Piezo-electric actuators (PEAs) have been widely used in nanopositioning applications due to their high stiffness, fast responses, and large actuating forces. However, the existence of nonlinearities such as hysteresis can greatly deteriorate their performance and, as such, modeling and control of PEAs for improved performance has drawn considerable attention in the literature. This paper presents a brief survey of recent achievements in modeling and control of PEAs as well as the relevant issues that remain to be resolved. Specifically, various methods for modeling hysteresis, creep, and vibration dynamics in PEAs are examined, followed by a discussion of the issues leading to modeling errors. Recently reported PEA control schemes are surveyed along with their advantages and disadvantages. The challenges associated with control problems are also discussed.
Issue Section:
Technology Review
References
1.
Ouyang
, P. R.
, Tjiptoprodjo
, R. C.
, Zhang
, W. J.
, and Yang
, G. S.
, 2008
, “Micro-Motion Devices Technology: The State of Arts Review
,” Int. J. Adv. Manuf. Technol.
, 38
(5–6
), pp. 463
–478
.10.1007/s00170-007-1109-62.
Devasia
, S.
, and Moheimani
, S. O. R.
, 2007
, “A Survey of Control Issues in Nano-Positioning
,” IEEE Trans. Control Syst. Technol.
, 15
(5
), pp. 802
–823
.10.1109/TCST.2007.9033453.
Chapman
, D.
, Thomlinson
, W.
, Johnston
, R. E.
, and Washburn
, D.
, 1997
, “Diffraction Enhanced X-Ray Imaging
,” Phys. Med. Biol.
, 42
(11
), pp. 2015
–2025
.10.1088/0031-9155/42/11/0014.
Cao
, Y.
, Chen
, X. B.
, and May
, T.
, 2013
, “Sliding Mode Control on the Active Optics for the Far Infrared Beamline
,” Proceedings of 24th Canadian Congress of Applied Mechanics
, (CANCAM), No. CS04, Saskatoon, SK, Canada
, June 2–6.5.
Sebastian
, A.
, and Salapaka
, S. M.
, 2005
, “Design Methodologies for Robust Nano-Positioning
,” IEEE Trans. Control Syst. Technol.
, 13
(6
), pp. 868
–876
.10.1109/TCST.2005.8543366.
Ishitobi
, M.
, Nishi
, M.
, and Miyachi
, M.
, 2003
, “A Survey of Recent Innovations in Vibration Damping and Control Using Shunted Piezoelectric Transducers
,” IEEE Trans. Control Syst. Technol.
, 11
(4
), pp. 482
–494
.10.1109/TCST.2003.8133717.
Corft
, D.
, Shed
, G.
, and Devasia
, S.
, 2001
, “Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application
,” ASME J. Dyn. Syst.
, 123
(1
), pp. 35
–43
.10.1115/1.13411978.
Leang
, K. K.
, and Devasia
, S.
, 2007
, “Feedback-Linearized Inverse Feedforward for Creep, Hysteresis, and Vibration Compensation in AFM Piezoactuators
,” IEEE Trans. Control Syst. Technol.
, 15
(5
), pp. 927
–935
.10.1109/TCST.2007.9029569.
Schitter
, G.
, Menold
, P.
, and Knapp
, H. F.
, 2001
, “High Performance Feedback for Fast Scanning Atomic Force Microscopes
,” Rev. Sci. Instrum.
72
(8
), pp. 3320
–3327
.10.1063/1.138725310.
Tien
, S. C.
, Zou
, Q. Z.
, and Devasia
, S.
, 2005
, “Iterative Control of Dynamics-Coupling-Caused Errors in Piezoscanners During High-Speed AFM Operation
,” IEEE Trans. Control Syst. Technol.
, 13
(6
), pp. 921
–931
.10.1109/TCST.2005.85433411.
Leang
, K. K.
, and Devasia
, S.
, 2002
, “Creep and Vibration Compensation for Piezo-actuators: Feedback and Feedforward Control,” Proc. 2nd IFAC Conference on Mechatronic System, Berkeley, CA, Dec. 9–11, pp. 283–289.12.
Visintin
, A.
, 1994
, Differential Models of Hysteresis
, Springer-Verlag
, Berlin Heidelberg
.13.
Bashash
, S.
, and Jalili
, N.
, 2007
, “Intelligence Rules of Hysteresis in the Feedforward Trajectory Control of Piezoelectrically-Driven Nanostagers
,” J. Micromech. Microeng.
, 17
(2
), pp. 342
–349
.10.1088/0960-1317/17/2/02114.
Tian
, Y.
, Shirinzadeh
, B.
, and Zhang
, D.
, 2010
, “Design and Dynamics of a Three-DOF Flexure-Based Parallel Mechanism for Micro/Nano Manipulation
,” Microelectron. Eng.
, 87
(2)
, pp. 230
–241
.10.1016/j.mee.2009.08.00115.
Yong
, Y. K.
, Aphale
, S. S.
, and Moheimani
, S. O. R.
, 2009
, “Design, Identification and Control of a Flexure-Based Stage for Fast Nanoscale Positioning
,” IEEE Trans. Nanotechnol.
, 8
(1
), pp. 46
–54
.10.1109/TNANO.2008.200582916.
Kim
, H. S.
, and Cho
, Y. M.
, 2009
, “Design and Modeling of a Novel Three-DOF Precision Micro-Stage
,” Mechatronics
, 19
(5
), pp. 598
–608
.10.1016/j.mechatronics.2009.01.00417.
Gao
, P.
, and Swei
, S. M.
, 1999
, “A Six-Degree-of-Freedom Micro-Manipulator Based on Piezoelectric Actuator
,” Nanotechnology
, 10
(4)
, pp. 447
–452
.10.1088/0957-4484/10/4/31518.
Hui
, C.
, 2001
, “Dynamics and Control of Parallel Manipulators With Redundant Actuation
,” M.Sc. thesis, Electrical and Electronic Engineering at the Hong Kong University of Science and Technology, Hong Kong, China.19.
