O. Model

validation for control and controller validation in a prediction error identification

framework - part I: Theory. Automatica, 39(3):403–415, 2003.

Golub, G. H. and Van Loan, C. F. Matrix Computations. The John Hoplins University

Press, Baltimore, Maryland, United States, third edition, 1996.

Goodman, N. R. Statistical analysis based on a certain multivariate complex Gaussian

distribution (an introduction). The Annals of Mathematical Statistics, 34(1):152–

177, 1953.

Goodwin, G. C., Braslavsky, J. H., and Seron, M. M. Non-stationary stochastic em-

bedding for transfer function estimation. Automatica, 38(1):47–62, 2002.

Goodwin, G. C., Graebe, S. F., and Salgado, M. E. Control System Design. Prentice

Hall, Upper Saddle River, New Jersey, United States, 2001. ISBN 0-13-958653-9.

Gorinevsky, D. Loop shaping for iterative control of batch processes. IEEE Control

Systems Magazine, 22(6):55–65, 2002.

Graham, M. R. and de Callafon, R. A. Performance weight adjustment for iterative

cautious control design. In Proceedings of the 2007 European Control Conference,

pages 217–222. Kos, Greece, 2007.

Grassens, E. Master’s thesis, Eindhoven University of Technology, Eindhoven, The

Netherlands, 2010. To appear.

Grimble, M. J. 312

DOF polynomial solution of the inferential H2/H∞ control problem

with application to metal rolling. Journal of Dynamic Systems, Measurements, and

Control, 120(4):445–455, 1998.

Groot Wassink, M., van de Wal, M., Scherer, C., and Bosgra, O. LPV control for a

wafer stage: Beyond the theoretical solution. Control Engineering Practice, 13:231–

245, 2003.

Gu, G. Modeling of normalized coprime factors with ν-metric uncertainty. IEEE


Guillaume, P., Pintelon, R., and Schoukens, J. Accurate estimation of multivariable

frequency response functions. In IFAC 13th Triennial World Congress, pages 423–

428. San Francisco, California, United States, 1996.

Gunnarsson, S. and Norrlof, M. On the design of ILC algorithms using optimization.

Automatica, 37:2011–2016, 2001.

Gysen, B. L. J. Design Aspects of H∞ Optimal Controllers for Electromechanical Servo

Systems. Eindhoven University of Technology, Eindhoven, The Netherlands, 2006.

Hakvoort, R. G. and Van den Hof, P. M. J. Consistent parameter bounding identifica-

tion for linearly parametrized model sets. Automatica, 31(7):957–969, 1995.

Bibliography 307

Hakvoort, R. G. and Van den Hof, P. M. J. Identification of probabilistic system uncer-

tainty regions by explicit evaluation of bias and variance errors. IEEE Transactions

on Automatic Control, 42(11):1516–1528, 1997.

Hara, S., Tetsuka, M., and Kondo, R. Ripple attenuation in digital repetitive control

systems. In Proceedings of the 29th Conference on Decision and Control, pages

1679–1684. Honolulu, Hawaii, United States, 1990.

Heath, W. P. Bias of indirect non-parametric transfer function estimates for plants in

closed loop. Automatica, 37(10):1529–1540, 2001.

Heath, W. P. The variation of non-parametric estimates in closed-loop. Automatica,

39(11):1849–1863, 2003.

Helmicki, A. J., Jacobson, C. A., and Nett, C. N. Control oriented system identifica-

tion: A worst-case/deterministic approach in H∞. IEEE Transactions on Automatic

Control, 36(10):1163–1176, 1991.

Hendriks, F. B. J. W. M. Achieving Beyond Flexible Dynamics Control of a Prototype

Lightweight Positioning System: A Theory-Driven Experimental Approach. Master’s

thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 2009. Re-

port DCT 2009.032.

van Herpen, R. Experimental Modeling and Validation for Robust Motion Control of

Next-Generation Wafer Stages. Master’s thesis, Eindhoven University of Technology,

Eindhoven, The Netherlands, 2009.

van Herpen, R., Oomen, T., van de Wal, M., and Bosgra, O. Experimental evaluation

of robust-control-relevance: A confrontation with a next-generation wafer stage. In

Proceedings of the 2010 American Control Conference. Baltimore, Maryland, United

States, 2010.

Hjalmarsson, H. Aspects on Incomplete Modeling in System Identification. Ph.D. thesis,

Linkoping University, Linkoping, Sweden, 1993.

Hjalmarsson, H. From experiment design to closed-loop control. Automatica, 41:393–

438, 2005.

Hjalmarsson, H. System identification of complex and structured systems. In Proceed-

ings of the 2009 European Control Conference, pages 3424–3452. Budapest, Hungary,

2009.

Hjalmarsson, H., Gunnarsson, S., and Gevers, M. Optimality and sub-optimality of

iterative identification and control design schemes. In Proceedings of the 15th Ameri-

can Control Conference, pages 2559–2563. Seattle, Washington, United States, 1995.

Hjalmarsson, H. and Ljung, L. A discussion of ”unknown - but - bounded” disturbances

in system identification. In Proceedings of the 32nd Conference on Decision and

Control, pages 535–536. San Antonio, Texas, United States, 1993.

Hoyle, D. J., Hyde, R. A., and Limebeer, D. J. N. An H∞ approach to two degree

of freedom design. In Proceedings of the 30th Conference on Decision and Control,

pages 1581–1585. Brighton, United Kingdom, 1991.

