The present paper is concerned with the design of dynamic anti-integrator-windup controllers for critically stable linear systems with a single pole at the origin. The constant gain term in the conventional anti-windup controller is extended to have dynamics represented by a transfer function. The proposed dynamic anti-windup compensator is similar to the one based on co-prime factorization of the plant. The overall controller includes an internal model for constant signals and achieves regulation for constant disturbance and reference inputs as long as the asymptotic control input stays within the saturation limits. The effectiveness of the proposed method is demonstrated on a one-link flexible arm through simulations and experiments.
1.
Kothare
, M. V.
, Campo
, P. J.
, Morari
, M.
, and Nett
, C. N.
, 1994, “A Unified Framework for the Study of Anti-Windup Design
,” Automatica
0005-1098, 30
, pp. 1869
–1883
.2.
Khalil
, H.
, 1996, Nonlinear Systems
, Prentice-Hall
, Englewood Cliffs, NJ
pp. 261
–288
.3.
Megretski
, A.
, 1996, “L2 BIBO Output Feedback Stabilization With Saturated Control
,” Proc. of 13th IFAC World Congress
, Pergamon
, New York
, D
, pp. 435
–440
.4.
Teel
, A. R.
, and Kapoor
, N.
, 1997, “The L2 Anti-Windup Problem: Its Definition and Solution
,” Proc. of European Control Conference
, Brussels
, Belgian Interuniversity Attraction Pole (CD-ROM)
, Brussels, Belgium
.5.
Teel
, A. R.
, 1999, “Anti-Windup for Exponentially Unstable Linear Systems
,” Int. J. Robust Nonlinear Control
1049-8923, 9
, pp. 701
–716
.6.
Zaccarian
, L.
, Teel
, A. R.
, and Marcinkowski
, J. J.
, 2000, “Anti-Windup for an Active Vibration Isolation Device: Theory and Experiments
,” Proc. of American Control Conference
, Chicago
, IEEE
, New York
, pp. 3585
–3589
.7.
Zaccarian
, L.
, and Teel
, A. R.
, 2001, “Anti-Windup, Bumpless Transfer and Reliable Designs: A Model Based Approach
,” Proc. of American Control Conference
, Arlington, VA
, IEEE
, New York
, pp. 4902
–4907
.8.
Marcopoli
, V. R.
, and Phillips
, S. M
, 1996, “Analysis and Synthesis Tools for a Class of Actuator-Limited Multivariable Control Systems: A Linear Matrix Inequality Approach
,” Int. J. Robust Nonlinear Control
1049-8923, 6
, pp. 1045
–1063
.9.
Kothare
, M. V.
, and Morari
, M.
, 1997, “Multivariable Anti-Windup Controller Synthesis Using Multi-Objective Optimization
,” Proc. of American Control Conference
, Albuquerque, New Mexico
, IEEE
, New York
, pp. 3093
–3097
.10.
Kothare
, M. V.
, and Morari
, M.
, 1999, “Multiplier Theory for Stability Analysis of Anti-Windup Control Systems
,” Automatica
0005-1098, 35
, pp. 917
–928
.11.
Mulder
, E. F.
, Kothare
, M. V.
, and Morari
, M.
, 2001, “Multivariable Anti-Windup Controller Synthesis Using Linear Matrix Inequalities
,” Automatica
0005-1098, 37
, pp. 1407
–1416
.12.
Grimm
, G.
, Postlethwaite
, I.
, Teel
, A. R.
, Turner
, M. C.
, and Zaccarian
, L.
, 2001, “Linear Matrix Inequalities for Full and Reduced Order Anti-Windup Synthesis
,” Proc. of American Control Conference
, Arlington, VA
, IEEE
, New York
, pp. 4134
–4139
.13.
Grimm
, G.
, Hatfield
, J.
, Postlethwaite
, I.
, Teel
, A. R.
, Turner
, M. C.
, and Zaccarian
, L.
, 2003, “Antiwindup for Stable Linear Systems With Input Saturation: An LMI-Based Synthesis
,” IEEE Trans. Autom. Control
0018-9286, 48
(9
), pp. 1509
–1525
.14.
Liu
, W.
, Chitour
, Y.
, and Sontag
, E.