Kock
, S.
, and Schumacher
, W.
, 1998
, “A Parallel X-Y Manipulator With Actuation Redundancy for High-Speed and Active-Stiffness Applications
,” Proceedings of IEEE International Conference on Robotics and Automation
, Leuven, Belgium
, May 20, Vol. 3, pp. 2295–2300.20.
Kim
, J. W.
, Park
, F. C.
, Ryu
, S. J.
, Kim
, J.
, Hwang
, J. C.
, Park
, C.
, and Iurascu
, C. C.
, 2001
, “Design and Analysis of a Redundantly Actuated Parallel Mechanism for Rapid Machining
,” IEEE Trans. Robot. Autom.
, 17
(4
), pp. 423
–434
.10.1109/70.95475521.
Kurtz
, R.
, and Hayward
, V.
, 1992
, “Multiple-Goal Kinematic Optimization of a Parallel Spherical Mechanical With Actuator Redundancy
,” IEEE Trans. Robot. Autom.
, 8
(5
), pp. 644
–651
.10.1109/70.16378822.
Walker
, I. D.
, and Marcus
, S. I.
, 1988
, “Subtask Performance by Redundancy Resolution for Redundant Robot Manipulators
,” IEEE Trans. Robot. Autom.
, 4
(3
), pp. 350
–354
.10.1109/56.79523.
Du
, X.
, Dixon
, R.
, Goodall
, R. M.
, and Zolotas
, A. C.
, 2010
, “Modeling and Control of a High Redundancy Actuator
,” Mechatronics
, 20
(1
), pp. 102
–112
.10.1016/j.mechatronics.2009.09.00924.
Jung
, H.
, Shim
, J. Y.
, and Gweon
, D.
, 2000
, “New Open-Loop Actuating Method of Piezoelectric Actuators for Removing Hysteresis and Creep
,” Rev. Sci. Instrum.
, 71
(9
), pp. 3436
–3440
.10.1063/1.128762725.
Jung
, H.
, and Gweon
, D.
, 2000
, “Creep Characteristics of Piezoelectric Actuators
,” Rev. Sci. Instrum.
, 71
(4
), pp. 1896
–1900
.10.1063/1.115055926.
Zhong
, J. H.
, 2003
, “Modeling and Control Piezoceramic Actuator for Nanopositioning
,” M.Sc. thesis, Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC.27.
Mrad
, R. B.
, and Hu
, H.
, 2001
, “Dynamic Modeling of Hysteresis in Piezoceramics
,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, Como, Italy
, July 8–12, Vol. 1, pp. 510–515.28.
Telba
, A.
, and Ali
, W. G.
, 2011
, “Hysteresis Modeling in a Piezoelectric Nanopositioner Stage
,” Proceedings of the World Congress on Engineering
, London, UK, July 6–8, Vol. 2, pp. 1493–1495.29.
Henze
, O.
, and Rucker
, W. M.
, 2002
, “Identification Procedures of Preisach Model
,” IEEE Trans. Magn.
, 38
(2
), pp. 833
–836
.10.1109/20.99621530.
Mayergoyz
, I. D.
, 1986
, “Mathematical Models of Hysteresis
,” Phys. Rev. Lett.
, 56
(15
), pp. 603
–608
.10.1103/PhysRevLett.56.151831.
Lee
, S. H.
, Royston
, T. J.
, and Friedman
, G.
, 2000
, “Modeling and Compensation of Hysteresis in Piezoceramic Transducers for Vibration Control
,” J. Intell. Mater. Syst. Struct.
, 11
(10
), pp. 781
–790
.10.1106/GQLJ-JGEU-MHG1-7JDF32.
Lee
, S. H.
, and Royston
, T. J.
, 2000
, “Modeling Piezoceramic Transducer Hysteresis in the Structural Vibration Control Problem
,” J. Acoust. Soc. Am.
, 108
(6
), pp. 2843
–2855
.10.1121/1.132346433.
Hu
, H.
, and Mrad
, R. B.
, 2003
, “On the Classical Preisach Model for Hysteresis in Piezoceramic Actuators
,” Mechatronics
, 13
(2
), pp. 85
–94
.10.1016/S0957-4158(01)00043-534.
Kuhnen
, K.
, and Janocha
, H.
, 2001
, “Inverse Feedforward Controller for Complex Hysteretic Nonlinearities in Smart-Material Systems
,” Control Intell. Syst.
, 29
(3
), pp. 74
–83
, Available at http://www.lpa.uni-saarland.de/pdf/mic01art.pdf35.
Qin
, Y. D.
, Tian
, Y. L.
, Zhang
, D. W.
, Shirinzadeh
, B.
, and Fatikow
, S.
, 2013
, “A Novel Direct Inverse Modeling Approach for Hysteresis Compensation of Piezoelectric Actuator in Feedforward Applications
,” IEEE/ASME Trans. Mechatron.
, 18
(3
), pp. 981
–989
.10.1109/TMECH.2012.219430136.
Janaideh
, M. A.
, Rakheja
, S.
, and Su
, C. Y.
, 2011
, “An Analytical Generalized Prandtl-Ishlinskii Model Inversion for Hysteresis Compensation in Micropositioning Control
,” IEEE/ASME Trans. Mechatron.
, 16
(4
), pp. 734
–744
.10.1109/TMECH.2010.205236637.
Jiang
, H.
, Ji
, H. L.
, Qiu
, J. H.
, and Chen
, Y. S.
, 2010
, “A Modified Prandtl-Ishlinskii Model for Modeling Asymmetric Hysteresis of Piezoelectric Actuators
,” IEEE Trans. Ultrason., Ferroelectr. Freq. Control
, 57
(5
), pp. 1200
–1210
.10.1109/TUFFC.2010.153338.
Gu
, G. Y.
, Yang
, M. J.
, and Zhu
, L. M.
, 2012
, “Real-Time Inverse Hysteresis Compensation of Piezoelectric Actuators With a Modified Prandtl-Ishlinskii Model
,” Rev. Sci. Instrum.