Huang, X., Horowitz, R., and Li, Y. A comparative study of MEMS microactuators

308 Bibliography

for use in a dual-stage servo with an instrumented suspension. IEEE Transactions

on Mechatronics, 11(5):524–532, 2006.

Hughes, P. C. Space structure vibration modes: How many exist? Which ones are

important? IEEE Control Systems Magazine, 7(1):22–28, 1987.

Hutcheson, G. D. The first nanochips. Scientific American, pages 48–55, 2004.

Hyde, R. A. and Glover, K. The application of scheduled H∞ controllers to a VSTOL

aircraft. IEEE Transactions on Automatic Control, 38(7):1021–1039, 1993.

Iglesias, P. A. and Glover, K. State-space approach to discrete-time H∞ control.

International Journal of Control, 54(5):1031–1073, 1991.

Ishii, H. and Yamamoto, Y. Periodic compensation for sampled-data H∞ repetitive

control. In Proceedings of the 37th Conference on Decision and Control, pages 331–

336. Tampa, Florida, United States, 1998.

Kailath, T. Linear Systems. Prentice-Hall, Englewood Cliffs, New Jersey, United

States, 1980.

Kailath, T. and Koltracht, I. Matrices with block Toeplitz inverses. Linear Algebra

and its Applications, 75:145–153, 1986.

Kalman, R. E., Ho, Y. C., and Narendra, K. S. Contributions to Differential Equations,

volume 1, chapter Controllability of Linear Dynamical Systems, pages 189–213. In-

terscience, New York, New York, United States, 1963.

Kannai, Y. and Weiss, G. Approximating signals by fast impulse sampling. Mathe-

matics of Control, Signals, and Systems, 6(2):166–179, 1993.

Katayama, T. Subspace Methods for System Identification: A Realization Approach.

Springer, Leipzig, Germany, 2005. ISBN 1-85233-981-0.

Kelly, S. G. Fundamentals of Mechanical Vibrations. McGraw-Hill, Singapore, second

edition, 2000. ISBN 0-07-116325-5.

Kinney, C. E., de Callafon, R. A., and de Oliveira, M. Spectral over-bounding of

frequency data for modeling product variability in hard disk drive actuators. In

Proceedings of the 2007 European Control Conference, pages 2902–2907. Kos, Greece,

2007.

Kosut, R. L. Uncertainty model unfalsification: A system identification paradigm

compatible with robust control design. In Proceedings of the 34th Conference on

Decision and Control, pages 3492–3497. New Orleans, Louisiana, United States,

1995.

Kosut, R. L. Uncertainty model unfalsification for robust adaptive control. Annual

Reviews in Control, 25:65–76, 2001.

Kranc, G. M. Input-output analysis of multirate feedback systems. IRE Transactions

on Automatic Control, 3(1):21–28, 1957.

Krause, J. M. Comments on Grimble’s comments on Stein’s comments on rolloff of

H∞ optimal controllers. IEEE Transactions on Automatic Control, 37(5):702, 1992.

Kreyszig, E. Introductory Functional Analysis with Applications. John Wiley & Sons,

New York, New York, United States, 1978. ISBN 0-471-50731-8.

Bibliography 309

Kumar, A. and Balas, G. J. An approach to model validation in the µ framework. In

Proceedings of the 13th American Control Conference, pages 3021–3026. Baltimore,

Maryland, United States, 1994.

Langari, A. and Francis, B. A. Sampled-data repetitive control systems. In Proceedings

of the 13th American Control Conference, pages 3234–3235. Baltimore, Maryland,

United States, 1994.

Lawson, C. L. and Hanson, R. J. Solving Least Squares Problems. Prentice-Hall, Inc.,

Englewood Cliffs, New Jersey, United States, 1974. ISBN 0-13-822585-0.

Lechner, G. and Naunheimer, H. Automotive Transmissions: Fundamentals, Selection,

Design and Application. Springer, Berlin, Germany, 1999. ISBN 3-540-65903-X.

Lee, W. S., Anderson, B. D. O., Mareels, I. M. Y., and Kosut, R. L. On some key issues

in the windsurfer approach to adaptive robust control. Automatica, 31(11):1619–

1636, 1995.

LeVoci, P. A. and Longman, R. W. Intersample error in discrete time learning and

repetitive control. In Proceedings of the AIAA/AAS Astrodynamics Specialist Con-

ference and Exhibit, pages 1–24. Providence, Rhode Island, United States, 2004.

Lewis, F. L. and Syrmos, V. L. Optimal Control. John Wiley & Sons, Inc., New York,

New York, United States, second edition, 1995. ISBN 0-471-03378-2.

Li, D., Shah, S. L., and Chen, T. Identification of fast-rate models from multirate data.

International Journal of Control, 74(7):680–689, 2001.

Lim, K. B. and Giesy, D. P. Parameterization of model validating sets for uncertainty

bound optimizations. Journal of Guidance, Control, and Dynamics, 23(2):222–230,

2000.

Limebeer, D. J. N., Kasenally, E. M., and Perkins, J. D. On the design of robust two

degree of freedom controllers. Automatica, 29(1):157–168, 1993.

