This paper proposes an adaptive control scheme that minimizes the least-mean-square (LMS) value of the plant output while meeting the constraints of canceling deterministic exogenous signals generated by a priori dynamics. This scheme may be applied to a broad range of applications in which the exogenous input signals to the plant contain both deterministic and stochastic components. The adaptive control includes both feedback and previewed feedforward actions. In both actions, the deterministic signal model is included as a constraint of the dynamics from the external input to the plant output by determining solutions for a Bezout identity. The proposed scheme is applied to a fast-acting piezoelectric actuator (PZT) to generate precise dynamic motion profiles. This paper presents the experimental results to demonstrate the effectiveness of the proposed adaptive control scheme.
Issue Section:
Research Papers
References
1.
Tomizuka
, M.
, 1987
, “Zero Phase Error Tracking Algorithm for Digital Control
,” ASME J. Dyn. Syst., Meas., Control.
, 109
(1
), pp. 65
–68
.10.1115/1.31438222.
Tsao
, T. C.
, 1994
, “Optimal Feed-Forward Digital Tracking Controller Design
,” ASME J. Dyn. Syst., Meas., Control
, 116
(4
), pp. 583
–592
.10.1115/1.28992563.
Tsao
, T. C.
, and Tomizuka
, M.
, 1987
, “Adaptive Zero Phase Error Tracking Algorithm for Digital Control
,” ASME J. Dyn. Syst., Meas., Control
, 109
(2
), pp. 349
–354
.10.1115/1.31438664.
Bodson
, M.
, and Douglas
, S. C.
, 1997
, “Adaptive Algorithms for the Rejection of Sinusoidal Disturbances With Unknown Frequency
,” Automatica
, 33
(12
), pp. 2213
–2221
.10.1016/S0005-1098(97)00149-05.
Widrow
, B.
, and Walach
, E.
, 1995
, Adaptive Inverse Control
, Prentice-Hall
, Upper Saddle River, NJ
.6.
Pérez Arancibia
, N. O.
, Chen
, N.
, Gibson
, S.
, and Tsao
, T. C.
, 2005
, “Adaptive Control of a MEMS Steering Mirror for Supression of Laser Beam Jitter
,” Proceedings of the American Control Conference
, pp. 3586
–3591
.7.
Orzechowski
, P. K.
, Chen
, N.
, Gibson
, S.
, and Tsao
, T. C.
, 2006
, “Adaptive Control of Jitter in a Laser Beam Pointing System
,” Proceedings of the American Control Conference
, pp. 2700
–2705
.8.
Pérez Arancibia
, N. O.
, Gibson
, S.
, and Tsao
, T. C.
, 2007
, “Adaptive Tuning and Control of a Hard Disk Drive
,” Proceedings of the American Control Conference
, pp. 1526
–1531
.9.
Tomizuka
, M.
, Tsao
, T. C.
, and Chew
, K. K.
, 1989
, “Analysis and Synthesis of Discrete-Time Repetitive Controllers
,” ASME J. Dyn. Syst., Meas., Control
, 111
(3
), pp. 353
–358
.10.1115/1.315306010.
Li
, J.
, and Tsao
, T. C.
, 2001
, “Robust Performance Repetitive Control Systems
,” ASME J. Dyn. Syst., Meas., Control
, 123
(3
), pp. 330
–337
.10.1115/1.138701511.
Sun
, Z.
, and Tsao
, T. C.
, 2000
, “Adaptive Control With Asymptotic Tracking Performance and Its Application to an Electro-Hydraulic Servo System
,” ASME J. Dyn. Syst., Meas., Control
, 122
(1
), pp. 188
–195
.10.1115/1.48244112.
Tsao
, T. C.
, and Tomizuka
, M.
, 1994
, “Robust Adaptive and Repetitive Digital Tracking Control and Application to a Hydraulic Servo for Noncircular Machining
,” ASME J. Dyn. Syst., Meas., Control
, 116
(1
), pp. 24
–32
.10.1115/1.290067613.
Li
, J.
, and Tsao
, T. C.
, 1999
, “Rejection of Repeatable and Non-Repeatable Disturbances for Disk Drive Actuators
,” Proceedings of the American Control Conference
, pp. 3615
–3619
.14.