, 83
(6
), pp. 198
–209
.10.1063/1.472857539.
Oh
, J. H.
, and Bernstein
, D. S.
, 2005
, “Semilinear Duhem Model for Rate-Independent and Rate-Dependent Hysteresis
,” IEEE Trans. Autom. Control
, 50
(5
), pp. 631
–645
.10.1109/TAC.2005.84703540.
Oh
, J. H.
, and Padthe
, A. K.
, 2005
, “Duhem Models for Hysteresis in Sliding and Presliding Friction
,” Proceedings of 44th IEEE Conference on Decision and Control, and the European Control Conference
, Seville, Spain
, Dec. 12–15, pp. 8132–8137.41.
Padthe
, A. K.
, and Bernstein
, D. S.
, 2007
, “A Delay Duhem Model for Jump Resonance Hysteresis
,” Proceedings of 46th IEEE Conference on Decision and Control
, New Orleans, LA
, Dec. 12–14, pp 1609–1614.42.
Ikhouane
, F.
, Manosa
, V.
, and Rodellar
, J.
, 2007
, “Dynamic Properties of the Hysteretic Bouc-Wen Model
,” Syst. Control Lett.
, 56
(3
), pp. 197
–205
.10.1016/j.sysconle.2006.09.00143.
Bellmunt
, O. G.
, Ikhouane
, F.
, and Miracle
, D. M.
, 2008
, “Control of Bouc-Wen Hysteretic Systems: Application to a Piezoelectric Actuator
,” Proceedings of the 13th IEEE on International Power Electronics and Motion Control Conference
, Poznan, Poland, Sep. 1–3, pp. 1670
–1675
.44.
Song
, J.
, and Kiureghian
, A.
, 2006
, “Generalized Bouc-Wen Model for Highly Asymmetric Hysteresis
,” J. Eng. Mech.
, 132
(6
), pp. 610
–618
.10.1061/(ASCE)0733-9399(2006)132:6(610)45.
Bellmunt
, O. G.
, Ikhouane
, F.
, Vilanova
, P. C.
, and Jane
, J. B.
, 2007
, “Modeling and Validation of a Piezoelectric Actuator
,” Electric. Eng.
, 89
(8
), pp. 629
–638
.10.1007/s00202-006-0049-846.
Lin
, C. J.
, and Yang
, S. R.
, 2005
, “Modeling of a Piezo-Actuated Positioning Stage Based on a Hysteresis Observer
,” Asian J. Control
, 7
(1
), pp. 73
–80
.10.1111/j.1934-6093.2005.tb00230.x47.
Rakotondrabe
, M.
, 2011
, “Bouc-Wen Modeling and Inverse Multiplicative Structure to Compensate Hysteresis Nonlinearity in Piezoelectric Actuators
,” IEEE Trans. Autom., Sci. Eng.
, 8
(2
), pp. 428
–431
.10.1109/TASE.2010.208197948.
Adriaens
, H. J. M. T. A.
, Koning
, W. L.
, and Banning
, R.
, 2000
, “Modeling Piezoelectric Actuators
,” IEEE/ASME Trans. Mechatron.
, 5
(4
), pp. 331
–341
.10.1109/3516.89104449.
Banning
, R.
, and Koning
, W. L.
, 2001
, “State-Space Analysis and Identification for a Class of Hysteresis System
,” Automatica
, 37
, pp. 1883
–1892
.10.1016/S0005-1098(01)00157-150.
Clayton
, G. M.
, Tien
, S.
, and Fleming
, A. J.
, 2008
, “Inverse-Feedforward of Charge-Controlled Piezopositioners
,” Mechatronics,
18
(5–6
), pp. 273
–281
.10.1016/j.mechatronics.2007.07.00651.
Cao
, Y.
, and Chen
, X. B.
, 2012
, “A Novel Discrete ARMA-based Model for Piezoelectric Actuator Hysteresis
,” IEEE/ASME Trans. Mechatron.
, 17
(4
), pp. 737
–744
.10.1109/TMECH.2011.212833952.
Chen
, X. B.
, Zhang
, Q. S.
, Kang
, D.
, and Zhang
, W. J.
, 2008
, “On the Dynamics of Piezoelectric Positioning Systems
,” Rev. Sci. Instrum.
, 79
(11
), p. 116101
.10.1063/1.298223853.
Salapaka
, S.
, Sebastian
, A.
, Cleveland
, J. P.
, and Salapaka
, M. V.
, 2002
, “High Bandwidth Nano-Positioner: A Robust Control Approach
,” Rev. Sci. Instrum.
, 73
(9
), pp. 3232
–3241
.10.1063/1.149953354.
Bhikkaji
, B.
, Ratnam
, M.
, Fleming
, A. J.
, and Moheimani
, S. O. R.
, 2007
, “High-Performance Control of Piezoelectric Tube Scanners
,” IEEE Trans. Control Syst. Technol.
, 15
(5
), pp. 853
–866
.10.1109/TCST.2007.90294755.
Clayton
, G. M.
, Tien
, S.
, and Fleming
, A. J.
, 2006
, “Hysteresis and Vibration Compensation in Piezoelectric Actuators by Integrating Charge Control and Inverse Feedforward
,” Proceedings of 4th IFAC Symposium on Mechatronic Systems
, Heidelberg, Germany
, September 12–14, Vol. 4, pp. 812–818.56.
Schitter
, G.
, and Stemmer
, A.
, 2004
, “Identification and Open-Loop Tracking Control of a Piezoelectric Tube Scanner for High-Speed Scanning-Probe Microscopy
,” IEEE Trans. Control Syst. Technol.
, 12
(3
), pp. 449
–454
.10.1109/TCST.2004.82429057.
Croft
, D.
, and Devasia
, S.
, 1999
, “Vibration Compensation for High Speed Scanning Tunnelling Microscopy
,” Rev. Sci. Instrum.
, 70
(12
), pp. 4600
–4605
.10.1063/1.115011958.