Liu, W. and Chen, J. Probabilistic model validation problems with H∞ type uncer-

tainties. In Proceedings of the 2005 American Control Conference, pages 1539–1544.

Portland, Oregon, United States, 2005.

Ljung, L. Model validation and model error modeling. In B. Wittenmark and

A. Rantzer, editors, The Astrom Symposium on Control, pages 15–42. Studentlitter-

atur, Lund, Sweden, 1999a.

Ljung, L. System Identification: Theory for the User. Prentice Hall, Upper Saddle

River, New Jersey, United States, second edition, 1999b.

Ljung, L. System Identification ToolboxTM User’s Guide. The Mathworks, Inc., Natick,

Massachusetts, United States, 7 edition, 2008.

Ljung, L., Wahlberg, B., and Hjalmarsson, H. Model quality: The roles of prior

knowledge and data information. In Proceedings of the 30th Conference on Decision

and Control, pages 273–278. Brighton, United Kingdom, 1991.

Loh, A. P., Correa, G. O., and Postlethwaite, I. Estimation of uncertainty bounds

for robustness analysis. IEE Proceedings Control Theory & Applications Part D,

134(1):9–16, 1987.

310 Bibliography

Longman, R. W. and Lo, C.-P. Generalized holds, ripple attenuation, and tracking

additional outputs in learning control. Journal of Guidance, Control, and Dynamics,

20(6):1207–1214, 1997.

Longman, R. W. and Phan, M. Q. Iterative learning control as a method of experi-

ment design for improved system identification. Optimization Methods and Software,

21(6):919–941, 2006.

Ma, C. C. H. Comments on “a necessary and sufficient condition for stability of a

perturbed system”. IEEE Transactions on Automatic Control, 33(8):796–797, 1988.

Maciejowksi, J. M. Multivariable Feedback Design. Addison-Wesley, Wokingham,


Makila, P. M. and Partington, J. R. On linear models for nonlinear systems. Auto-

matica, 39(1):1–13, 2003.

Martinez, V. M. and Edgar, T. F. Control of lithography in semiconductor manufac-

turing. IEEE Control Systems Magazine, 26(6):46–55, 2006.

Mazzaro, M. C. and Sznaier, M. Convex necessary and sufficient conditions for fre-

quency domain model (in)validation under SLTV structured uncertainty. IEEE


McFarlane, D. C. and Glover, K. Robust Controller Design Using Normalized Coprime

Factor Plant Descriptions, volume 138 of Lecture Notes in Control and Information

Sciences. Springer-Verlag, Berlin, Germany, 1990.

Meinsma, G. Unstable and nonproper weights inH∞ control. Automatica, 31(11):1655–

1658, 1995.

van der Meulen, S., de Jager, B., van der Noll, E., Veldpaus, F., van der Sluis, F., and

Steinbuch, M. Improving pushbelt continuously variable transmission efficiency via

extremum seeking control. In Proceedings of the 2009 Multi-conference on Systems

and Control, pages 357–362. Saint Petersburg, Russia, 2009.

Milanese, M. and Taragna, M. Optimality, approximation, and complexity in set mem-

bership H∞ identification. IEEE Transactions on Automatic Control, 47(10):1682–

1690, 2002.

Milanese, M. and Vicino, A. Optimal estimation theory for dynamic systems with set

membership uncertainy: An overview. Automatica, 27(6):997–1009, 1991.

Miller, K. S. Complex Stochastic Systems: An Introduction to Theory and Application.

Addison-Wesley Publishing Company, Reading, Massachusetts, United States, 1974.

Mita, T., Xin, X., and Anderson, B. D. O. Extended H∞ control - H∞ control with

unstable weights. Automatica, 36(5):735–741, 2000.

Moore, G. E. Progress in digital integrated circuits. IEEE International Electron

Devices Meeting, pages 11–13, 1975.

Moore, K. L. Iterative Learning Control for Deterministic Systems. Springer-Verlag,

London, United Kingdom, 1993. ISBN 3-540-19707-9.

Moore, K. L. Iterative learning control an expository overview. Applied and Compu-

tational Controls, Signal Processing, and Circuits, 1:151–214, 1999.

Bibliography 311

Newlin, M. P. and Smith, R. S. Model validation and a generalization of µ. In Proceed-

ings of the 30th Conference on Decision and Control, pages 1257–1258. Brighton,


Newlin, M. P. and Smith, R. S. A generalization of the structured singular value

and its application to model validation. IEEE Transactions on Automatic Control,

43(7):901–907, 1998.

Niemann, H. Dual Youla parameterisation. IEE Proceedings Control Theory & Appli-

cations, 150(5):493–497, 2003.

Ninness, B. and Goodwin, G. C. Estimation of model quality. Automatica, 31(12):1771–

1797, 1995.

Oomen, T. and Bosgra, O. Estimating disturbances and model uncertainty in model

validation for robust control. In Proceedings of the 47th Conference on Decision and

Control, pages 5513–5518. Cancun, Mexico, 2008a.

Oomen, T. and Bosgra, O. Robust-control-relevant coprime factor identification: A nu-

merically reliable frequency domain approach. In Proceedings of the 2008 American

Control Conference, pages 625–631. Seattle, Washington, United States, 2008b.

Oomen, T. and Bosgra, O. Well-posed model uncertainty estimation by design of

validation experiments. In 15th IFAC Symposium on System Identification, pages

1199–1204. Saint-Malo, France, 2009.