, 1993, “Remarks on Finite Gain Stabilizability of Linear Systems Subject to Input Saturation
,” Proc. of 32nd Conference on Decision and Control
, San Antonio
, IEEE
, New York
, pp. 1808
–1813
.15.
Miyamoto
, S.
, and Vinnicombe
, G.
, 1996, “Robust Control of Plants With Saturation Nonlinearity Based on Co-prime Factor Representations
,” Proc. of 35th Conference on Decision and Control
, Kobe, Japan, IEEE
, New York
, pp. 2838
–2840
.16.
Weston
, P. F.
, and Postlethwaite
, I.
, 2000, “Linear Conditioning for Systems Containing Saturating Actuators
,” Automatica
0005-1098, 36
, pp. 1347
–1354
.17.
Sontag
, E. D.
, and Sussmann
, H. J.
, 1990, “Nonlinear Output Feedback Design for Linear Systems With Saturating Controls
,” Proc. on 29th Conference on Decision and Control
, Honolulu
, IEEE
, New York
, pp. 3414
–3416
.18.
Kapoor
, N.
, Teel
, A. R.
, and Daoutidis
, P.
, 1996, “On Anti-Integrator-Windup and Global Asymptotic Stability
,” Proc. of 13th IFAC World Congress
, Pergamon
, New York
, Vol. D
, pp. 67
–72
.19.
Kapoor
, N.
, Teel
, A. R.
, and Daoutidis
, P.
, 1998, “An Anti-Windup Design for Linear Systems with Input Saturation
,” Automatica
0005-1098, 34
(5
), 559
–574
.20.
Niu
, W.
, and Tomizuka
, M.
, 1998, “An Anti-Windup Design for the Asymptotic Tracking of Linear System Subjected to Actuator Saturation
,” Proc. of American Control Conference
, Philadelphia
, IEEE
, New York
, pp. 1458
–1462
.21.
Niu
, W.
, and Tomizuka
, M.
, 2000, “An Anti-Windup Design for Linear System With Asymptotic Tracking Subjected to Actuator Saturation
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 122
, pp. 369
–374
.22.
Kanamori
, M.
, and Tomizuka
, M.
, 2001, “Asymptotic Tracking for Linear Systems With Actuator Saturation by Output Feedback Control
,” Proc. of American Control Conference
, Arlington, Virginia
, IEEE
, New York
, pp. 4920
–4925
.23.
Liu
, W.
, Chitour
, Y.
, and Sontag
, E.
, 1996, “On Finite Gain Stabilizability of Linear Systems Subject to Input Saturation
,” SIAM J. Control Optim.
0363-0129, 34
(4
), pp. 1190
–1219
.24.
Hou
, P.
, Saberi
, A.
, Lin
, Z.
, and Sannuti
, P.
, 1998, “Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems With Saturating Actuators
,” Automatica
0005-1098, 34
(12
), pp. 1547
–1557
.25.
Shi
, G.
, Saberi
, A.
, and Stoorvogel
, A. A.
, 2003, “On the Lp (lp) Stabilization of Open-Loop Neutrally Stable Linear Plants With Input Subject to Amplitude Saturation
,” Int. J. Robust Nonlinear Control
1049-8923, 13
, pp. 735
–754
.26.
Desoer
, C. A.
, and Wang
, Y. T.
, 1980, “Linear Time-Invariant Robust Servomechanism Problem: A Self-Contained Exposition
,” Control. Dyn. Syst.
0090-5267, 16
, pp. 81
–129
.27.
Nemirovski
, A.
, and Gahinet
, P.
, 1994, “The Projective Method for Solving Linear Matrix Inequalities
,” Proc. of American Control Conference
, Baltimore
, IEEE
, New York
, pp. 840
–844
.28.
Gahinet
, P.
, Nemirovski
, A.
, Laub
, A. J.
, and Chilali
, M.
, 1996, LMI Control Toolbox For Use With MATLAB
, The Math Works Inc., Natick, Mass.
, pp. 8
-40–8-41
, pp. 9
-31–9-34
.29.
Zhou
, K.
, Doyle
, J. C.
, and Glover
, K.
, 1996, “Robust and Optimal Control
,” Prentice-Hall
, Englewood Cliffs, NJ
, pp. 126
–130
, pp. 323
–326
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