Deng
, L.
, and Tan
, Y. H.
, 2009
, “Modeling Hysteresis in Piezoelectric Actuators Using NARMAX Models
,” Sens. Actuators, A
, 149
(1
), pp. 106
–112
.10.1016/j.sna.2008.09.02259.
Song
, D.
, and Li
, C. J.
, 1999
, “Modeling of Piezo Actuator's Nonlinear and Frequency Dependent Dynamics
,” Mechatronics
, 9
(4
), pp. 391
–410
.10.1016/S0957-4158(99)00005-760.
Xiao
, S. L.
, and Li
, Y. M.
, 2013
, “Modeling and High Dynamic Compensating the Rate-Dependent Hysteresis of Piezoelectric Actuators Via a Novel Modified Inverse Preisach Model
,” IEEE Trans. Control Syst. Technol.
, 21
(5
), pp. 1549
–1557
.10.1109/TCST.2012.220602961.
Zhang
, X. L.
, and Tan
, Y. H.
, 2010
, “A Hybrid Model for Rate-Dependent Hysteresis in Piezoelectric Actuators
,” Sens. Actuators, A
, 157
(1
), pp. 54
–60
.10.1016/j.sna.2009.10.00962.
Li
, P. Z.
, Yan
, F.
, Ge
, C.
, Wang
, X. L.
, Xu
, L. S.
, Guo
, J. L.
, and Li
, P. Y.
, 2013
, “A Simple Fuzzy System for Modeling of Both Rate-Independent and Rate-Dependent Hysteresis in Piezoelectric Actuators
,” Mech. Syst. Signal Process.
, 36
(1
), pp. 182
–192
.10.1016/j.ymssp.2012.10.00463.
Xu
, Q. S.
, 2013
, “Identification and Compensation of Piezoelectric Hysteresis Without Modeling Hysteresis Inverse
,” IEEE Trans. Ind. Electron.
, 60
(9
), pp. 3927
–3937
.10.1109/TIE.2012.220633964.
Lien
, J. P.
, York
, A.
, Fang
, T. G.
, and Buckner
, G. D.
, 2010
, “Modeling Piezoelectric Actuators With Hysteretic Recurrent Neural Networks
,” Sens. Actuators, A
, 163
, pp. 516
–525
.10.1016/j.sna.2010.08.01365.
Zhang
, X. L.
, Tan
, Y. H.
, and Su
, M. Y.
, 2009
, “Modeling of Hysteresis in Piezoelectric Actuators Using Neural Networks
,” Mech. Syst. Signal Process.
, 23
(8
), pp. 2699
–2711
.10.1016/j.ymssp.2009.05.00266.
Dang
, X. J.
, and Tan
, Y. H.
, 2005
, “An Inner Product-Based Dynamic Neural Network Hysteresis Model for Piezoceramic Actuators
,” Sens. Actuators, A
, 121
(2
), pp. 535
–542
.10.1016/j.sna.2005.04.00367.
Tong
, Z.
, Tan
, Y. H.
, and Zeng
, X. W.
, 2005
, “Modeling Hysteresis Using Hybrid Method of Continuous Transformation and Neural Networks
,” Sens. Actuators, A
, 119
(1
), pp. 254
–262
.10.1016/j.sna.2004.09.01968.
Chiena
, C. J.
, Lee
, F. S.
, and Wang
, J. C.
, 2007
, “Enhanced Iterative Learning Control for a Piezoelectric Actuator System Using Wavelet Transform Filtering
,” J. Sound Vib.
, 299
(3
), pp. 605
–620
.10.1016/j.jsv.2006.07.02169.
Lin
, E.
, 2009
, “Generalized Wavelet Formulation of Hysteresis Models for Smart Material Systems
,” Hysteresis Modeling and Micromagnetics
, NIST
, Gaithersburg, MD
.70.
Yu
, Y. H.
, Xiao
, Z. C.
, Lin
, E. B.
, and Naganathan
, N.
, 2000
, “Analytic and Experimental Studies of a Wavelet Identification of Preisach Model of Hysteresis
,” J. Magn. Magn. Mater.
, 208
(3
), pp. 255
–263
.10.1016/S0304-8853(99)00590-971.
Gu
, G. Y.
, and Zhu
, L. M.
, 2011
, “Modeling of Rate-Dependent Hysteresis in Piezoelectric Actuators Using a Family of Ellipses
,” Sens. Actuators, A
, 165
(2
), pp. 303
–309
.10.1016/j.sna.2010.09.02072.
Zhang
, Y. L.
, Han
, M. L.
, Yu
, M. Y.
, Shee
, C. Y.
, and Ang
, W. T.
, 2012
, “Automatic Hysteresis Modeling of Piezoelectric Micromanipulator in Vision-Guided Micromanipulation Systems
,” IEEE/ASME Trans. Mechatron.
, 17
(3
), pp. 547
–553
.10.1109/TMECH.2011.210613673.
Fett
, T.
, and Thun
, G.
, 1998
, “Determination of Room-Temperature Tensile Creep of PZT
,” J. Mater. Sci. Lett.
, 17
(22
), pp. 1929
–1931
.10.1023/A:100660850987674.
Ge
, P.
, and Jouaneh
, M.
, 1996
, “Tracking Control of a Piezoceramic Actuator
,” IEEE Trans. Control Syst. Technol.
, 4
(3
), pp. 209
–216
.10.1109/87.49119575.
Leang
, K. K.
, and Devasia
, S.
, 2006
, “Design of Hysteresis Compensating Iterative Control for Piezo-Positioners: Application on Atomic Force Microscopes
,” Mechatronics,
16
(3–4
), pp. 141
–158
.10.1016/j.mechatronics.2005.11.00676.
Lin
, C. J.
, and Yang
, S. R.
, 2006
, “Precise Positioning of Piezo-Actuated Stages Using Hysteresis-Observer Based Control
,” Mechatronics
, 16
(7
), pp. 417
–426
.10.1016/j.mechatronics.2006.03.00577.