Oomen, T., Bosgra, O., and van de Wal, M. Identification for robust inferential control.

In Proceedings of the 48th Conference on Decision and Control, pages 2581–2586.

Shanghai, China, 2009a.

Oomen, T., van de Wal, M., and Bosgra, O. Exploiting H∞ sampled-data control

theory for high-precision electromechanical servo control design. In Proceedings of

the 2006 American Control Conference, pages 1086–1091. Minneapolis, Minnesota,


Oomen, T., van de Wal, M., and Bosgra, O. Aliasing of resonance phenomena in

sampled-data control design: Hazards, modeling, and a solution. In Proceedings

of the 2007 American Control Conference, pages 2881–2886. New York, New York,

United States, 2007a.

Oomen, T., van de Wal, M., and Bosgra, O. Design framework for high-performance

optimal sampled-data control with application to a wafer stage. International Journal

of Control, 80(6):919–934, 2007b.

Oomen, T., van de Wijdeven, J., and Bosgra, O. Suppressing intersample behavior

in iterative learning control. In Proceedings of the 47th Conference on Decision and

Control, pages 2391–2397. Cancun, Mexico, 2008.

Oomen, T., van de Wijdeven, J., and Bosgra, O. Low-order system identification and

optimal control of intersample behavior in ILC. In Proceedings of the 2009 American

Control Conference, pages 271–276. St. Louis, Missouri, United States, 2009b.

Oomen, T., van de Wijdeven, J., and Bosgra, O. Suppressing intersample behavior in

iterative learning control. Automatica, 45(4):981–988, 2009c.

312 Bibliography

Oomen, T., van der Meulen, S., Bosgra, O., Steinbuch, M., and Elfring, J. A robust-

control-relevant model validation approach for continuously variable transmission

control. In Proceedings of the 2010 American Control Conference. Baltimore, Mary-

land, United States, 2010.

Oomen, T., van Herpen, R., and Bosgra, O. Robust-control-relevant coprime factor

identification with application to model validation of a wafer stage. In 15th IFAC

Symposium on System Identification, pages 1044–1049. Saint-Malo, France, 2009d.

Oomen, T. A. E. Optimal Digital Control of High-Precision Electromechanical Servo

Systems: Concepts and Applications. Master’s thesis, Eindhoven University of Tech-

nology, Eindhoven, The Netherlands, 2005.

van Overschee, P. and De Moor, B. Subspace Identification for Linear Systems: The-

ory - Implementation - Applications. Kluwer Academic Publishers, Boston, Mas-

sachusetts, United States, 1996. ISBN 0-7923-9717-7.

Ozay, N. and Sznaier, M. A pessimistic approach to frequency domain model

(in)validation. In Proceedings of the 46th Conference on Decision and Control, pages

4895–4900. New Orleans, Louisiana, United States, 2007.

Packard, A. and Doyle, J. The complex structured singular value. Automatica,

29(1):71–109, 1993.

Paganini, F. A set-based approach for white noise modeling. IEEE Transactions on


Paganini, F. and Doyle, J. Analysis of implicitly defined systems. In Proceedings of

the 33rd Conference on Decision and Control, pages 3673–3678. Lake Buena Vista,

Florida, United States, 1994.

Papageorgiou, G. and Glover, K. H∞ loop shaping: Why is it a sensible procedure

for designing robust flight controllers? In AIAA Guidance, Navigation, and Control

Conference, pages 1–14. Portland, Oregon, United States, 1999.

Parrish, J. R. and Brosilow, C. B. Inferential control applications. Automatica,

21(5):527–538, 1985.

Pfiffner, R. and Guzella, L. Optimal operation of CVT-based powertrains. International

Journal of Robust and Nonlinear Control, 11(11):1003–1021, 2001.

Phan, M. and Longman, R. W. A mathematical theory of learning control for linear

discrete multivariable systems. In Proceedings of the AIAA/AAS Astrodynamics

Conference, pages 740–746. Minneapolis, Minnesota, United States, 1988.

Phan, M. Q. and Frueh, J. A. System identification and learning control. In Z. Bien

and J.-X. Xu, editors, Iterative Learning Control: Analysis, Design, Integration and


1998. ISBN 0-7923-8213-7.

Pintelon, R. and Schoukens, J. System Identification: A Frequency Domain Approach.

IEEE Press, New York, New York, United States, 2001.

Poolla, K., Khargonekar, P., Tikku, A., Krause, J., and Nagpal, K. A time-domain

Bibliography 313

approach to model validation. IEEE Transactions on Automatic Control, 39(5):951–

959, 1994.

Preumont, A. Vibration Control of Active Structures: An Introduction, volume 96 of

Solid Mechanics and Its Applications. Kluwer Academic Publishers, New York, New

York, United States, second edition, 2004. ISBN 1-4020-0496-6.

Quist, S. Improving Wafer Stage Motion Performance through Robust-Control-Relevant

Model Set Identification and Multivariable Control. Master’s thesis, Eindhoven Uni-

versity of Technology, Eindhoven, The Netherlands, 2010.

Reinelt, W., Garulli, A., and Ljung, L. Comparing different approaches to model error

modeling in robust identification. Automatica, 38(5):787–803, 2002.