Krishnamoorthy
, K.
, and Tsao
, T. C.
, 2005
, “Robust Adaptive-Q With Two Period Repetitive Control for Disk Drive Track Following
,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, pp. 13
–18
.15.
Pérez Arancibia
, N. O.
, Lin
, C. Y.
, Gibson
, S.
, and Tsao
, T. C.
, 2007
, “Adaptive and Repetitive Control for Rejecting Repeatable and Non-Repeatable Runout in Rotating Devices
,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition
.16.
Tay
, T. T.
, Mareels
, I.
, and Moore
, J. B.
, 1998
, High Performance Control
, Birkhäuser
, Boston, MA
.17.
Haykin
, S.
, and Widrow
, B.
, 2003
, Least-Mean-Square Adaptive Filters
, John Wiley & Sons
, New York
.18.
Umeno
, T.
, and Hori
, Y.
, 1991
, “Robust Speed Control of DC Servomotors Using Modern Two Degrees-of-Freedom Controller Design
,” IEEE Trans. Ind. Electron.
, 38
(5
), pp. 363
–368
.10.1109/41.9755619.
Lee
, H. S.
, and Tomizuka
, M.
, 1996
, “Robust Motion Controller Design for High-Accuracy Positioning Systems
,” IEEE Trans. Ind. Electron.
, 43
(1
), pp. 48
–55
.10.1109/41.48141320.
Ru
, C.
, Chen
, L.
, Shao
, B.
, Rong
, W.
, and Sun
, L.
, 2009
, “A Hysteresis Compensation Method of Piezoelectric Actuator: Model, Identification and Control
,” Control Eng. Pract.
, 17
(9
), pp. 1107
–1114
.10.1016/j.conengprac.2009.04.01321.
Gu
, G.
, and Zhu
, L.
, 2010
, “High-Speed Tracking Control of Piezoelectric Actuators Using an Ellipse-Based Hysteresis Model
,” Rev. Sci. Instrum.
, 81
(8
), p. 085104
.10.1063/1.347011722.
Xu
, Q.
, and Li
, Y.
, 2010
, “Dahl Model-Based Hysteresis Compensation and Precise Positioning Control of an XY Parallel Micromanipulator With Piezoelectric Actuation
,” ASME J. Dyn. Syst., Meas., Control
, 132
(4
), p. 041011
.10.1115/1.400171223.
Aphale
, S. S.
, Devasia
, S.
, and Moheimani
, S. O. R.
, 2008
, “High-Bandwidth Control of a Piezoelectric Nanopositioning Stage in the Presence of Plant Uncertainties
,” Nanotechnology
, 19
(12
), p. 125503
.10.1088/0957-4484/19/12/12550324.
Wu
, Y.
, and Zou
, Q.
, 2009
, “Robust-Inversion-Based 2-DOF Control Design for Output Tracking: Piezoelectric Actuator Example
,” IEEE Trans. Control Syst. Technol.
, 17
(5
), pp. 1069
–1082
.10.1109/TCST.2008.200511125.
Fleming
, A. J.
, and Leang
, K. K.
, 2010
, “Integrated Strain and Force Feedback for High Performance Control of Piezoelectric Actuators
,” Sens. Actuators, A
, 161
(1–2
), pp. 256
–265
.10.1016/j.sna.2010.04.00826.
Krishnamoorthy
, K.
, Lin
, C. Y.
, and Tsao
, T. C.
, 2004
, “Design and Control of a Dual Stage Fast Tool Servo for Precision Machining
,” Proceedings of the IEEE Conference on Control Appliciations
, pp. 742
–747
.27.
Skogestad
, S.
, and Postlethwaite
, I.
, 1996
, Multivariable Feedback Control—Analysis and Design
, John Wiley & Sons
, New York
.28.
Overschee
, P. V.
, and Moor
, B. D.
, 1994
, “N4SID: Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems
,” Automatica
, 30
(1
), pp. 75
–93
.10.1016/0005-1098(94)90230-529.
Viberg
, M.
, 1995
, “Subspace-Based Methods for the Identification of Linear Time-Invariant Systems
,” Automatica
, 31
(12
), pp. 1835
–1851
.10.1016/0005-1098(95)00107-5Copyright © 2013 by ASME
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