Lin
, C. Y.
, and Chen
, P. Y.
, 2011
, “Precision Tracking Control of a Biaxial Piezo Stage Using Repetitive Control and Double-Feedforward Compensation
,” Mechatronics
, 21
(1
), pp. 239
–249
.10.1016/j.mechatronics.2010.11.00278.
Wang
, F. C.
, Tsai
, Y. C.
, Hsieh
, C. H.
, Chen
, L. S.
, and Yu
, C. H.
, 2011
, “Robust Control of a Two-Axis Piezoelectric Nano-Positioning Stage
,” Preprints of the 18th IFAC World Congress
, Milano, Italy
, Aug. 28–Sep. 2, Vol. 18, 3539–3544.79.
Fung
, R. F.
, and Lin
, W. C.
, 2010
, “System Identification and Contour Tracking of a Plane-Type 3-DOF (X, Y, θz) Precision Positioning Table
,” IEEE Trans. Control Syst. Technol.
, 18
(1
), pp. 22
–34
.10.1109/TCST.2008.200952880.
Cao
, Y.
, and Chen
, X. B.
, 2010
, “System Identification of a Three-DOF Nano-Positioning Stage by Hankel Matrix
,” Actuators
, 2
, pp. 1
–18
.10.3390/act201000181.
Chen
, T. W.
, and Francis
, B.
, 1995
, Optimal Sampled-Data Control Systems
, Springer-Verlag Berlin
, Heidelberg, Germany
.82.
Vörös
, J.
, 2009
, “Modeling and Identification of Hysteresis Using Special Forms of the Coleman-Hodgdon Model
,” J. Electr. Eng., 60
(2
), pp. 100
–105
. Available at: http://iris.elf.stuba.sk/JEEEC/data/pdf/2_109-06.pdf83.
Cao
, Y.
, Cheng
, L.
, Chen
, X. B.
, and Peng
, J. Y.
, 2013
, “An Inversion-Based Model Predictive Control With an Integral-of-Error State Variable for Piezoelectric Actuators
,” IEEE/ASME Trans. Mechatron.
, 18
(3
), pp. 895
–904
.10.1109/TMECH.2012.219479284.
Comstock
, R. H.
, and Acton
, W.
, 1981
, “Charge Control of Piezoelectric Actuators to Reduce the Hysteresis Effects
,” U.S. Patent No. US4263527.85.
Fleming
, A. J.
, and Moheimani
, S. O. R.
, 2005
, “A Grounded-Load Charge Amplifier for Reducing Hysteresis in Piezoelectric Tube Scanners
,” Rev. Sci. Instrum.
, 76
, p. 073707
.10.1063/1.193895286.
Fleming
, A. J.
, and Moheimani
, S. O. R.
, 2004
, “Improved Current and Charge Amplifiers for Driving Piezoelectric Loads, and Issues in Signal Processing Design for Synthesis of Shunt Damping Circuits
,” J. Intell. Mater. Syst. Struct.
, 15
(2
), pp. 77
–92
.10.1177/1045389X0403970187.
Tsai
, M. S.
, and Chen
, J. S.
, 2003
, “Robust Tracking Control of a Piezoactuator Using a New Approximate Hysteresis Model
,” ASME J. Dyn. Syst. Meas. Control
, 125
(1
), pp. 96
–102
.10.1115/1.154011488.
Cruz-Hernández
, J. M.
, and Hayward
, V.
, 2001
, “Phase Control Approach to Hysteresis Reduction
,” IEEE Trans. Control Syst. Technol.
, 9
(1
), pp. 17
–26
.10.1109/87.89674289.
Gu
, G. Y.
, Zhu
, L. M.
, Su
, C. Y.
, and Ding
, H.
, 2013
, “Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design and Experimental Evaluation
,” IEEE/ASME Trans. Mechatron.
, 18
(5
), pp. 1459
–1471
.10.1109/TMECH.2012.220331590.
Tan
, X. B.
, and Baras
, J. S.
, 2005
, “Adaptive Identification and Control of Hysteresis in Smart Materials
,” IEEE Trans. Autom. Control
, 50
(6
), pp. 827
–839
.10.1109/TAC.2005.84921591.
Tao
, G.
, and Kokotović
, P. V.
, 1995
, “Adaptive Control of Plants With Unknown Hysteresis
,” IEEE Trans. Autom. Control
, 40
(2
), pp. 200
–212
.10.1109/9.34177892.
Wu
, Y.
, and Zou
, Q. Z.
, 2007
, “Iterative Control Approach to Compensate for Both the Hysteresis and the Dynamics Effects of Piezo Actuators
,” IEEE Trans. Control Syst. Technol.
, 15
(5
), pp. 936
–944
.10.1109/TCST.2007.89972293.
Ahn
, H. S.
, Chen
, Y. Q.
, and Moore
, K. L.
, 2007
, “Iterative Learning Control: Brief Survey and Categorization
,” IEEE Trans. Syst., Man, Cybern
, 37
(6
), pp. 1099
–1121
.10.1109/TSMCC.2007.90575994.
Ghosh
, J.
, and Paden
, B.
, 2001
, “Iterative Learning Control for Nonlinear Nonminimum Phase Plants
,” ASME J. Dyn. Syst
, 123
(1), pp. 21
–30
.10.1115/1.134120095.
Bristow
, D. A.
, Tharayil
, M.
, and Alleyne
, A. G.
, 2006
, “A Survey of Iterative Learning Control
,” IEEE Control Syst.
, 26
(3
), pp. 96
–114
.10.1109/MCS.2006.163631396.
Kim
, K. S.
, and Zou
, Q. Z.
, 2013
, “A Modeling-Free Inversion-Based Iterative Feedforward Control for Precision Output Tracking of Linear Time-Invariant Systems
,” IEEE/ASME Trans. Mechatron.
, 18
(6
), pp. 1767
–1777
.10.1109/TMECH.2012.221291297.
Xu
, J. X.
, Huang
, D. Q.
, Venkataramanan
, V.