Rice, J. R. The Approximation of Functions, volume 2: Nonlinear and Multivari-

ate Theory. Addison-Wesley Publishing Company, Reading, Massachusetts, United

States, 1964.

Saelid, S. Process identification techniques. In R. Berber, editor, Methods of Model

Based Process Control, pages 81–97. Kluwer Academic Publishers, Dordrecht, The

Netherlands, 1995. ISBN 0-7923-3524-4.

Sanathanan, C. K. and Koerner, J. Transfer function synthesis as a ratio of two complex

polynomials. IEEE Transactions on Automatic Control, 8(1):56–58, 1963.

Sarason, D. Nevanlinna-Pick interpolation with boundary data. Integral Equations and

Operator Theory, 30:231–250, 1998.

Scheid, R. E. and Bayard, D. S. A globally optimal minimax solution for spectral over-

bounding and factorization. IEEE Transactions on Automatic Control, 40(4):712–

716, 1995.

Schrama, R. Approximate Identification and Control Design - with Application to a

Mechanical System. Ph.D. thesis, Technische Universiteit Delft, Delft, The Nether-

lands, 1992a.

Schrama, R. J. P. Accurate identification for control: The necessity of an iterative

scheme. IEEE Transactions on Automatic Control, 37(7):991–994, 1992b.

Schrama, R. J. P. and Bosgra, O. H. Adaptive performance enhancement by iterative

identification and control design. International Journal of Adaptive Control and

Signal Processing, 7(5):475–487, 1993.

Schroeck, S. J., Messner, W. C., and McNab, R. J. On compensator design for linear

time-invariant dual-input single-output systems. IEEE Transactions on Mechatron-

ics, 6(1):50–57, 2001.

Schroeder, M. R. Synthesis of low-peak-factor signals and binary sequences with low

autocorrelation. IEEE Transactions on Information Theory, 16(1):85–89, 1970.

Seron, M. M., Braslavsky, J. H., and Goodwin, G. C. Fundamental Limitations in

Filtering and Control. Springer-Verlag, London, United Kingdom, 1997. ISBN 3-

540-76126-8.

Shamma, J. S. Robust stability with time-varying structured uncertainty. IEEE Trans-

actions on Automatic Control, 39(4):714–724, 1994.

314 Bibliography

Singh, T. and Singhose, W. Tutorial on input shaping/time delay control of maneu-

vering flexible structures. In Proceedings of the 2002 American Control Conference,

pages 1717–1731. Anchorage, Alaska, United States, 2002.

Skogestad, S. and Postlethwaite, I. Multivariable Feedback Control: Analysis and De-

sign. John Wiley & Sons, West Sussex, United Kingdom, second edition, 2005.

Smith, R., Dullerud, G., Rangan, S., and Poolla, K. Model validation for dynamically

uncertain systems. Mathematical Modelling of Systems, 3(1):43–58, 1997.

Smith, R. and Dullerud, G. E. Continuous-time control model validation using fi-

nite experimental data. IEEE Transactions on Automatic Control, 41(8):1094–1105,

1996.

Smith, R. S. Closed-loop identification of flexible structures: An experimental example.

Journal of Guidance, Control, and Dynamics, 21(3):435–440, 1998.

Smith, R. S. and Doyle, J. C. Model validation: A connection between robust control

and identification. IEEE Transactions on Automatic Control, 37(7):942–952, 1992.

Soderstrom, T. and Stoica, P. System Identification. Prentice Hall, Hemel Hempstead,

United Kingdom, 1989. ISBN 0-13-881236-5.

Steinbuch, M. and Norg, M. L. Advanced motion control: An industrial perspective.

European Journal of Control, 4(4):278–293, 1998a.

Steinbuch, M. and Norg, M. L. Industrial perspective on robust control: Application

to storage systems. Annual Reviews in Control, 22:47–58, 1998b.

Steinbuch, M., van de Molengraft, R., and van der Voort, A.-J. Experimental modelling

and LPV control of a motion system. In Proceedings of the 2003 American Control

Conference, pages 1374–1379. Denver, Colorado, United States, 2003.

Stix, G. Getting more from Moore’s. Scientific American, pages 20–24, 2001.

Sun, M. and Wang, D. Sampled-data iterative learning control for nonlinear systems

with arbitrary relative degree. Automatica, 37(2):283–289, 2001.

Sung, H.-K. and Hara, S. Properties of sensitivity and complementary sensitivity

functions in single-input single-output digital control systems. International Journal

of Control, 48(6):2429–2439, 1988.

Sznaier, M. and Mazzaro, M. C. An LMI approach to control-oriented identification

and model (in) validation of LPV systems. IEEE Transactions on Automatic Control,

48(9):1619–1624, 2003.

Tayebi, A. and Zaremba, M. B. Robust iterative learning control design is straightfor-

ward for uncertain LTI systems satisfying the robust performance condition. IEEE


Tikhonov, A. N. and Arsenin, V. Y. Solutions of Ill-Posed Problems. John Wiley &

Sons, New York, New York, United States, 1977.

Toker, O. and Ozbay, H. On the complexity of purely complex µ computation and

related problems in multidimensional systems. IEEE Transactions on Automatic

Control, 43(3):409–414, 1998.

Tousain, R., van der Meche, E., and Bosgra, O. Design strategy for iterative learning

Bibliography 315

control based on optimal control. In Proceedings of the 40th Conference on Decision

and Control, pages 4463–4468. Orlando, Florida, United States, 2001.