, and Huynh
, T. C. T.
, 2013
, “Extreme Precision Motion Tracking of Piezoelectric Positioning Stage Using Sampled-Data Iterative Learning Control
,” IEEE Trans. Control Syst. Technol.
, 21
(4
), pp. 1432
–1439
.10.1109/TCST.2012.220171898.
Huang
, D. Q.
, Xu
, J. X.
, Venkataramanan
, V.
, and Huynh
, T. C. T.
, 2014
, “High-Performance Tracking of Piezoelectric Positioning Stage Using Current-Cycle Iterative Learning Control With Gain Scheduling
,” IEEE Trans. Ind. Electron.
, 61
(2
), pp. 1085
–1098
.10.1109/TIE.2013.225307199.
Jain
, S.
, and Swarup
, A.
, 2013
, “Identification and Iterative Learning Control of Piezoelectric Actuator Based Nanopositioning System
,” Proceedings of 2nd International Conference on Emerging Trends in Engineering and Management
, Rohtak, India
, July 20–21, Vol. 3, pp. 88–93.100.
Ryoo
, J. R.
, Doh
, T. Y.
, and Chung
, M. J.
, 2004
, “Robust Disturbance Observer for the Track-Following Control System of an Optical Disk Drive
,” Control Eng. Pract.
, 12
(5
), pp. 577
–585
.10.1016/S0967-0661(03)00140-0101.
Choi
, Y. J.
, Yang
, K. J.
, Chung
, W. K.
, Kim
, H. R.
, and Suh
, H.
, 2003
, “On the Robustness and Performance of Disturbance Observers for Second-Order Systems
,” IEEE Trans. Autom. Control
, 48
(2
), pp. 315
–320
.10.1109/TAC.2002.808491102.
Yi
, J. G.
, Chang
, S.
, and Shen
, Y. T.
, 2009
, “Disturbance Observer Based Hysteresis Compensation for Piezoelectric Actuators
,” IEEE/ASME Trans. Mechatron.
, 14
(4
), pp. 456
–464
.10.1109/TMECH.2009.2023986103.
Tesfaye
, A.
, Lee
, H. S.
, and Tomizuka
, M.
, 2000
, “A Sensitivity Optimization Approach to Design of a Disturbance Observer in Digital Motion Control Systems
,” IEEE/ASME Trans. Mechatron.
, 5
(1
), pp. 32
–38
.10.1109/3516.828587104.
Cao
, Y.
, and Chen
, X. B.
, 2014
, “Two Modified Discrete PID-Based Sliding Mode Control for Piezoelectric Actuators
,” Int. J. Control
, 87
(1
), pp. 9
–20
.10.1080/00207179.2013.819125105.
Liawa
, H. C.
, Shirinzadeh
, B.
, and Smith
, J.
, 2007
, “Enhanced Sliding Mode Motion Tracking Control of Piezoelectric Actuators
,” Sens. Actuators, A
, 138
(1
), pp. 194
–202
.10.1016/j.sna.2007.04.062106.
Woronko
, A.
, Huang
, J.
, and Altintas
, Y.
, 2003
, “Piezoelectric Tool Actuator for Precision Machining on Conventional CNC Turning Centers
,” Precis. Eng.
, 27
(4
), pp. 335
–345
.10.1016/S0141-6359(03)00040-0107.
Hwang
, C. L.
, and Jan
, C.
, 2005
, “State Estimator Based Feedback Control for a Class of Piezoelectric Systems With Hysteresis Nonlinearity
,” IEEE Trans. Syst., Man, Cybern
, 35
(5
), pp. 654
–664
.10.1109/TSMCA.2005.851120108.
Khan
, S.
, Elitas
, M.
, Kunt
, E. D.
, and Sabanovic
, A.
, 2006
, “Discrete Sliding Model Control of Piezo Actuator in Nano-Scale Range
,” IEEE International Conference on Industrial Technology
, Mumbai, India
, Dec. 15–17, pp. 1454–1459.109.
Xue
, X.
, and Tang
, J.
, 2006
, “Robust and High Precision Control Using Piezoelectric Actuator Circuit and Integral Continuous Sliding Mode Control Design
,” J. Sound Vib.
, 293
(1–2
), pp. 335
–359
.10.1016/j.jsv.2005.10.009110.
Abidi
, K.
, Sabanovic
, A.
, and Yesilyurt
, S.
, 2004
, “Sliding Mode Control Based Disturbance Compensation and External Force Estimation for a piezoelectric actuator
,” 8th IEEE International Workshop on Advanced Motion Control
, Kawasaki, Janpan
, March 25–28, pp. 529–534.111.
Yu
, S. H.
, Shirinzadeh
, B.
, Alici
, G.
, and Smith
, J.
, 2005
, “Sliding Mode Control of a Piezoelectric Actuator With Neural Network Compensation Rate-Dependent Hysteresis
,” Proceedings of IEEE International Conference on Robotics and Automation
, Barcelona, Spain
, April 18–22, pp. 3641–3645.112.
Wang
, S.
, Habibi
, S.
, and Burton
, R.
, 2008
, “Sliding Mode Control for an Electrohydraulic Actuator System With Discontinuous Nonlinear Friction
,” Proc. Inst. Mech. Eng., Part I
, 222
(8
), pp. 799
–815
.10.1243/09596518JSCE637113.
Edwards
, C.
, and Spurgeon
, S. K.
, 1998
, Sliding Mode Control-Theory and Applications
, Taylor & Francis, Ltd
., London, UK.114.
Wang
, S.
, Burton
, R.
, and Habibi
, S.
, 2009
, “Filtering Controller in Sliding Mode: From the Estimation to Control
,” Proc. Inst. Mech. Eng., Part I
, 223
(6
), pp. 833
–846
.10.1243/09596518JSCE738115.
Young
, K. D.
, Utkin
, V. I.
, and Özgüner
, Ü.
, 1999
, “A Control Engineer's Guide to Sliding Mode Control
,” IEEE Trans. Control Syst. Technol.