Vaidyanathan, P. P. Multirate Systems and Filter Banks. Prentice Hall, Englewood

Cliffs, New Jersey, United States, 1993.

Van den Hof, P. M. J. Closed-loop issues in system identification. Annual Reviews in

Control, 22:173–186, 1998.

Van den Hof, P. M. J. and Schrama, R. J. P. Identification and control - closed-loop

issues. Automatica, 31(12):1751–1770, 1995.

Van den Hof, P. M. J., Schrama, R. J. P., de Callafon, R. A., and Bosgra, O. H. Iden-

tification of normalised coprime plant factors from closed-loop experimental data.

European Journal of Control, 1(1):62–74, 1995.

Verhoeven, S. L. H. Improving Inferential Performance of Flexible Motion Systems.

Master’s thesis, Eindhoven University of Technology, Eindhoven, The Netherlands,

2010. Report DCT 2010.006, APT536-10-0060.

Vidyasagar, M. Control System Synthesis: A Factorization Approach. The MIT Press,

Cambridge, Massachusetts, United States, 1985.

Vinnicombe, G. Uncertainty and Feedback: H∞ loop-shaping and the ν-gap metric.

Imperial College Press, London, United Kingdom, 2001.

Voss, D. Chips go nano. Technology Review, 102(2):55–57, 1999.

de Vries, D. Identification of Model Uncertainty for Control Design. Ph.D. thesis, Delft

University of Technology, Delft, The Netherlands, 1994.

de Vries, D. K. and Van den Hof, P. M. J. Quantification of model uncertainty from

data. International Journal of Robust and Nonlinear Control, 4(2):301–319, 1994.

de Vries, D. K. and Van den Hof, P. M. J. Quantification of uncertainty in trans-

fer function estimation: a mixed probabilistic-worst-case approach. Automatica,

31(4):543–557, 1995.

Wahlberg, B. and Ljung, L. Hard frequency-domain model error bounds from least-

squares like identification techniques. IEEE Transactions on Automatic Control,

37(7):900–912, 1992.

van de Wal, M., van Baars, G., and Sperling, F. Reduction of residual vibrations by

H∞ feedback control. In Motion and Vibration Conference, pages 481–487. Sydney,

Australia, 2000.

van de Wal, M., van Baars, G., Sperling, F., and Bosgra, O. Multivariable H∞/µ

feedback control design for high-precision wafer stage motion. Control Engineering

Practice, 10(7):739–755, 2002.

Weiss, G. Representation of shift-invariant operators on L2 by H∞ transfer functions:

An elementary proof, a generalization to Lp, and a counterexample for L∞. Mathe-

matics of Control, Signals, and Systems, 4:193–203, 1991.

Whitfield, A. H. Asymptotic behaviour of transfer function synthesis methods. Inter-

national Journal of Control, 45(3):1083–1092, 1987.

van de Wijdeven, J. and Bosgra, O. Hankel iterative learning control for residual vi-

316 Bibliography

bration suppression with MIMO flexible structure experiments. In Proceedings of the

46th Conference on Decision and Control, pages 258–263. New Orleans, Louisiana,


van de Wijdeven, J. and Bosgra, O. Residual vibration suppression using Hankel

iterative learning control. International Journal of Robust and Nonlinear Control,

18(10):1034–1051, 2008.

Wittenmark, B. Sampling of a system with a time delay. IEEE Transactions on


Xu, J.-X., Lee, T. H., and Zhang, H.-W. A multirate iterative learning control scheme.

In Proc. 2005 International Conference on Control and Automation, pages 403–408.

Budapest, Hungary, 2005.

Yaesh, I. and Shaked, U. Two-degree-of-freedom H∞-optimization of multivariable

feedback systems. IEEE Transactions on Automatic Control, 36(11):1272–1276,

1991.

Yamamoto, Y. A function space approach to sampled data control systems and tracking

problems. IEEE Transactions on Automatic Control, 39(4):703–713, 1994.

Zames, G. Feedback and optimal sensitivity: Model reference transformations, mul-

tiplicative seminorms, and approximate inverses. IEEE Transactions on Automatic

Control, 26(2):301–320, 1981.

Zattoni, E. Structural invariant subspaces of singular Hamiltonian systems and nonre-

cursive solutions of finite-horizon optimal control problems. IEEE Transactions on


Zhang, B., Wang, D., Ye, Y., Wang, Y., and Zhou, K. Two-mode ILC with pseudo-

downsampled learning in high frequency range. International Journal of Control,

80(3):349–362, 2007.

Zhang, B., Wang, D., Zhou, K., Ye, Y., and Wang, Y. Pseudo-downsampled it-

erative learning control. International Journal of Robust and Nonlinear Control,

18(10):1072–1088, 2008.

Zhou, K., Doyle, J. C., and Glover, K. Robust and Optimal Control. Prentice Hall,

Upper Saddle River, New Jersey, United States, 1996.

Zhou, K. and Ren, Z. A new controller architecture for high performance, robust, and

fault-tolerant control. IEEE Transactions on Automatic Control, 46(10):1613–1618,

2001.

Zhou, T. Nonparametric estimation for normalized coprime factors of a MIMO system.

Automatica, 41(4):655–662, 2005.

Zhou, T. and Xing, H.-W. Identification of normalized coprime factors through con-

strained curve fitting. Automatica, 40(9):1591–1601, 2004.

Zimmerman, D. L. Block Toeplitz products of block Toeplitz matrices. Linear and

Multilinear Algebra, 25(3):185–190, 1989.

Summary

System Identification for Robust and Inferential Control

with Applications to ILC and Precision Motion Systems

Feedback control is able to improve the performance of systems in the presence of

uncertain dynamical behavior and disturbances. Although a properly designed con-

troller can cope with large uncertainty, certain knowledge regarding the system be-

havior is crucial for control design. Hence, high performance control design requires a

mathematical model of the true system. System identification is a reliable, fast, and

inexpensive methodology to construct accurate models from experimentally obtained

data. The resulting model, however, is never an exact representation of the physical

system. Robust control design can be employed to deal with the model imperfections

by guaranteeing a certain performance for an uncertain model set.

In the last decades, important achievements have been obtained in the fields of

system identification and robust control. These results in these fields have mainly been

established independently of each other. As a result, the interrelation between system

identification and robust control is untransparent. To connect system identification and

robust control in a coherent methodology, the pursued approach involves 1. improved

system identification methodologies for nominal models; 2. quantification of model

uncertainty by confronting the identified model with new measurement data to test its

predictive power, as a result a model set is obtained that encompasses the true system

behavior; 3. the design of a robust controller that performs well with the entire model

set, hence also when implemented on the true system. New theoretical developments

and algorithms are presented that transparently connect Steps 1, 2, and 3.

Firstly, a new connection between control-relevant system identification and co-

prime factorization-based system identification is presented. The system identification

procedure directly delivers a model that is internally structured as a novel coprime

factorization. In addition, the resulting control-relevant model aims to accurately rep-

resent the phenomena of the true system that are to be compensated. The resulting

coprime factorization exploits the unexplored freedom in constructing a coordinate

frame for model uncertainty. As a result, a novel coprime factorization-based model

318 Summary

uncertainty structure is obtained that transparently connects Steps 1, 2, and 3, above.

In many high quality control applications, including precision motion systems, the

performance variables generally cannot be measured in real-time during normal op-

eration. In this case, model-based control design is essential, since a model can be

used in conjunction with the measured variables to infer the performance variables.

Although the performance of the resulting controlled system hinges on the model qual-

ity, standard robust control design approaches, system identification techniques, and

uncertainty models cannot deal with this inferential control situation. Thereto, new

controller interconnection structures, new control criteria, new system identification

techniques, and new model uncertainty structures are presented that can deal with the

inferential control situation. In addition, these new developments enable a transparent

connection between Steps 1, 2, and 3, above.

Besides the model uncertainty interconnection structure, the actual quantification of

model uncertainty is essential for a reliable and nonconservative robust control design.

In model validation, the nominal model is confronted with independent measurement

data to test its predictive power, thereby enabling a quantification of model quality. By

exploiting the freedom in experiment design, a suitable characterization of disturbances

is obtained and averaging properties of these disturbances are enforced. As a result, a

well-posed validation-based uncertainty modeling procedure is obtained that results in

correct asymptotic results and an uncertainty model that is directly useful for robust

control design.

The new developments and algorithms further intertwine system identification and

robust control. As a consequence, a non-conservative high performance robust con-

trol design can be obtained. The developed methodology is experimentally verified

on several systems, including an industrial wafer stage, a flexible beam setup, and a

continuously variable transmission system. Experimental results confirm an improved

robust control performance and the ability of the developed algorithms to reliably deal

with multivariable systems and unmeasured performance variables.

Finally, iterative learning control for sampled-data systems is investigated. Iter-

ative learning control enables the performance improvement for batch repetitive pro-

cesses by iteratively updating the command signal from one experiment to the next.

Although many physical systems evolve in the continuous time domain, common iter-

ative learning control algorithms are implemented in a digital computer environment.

Thereto, iterative learning control algorithms for sampled-data systems are presented

that explicitly address the intersample behavior. In addition, any iterative learning

algorithm requires a certain approximate system knowledge. To obtain such models,

parametric system identification algorithms for sampled-data iterative learning control

are developed. Furthermore, low-order iterative learning control synthesis algorithms

are presented.

Samenvatting

System Identification for Robust and Inferential Control

with Applications to ILC and Precision Motion Systems

Terugkoppeling van gemeten variabelen maakt het mogelijk de prestaties van sys-

temen te verbeteren in geval van onzeker dynamisch gedrag of verstoringen. Alhoewel

een goed ontworpen regeling om kan gaan met grote onzekerheden, is bepaalde kennis

omtrent het systeemgedrag cruciaal voor regelaarontwerp. Daarom vereist het ont-

werp van een hoogwaardige regeling een wiskundig model van het te regelen fysische

systeem. Systeem identificatie is een betrouwbare, snelle en voordelige methode om

nauwkeurige modellen te construeren uit experimentele data. Echter, het resulterende

model is nooit een exacte representatie van het fysische systeem. Robuuste regelaar-

ontwerpmethodieken kunnen omgaan met dergelijke modelimperfecties door een zeker

niveau van prestaties te garanderen voor een onzekere model set.