, 7
(3
), pp. 328
–342
.10.1109/87.761053116.
Levant
, A.
, 2005
, “Homogeneity Approach to High-Order Sliding Mode Design
,” Automatica
, 41
(5
), pp. 823
–830
.10.1016/j.automatica.2004.11.029117.
Rhif
, A.
, 2012
, “A High Order Sliding Mode Control With PID Sliding Surface: Simulation on a Torpedo
,” Int J. Inf. Tech., Control Autom.
, 2
(1
), pp. 1–13.118.
Fridman
, L.
, and Levant
, A.
, 2002
, “Higher Order Sliding Modes
,” Sliding Mode Control in Engineering
, W.
Perruquetti
, and J. P.
Barbot
, eds., Marcel Dekker
, New York
, pp. 53
–101
.119.
Peng
, J. Y.
, and Chen
, X. B.
, 2014
, “Integrated PID-Based Sliding Mode State Estimation and Control for Piezoelectric Actuators
,” IEEE/ASME Trans. Mechatron.
, 19
(1
), pp. 88
–99
.10.1109/TMECH.2012.2222428120.
Rafee
, N.
, Chen
, T. W.
, and Malik
, O. P.
, 1997
, “A Technique for Optimal Digital Redesign of Analog Controllers
,” IEEE Trans. Control Syst. Technol.
, 5
(1
), pp. 89
–99
.10.1109/87.553667121.
Gao
, W. B.
, Wang
, Y. F.
, and Homaifa
, A.
, 1995
, “Discrete-Time Variable Structure Control Systems
,” IEEE Trans. Ind. Electron.
, 42
(2
), pp. 117
–122
.10.1109/41.370376122.
Monsees
, G.
, 2002
, “Discrete-Time Sliding Mode Control
,” Ph.D. thesis, Delft University of Technology, Delft, Netherlands, p. 182
.123.
Bartoszewicz
, A.
, 1998
, “Discrete-Time Quasi-Sliding Mode Control Strategies
,” IEEE Trans. Ind. Electron.
, 45
(4
), pp. 633
–637
.10.1109/41.704892124.
Daafouz
, J.
, Riedinger
, P.
, and Iung
, C.
, 2002
, “Stability Analysis and Control Synthesis for Switched System: A Switched Lyapunov Function Approach
,” IEEE Trans. Autom. Control
, 47
(11
), pp. 1883
–1887
.10.1109/TAC.2002.804474125.
Fleming
, A. J.
, Aphale
, S. S.
, and Moheimani
, S. O. R.
, 2010
, “A New Method for Robust Damping and Tracking Control of Scanning Probe Microscope Positioning Stages
,” IEEE Trans. Nanotechnol.
, 9
(4
), pp. 438
–448
.10.1109/TNANO.2009.2032418126.
Wadikhaye
, S. P.
, Yong
, Y. K.
, Bhikkaji
, B.
, and Moheimani
, S. O. R.
, 2014
, “Control of a Piezoelectrically Actuated High-Speed Serial-Kinematic AFM nanopositioner
,” Smart Mater. Struct.
, 23
(2
), p. 025030
.10.1088/0964-1726/23/2/025030127.
Shen
, J. C.
, Jywe
, W. Y.
, and Wu
, C. H.
, 2014
, “Control of an Equipment for Fabricating Periodic Nanostructure
,” Precis. Eng.
, 38
(2
), pp. 391
–397
.10.1016/j.precisioneng.2013.12.005128.
Liang
, W. Y.
, Huang
, S. N.
, Chen
, S. L.
, and Tan
, K. K.
, 2013
, “Precision Motion Control of a Linear Piezoelectric Ultrasonic Motor Stage
,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, Wollongong, Australia
, Jul 9–12, pp.164–169.10.1109/AIM.2013.6584086129.
Fleming
, A. J.
, 2010
, “Nanopositioning System With Force Feedback for High-Performance Tracking and Vibration Control
,” IEEE/ASME Trans. Mechatron.
, 15
(3
), pp. 433
–447
.10.1109/TMECH.2009.2028422130.
Syahputra
, H. P.
, Ko
, T. J.
, and Chung
, B. M.
, 2014
, “Development of 2-Axis Hybrid Positioning System for Precision Contouring on Micro–Milling Operation
,” J. Mech. Sci. Technol.
, 28
(2
), pp. 691
–697
.10.1007/s12206-013-1132-5131.
Xie
, Y. Q.
, Tan
, Y. H.
, and Dong
, R. L.
, 2013
, “Nonlinear Modeling and Decoupling Control of XY Micropositioning Stages With Piezoelectric Actuators
,” IEEE/ASME Trans. Mechatron.
, 18
(3
), pp. 821
–832
.10.1109/TMECH.2012.2187794132.
Nise
, N. S.
, 2011
, Control System Engineering
, 6th ed., Wiley
, Hoboken, NJ.133.
Bentayeb
, A.
, Maamri
, N.
, and Trigeassou
, J. C.
, 2006
, “Design of PID Controller for Delayed MIMO Plants Using Moments Based Approach
,” J. Electr. Eng., 57
(6
), pp. 318
–328
. Available at: http://iris.elf.stuba.sk/JEEEC/data/pdf/6_106-02.pdf134.
Morgan
, B. S.
, 1964
, “The Synthesis of Linear Multivariable Systems by State Variable Feedback
,” IEEE Trans. Autom. Control
, 9
(4
), pp. 404
–411
.10.1109/TAC.1964.1105733135.
Wang
, W. H.
, Hou
, Z. S.
, and Jin
, S. T.
, 2009
, “Model-Free Indirect Adaptive Decoupling Control for Nonlinear Discrete Time MIMO Systems
,” Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference
, Shanghai, China
, Dec. 15–18, pp. 7663–7668.136.
Amin
, M. H.
, and Moness
, M.
, 1988
, “Design of Precompensators via Infinite-Zero Structure for Dynamic Decoupling of Linear Invertible Systems
,” Int. J. Control
, 47
(4
), pp. 993
–1009
.10.1080/00207178808906072137.