In de laatste decennia zijn reeds belangrijke successen behaald in de vakgebieden van

systeem identificatie en robuust regelaarontwerp. De resultaten in deze vakgebieden

zijn echter hoofdzakelijk onafhankelijk van elkaar verkregen. Hierdoor is het onderlinge

verband tussen systeem identificatie en robuust regelaarontwerp onvoldoende helder.

Om deze vakgebieden te verbinden in een coherente methodologie, omvat de ontwik-

kelde methodiek 1. verbeterde systeem identificatiemethoden voor nominale model-

len; 2. kwantificatie van modelkwaliteit door het confronteren van het geıdentificeerde

model met nieuwe meetdata om de voorspellende kracht van het model te testen,

het resultaat hiervan is een model set welke het echte systeemgedrag omvat; 3. het

ontwerpen van een robuuste regelaar die goede prestaties levert voor de gehele modelset,

dus ook indien deze geımplementeerd wordt op het echte systeem. Nieuwe theoretische

ontwikkelingen en algoritmen zijn gepresenteerd die een transparant verband leggen

tussen Stappen 1, 2 en 3.

Allereerst is er een nieuw verband gevonden tussen regelaar-relevante en copriem

factorisatie gebaseerde systeem identificatie. De ontwikkelde identificatie procedure

levert direct een model dat intern gestructureerd is als een copriem factorisatie, waar-

voor een nieuwe keuze gemaakt is. Daarnaast is het resulterende regelaar-relevante

320 Samenvatting

model gericht op het nauwkeurig representeren van de specifieke fenomenen van het

echte systeem die geregeld dienen te worden. Het resulterende model benut de on-

verkende vrijheid in coprieme factoren om een coordinatenstelsel voor modelonzeker-

heid te construeren. Het resultaat is een nieuwe modelonzekerheidsstructuur die een

transparant verband legt tussen bovenstaande Stappen 1, 2 en 3.

In veel hoogwaarde toepassingen van de regeltechniek, zoals precisie positioneersys-

temen, kunnen de prestaties niet in real-time gemeten worden onder normaal bedrijf. In

dit geval is een modelgebaseerde regeling essentieel, aangezien een model in combinatie

met gemeten variabelen gebruikt kan worden om de prestatie-variabelen af te schatten.

Alhoewel de prestaties van het resulterende model afhangen van de modelkwaliteit,

kunnen standaard robuuste regelaar ontwerpmethodieken, systeem identificatie aan-

pakken en modelonzekerheidsbeschrijvingen niet met deze situatie omgaan. Hiertoe

zijn nieuwe regelaar interconnectiestructuren, nieuwe regelaarcriteria, nieuwe identifi-

catietechnieken en nieuwe modelonzekerheidsstructuren gepresenteerd die om kunnen

gaan met niet-gemeten prestatie-variabelen. Daarnaast maken deze ontwikkelingen een

transparant verband mogelijk tussen bovenstaande Stappen 1, 2 en 3.

Naast de interconnectiestructuur van de modelonzekerheid, is het essentieel om de

actuele modelonzekerheid te kwantificeren voor een betrouwbaar en niet-conservatief

robuust regelaarontwerp. In modelvalidatie wordt het nominale model geconfronteerd

met onafhankelijke meetdata om de voorspellende kracht van het model te testen. Door

het benutten van de vrijheid in het ontwerp van experimenten, is een geschikte karak-

terisatie van verstoringen verkregen en worden uitmiddelingseigenschappen van deze

verstoringen afgedwongen. Het resultaat is een goed gestelde validatie-gebaseerde aan-

pak voor onzekerheidsmodelering welke resulteert in asymptotisch correcte resultaten

en een onzekerheidsmodel dat direct geschikt is voor robuust regelaarontwerp.

De nieuwe resultaten en algoritmen bewerkstelligen een verdere aansluiting tussen

systeem identificatie en robuust regelaarontwerp. Hierdoor is een niet-conservatieve

robuuste regelaar ontwerp met hoge prestaties mogelijk. De methodologie is geverifieerd

op verschillende systemen, waaronder een industriele wafer stage, een flexibele balk

en een continu variabele transmissie. Experimentele resultaten bevestigen verbeterde

robuuste regelaarprestaties. Daarnaast blijkt dat de ontwikkelde algoritmen geschikt

zijn voor multivariabele systemen en niet-gemeten prestatie-variabelen.

Tot slot is iteratief lerend regelen onderzocht. Iteratief lerend regelen maakt het

mogelijk de prestaties voor systemen te verbeteren die telkens dezelfde taak uitvoeren.

Dit wordt bereikt door het stuursignaal van het ene experiment naar het volgende aan

te passen. Alhoewel veel fysische systemen in het continue tijddomein evolueren, wor-

den dergelijke algoritmen typisch in een digitale computeromgeving geımplementeerd.

Hiertoe zijn iteratief lerende algoritmen ontwikkeld die expliciet het gedrag van het

systeem tussen de bemonstertijdstippen in beschouwing nemen. Daarnaast vereisen

iteratief lerende algoritmen bepaalde benaderende systeemkennis. Om dergelijke mod-

ellen te verkrijgen, zijn specifieke parametrische systeem identificatie algoritmen gep-

resenteerd. Daarnaast zijn lage orde iteratief lerende algoritmen gepresenteerd.

Documents

System Identiﬁcation for Robust and Inferential Control · I Introduction 1 1 Towards Next-Generation Motion Control 3 ... B. Introduction to Large Truncated Toeplitz Matrices