Moness
, M.
, and Amin
, M. H.
, 1988
, “Minimal-Order Precompensators for Decoupling Linear Multivariable Systems S (A, B, C, E)
,” Int. J. Control
, 47
(6
), pp. 1925
–1936
.10.1080/00207178808906147138.
Lin
, C. A.
, and Wu
, C. M.
, 1999
, “Block Decoupling Control of Linear Multivariable Systems
,” Asian J. Control
, 1
(3
), pp. 146
–152
.10.1111/j.1934-6093.1999.tb00015.x139.
Astrom
, K. J.
, Johansson
, K. H.
, and Wang
, Q. G.
, 2001
, “Design of Decoupled PID Controllers for MIMO Systems
,” Proceedings of the American Control Conference
, Arlington, VA
, pp. 2015
–2020
.140.
Wang
, Z. H.
, Tan
, J.
, Zou
, Q. Z.
, and Jiang
, W.
, 2013
, “Control-Based High-Speed Direct Mask Fabrication for Lighography via Mechanical Plowing
,” American Control Conference
, Washington, DC
, June 17–19, pp. 5183–5188.141.
Cao
, Y.
, and Chen
, X. B.
, 2013
, “An Output Tracking Based Discrete PID-Sliding Mode Control on MIMO Systems
,” IEEE/ASME Trans. Mechatron.
, 19
(4
), pp. 1183
–1194
.10.1109/TMECH.2013.2275743142.
Cao
, Y.
, and Chen
, X. B.
, 2013
, “Disturbance Observer Based Sliding Mode Control for a Three-DOF Nanopositioning Stage
,” IEEE/ASME Trans. Mechatron.
, 19
(3
), pp. 924
–931
.10.1109/TMECH.2013.2262802143.
Härkegård
, O.
, 2004
, “Resolving Actuator Redundancy-Control Allocation vs. Linear Quadratic Control
,” Report No. LiTH-ISY-R-2593, ECC’ 03, Cambridge, UK.144.
Härkegård
, O.
, and Glad
, S. T.
, 2005
, “Resolving Actuator Redundancy-Optimal Control vs. Control Allocation
,” Automatica
, 41
(1
), pp. 137
–144
.10.1016/j.automatica.2004.09.007145.
Brinkerhoff
, R.
, and Devasia
, S.
, 1999
, “Output Tracking for Actuator Deficient/Redundant Systems: Multiple Piezoactuator Example
,” J. Guid.
, 23
(2
), pp. 370
–373
.10.2514/2.4535146.
Liberzon
, D.
, and Morse
, A. S.
, 1999
, “Basic Problems in Stability and Design of Switched Systems
,” IEEE Control Syst.
, 19
(5
), pp. 59
–70
.10.1109/37.793443147.
Branicky
, M. S.
, 1994
, “Stability of Switched and Hybrid Systems
,” Proceedings of 33rd Conference on Decision and Control
, Lake Buena Vista, FL
, Dec. 14–16, pp. 3498–3503.148.
Ishii
, H.
, and Francis
, B. A.
, 2001
, “Stabilizing a Linear System by Switching Control With Dwell Time
,” Proceedings of American Control Conference
, Arlington, VA
, June 25–27, Vol. 3, pp. 1876–1881.149.
Lin
, H.
, and Antsaklis
, P. J.
, 2009
, “Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
,” IEEE Trans. Autom. Control
, 54
(2
), pp. 308
–322
.10.1109/TAC.2008.2012009150.
Shang
, W. W.
, Cong
, S.
, and Jiang
, S. L.
, 2009
, “Coordination Control of Parallel Manipulators With Actuation Redundancy
,” Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference
, Shanghai, China
, Dec. 15–18, pp. 8186–8191.151.
Garrido
, R.
, and Torres-Cruz
, D.
, 2004
, “On PD Control of Parallel Robots With Redundant Actuation
,” 1st International Conference on Electrical and Electronics Engineering
, June 24–27, pp. 356–360.152.
Braun
, D. J.
, Petit
, F.
, Huber
, F.
, Haddadin
, S.
, Smagt
, P.
, Schäffer
, A. A.
, and Vijayakumar
, S.
, 2013
, “Robots Driven by Compliant Actuators: Optimal Control Under Actuation Constraints
,” IEEE Trans. Robot.
, 29
(5
), pp. 1085
–1101
.10.1109/TRO.2013.2271099153.
Zaccarian
, L.
, 2007
, “On Dynamic Control Allocation for Input-Redundant Control Systems
,” Proceedings of 46th IEEE Conference on Decision and Control
, New Orleans, LA
, Dec. 12–14, pp. 1192–1197.154.
Fossen
, T. I.
, 2006
, “A Survey of Control Allocation Methods for Ships and Underwater Vehicles
,” 14th Mediterranean Conference on Control and Automation
, Ancona, Italy
, June 28–30, pp. 1–6.155.
Johansen
, T. A.
, and Fossen
, T. I.
, 2013
, “Control Allocation—A Survey
,” Automatica
, 49
(5
), pp. 1087
–1103
.10.1016/j.automatica.2013.01.035156.
Ruben
, S. D.
, 2010
, “Modeling, Control, and Real-Time Optimization for a Nano-Precision System
,” Ph.D. thesis, University of California, Los Angeles, CA.157.
Zheng
, J. C.
, and Fu
, M. Y.
, 2012
, “A Switching Controller for Piezoelectric Microactuators in Dual-Stage Actuator Hard Disk Drives
,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, Kaohsiung, Taiwan
, July 8–11, pp. 946–951.158.
Zheng
, J. C.
, and Fu
, M. Y.
, 2012
, “A Unified Dual-Stage Actuator Control Scheme for Track Seeking and Following in Hard Disk Drives
,” IET Control Theory Appl.
, 6
(10
), pp. 1468
–1477
.10.1049/iet-cta.2010.0117Copyright © 2015 by ASME
You do not currently have access to this content.
