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Journal of Dynamic Systems, Measurement, and Control | Volume 131 | Issue 4 | Technical Brief
Technical Briefs

Repetitive Control System Under Actuator Saturation and Windup Prevention

[+] Author and Article Information
D. Sbarbaro

Department of Electrical Engineering, Universidad de Concepción, Concepción 4070043, Chile

M. Tomizuka

Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740

B. León de la Barra

School of Engineering, University of Tasmania, Hobart 7001, Australia

J. Dyn. Sys., Meas., Control 131(4), 044505 (May 21, 2009) (8 pages) doi:10.1115/1.3117207 History: Received May 10, 2008; Revised January 26, 2009; Published May 21, 2009
Article
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Citing Articles

This work provides an analysis of the steady state response of a prototype repetitive controller applied to a class of nonlinear systems, i.e., systems with actuator saturation. First, it is shown that the steady state solution of the closed loop nonlinear system can be obtained by an iterative Picard process, which establishes the periodic nature of the steady state solution. Second, the conditions for obtaining bounded steady state responses are analyzed for a saturating nonlinearity commonly found in mechatronic applications. Valuable insight is provided into the effects of input signals and saturating actuators on the closed loop performance of a prototype repetitive controller. In order to improve the transient closed loop response, a simple antiwindup strategy tailored to repetitive controllers is proposed.
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Copyright © 2009 by American Society of Mechanical Engineers
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References

1
Chen, Y. Q., Moore, K., Yu, J., and Zhang, T., 2006, “Iterative Learning Control and Repetitive Control in Hard Disk Drive Industry—A Tutorial,” Proceedings of the IEEE International Conference on Decision and Control , San Diego, CA, pp. 13–15.
2
Li, C., Zhang, D., and Zhuang, X., 2004, “A Survey of Repetitive Control,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems , Sendai, Japan, Vol. 2 , pp. 1160–1166.
3
Escobar, G., Leyva-Ramos, J., Martinez, P. R., and Valdez, A. A., 2005, “A Repetitive-Based Controller for the Boost Converter to Compensate the Harmonic Distortion of the Output Voltage,” IEEE Trans. Control Syst. Technol., 13 (3), pp. 500–508.  [CrossRef]
4
Liang, J., Green, T. C., Weiss, G., and Zhong, Q. C., 2002, “Evaluation of Repetitive Control for Power Quality Improvement of Distributed Generation,” Proceedings of the IEEE Power Electronics Specialist Conference , pp. 1803–1808.
5
Ma, C. C. H., 1990, “Stability Robustness of Repetitive Control System With Zero Phase Compensation,” ASME J. Dyn. Syst., Meas., Control, 112 , pp. 320–324.  [CrossRef]
6
Vidal, P., 1968, "Systèmes échantillonnes non linéaires", Dunod, Paris.
7
Telang, N., and Hunt, L. R., 2001, “Frequency Domain Computations for Nonlinear Steady State Solutions,” IEEE Trans. Signal Process., 49 (8), pp. 1728–1733.  [CrossRef]
8
Galttfelder, A. H., and Schaufelberger, W., 2003, "Control Systems With Input and Output Constraints", Springer-Verlag, London.
9
Grimm, G., Teel, A. R., and Zaccarian, L., 2008, “The l2 Anti-Wind Up Problem for Discrete-Time Linear Systems: Definitions and Solutions,” Syst. Control Lett., 57 , pp. 356–364.  [CrossRef]
10
Gomes da Silva, J. M., and Tarbouriech, S., 2006, “Anti-Windup Design With Guaranteed Regions of Stability for Discrete-Linear Systems,” Syst. Control Lett., 55 , pp. 184–192.  [CrossRef]
11
Rönnbäck, S., Hillerström, G., and Sternby, J., 1993, “Periodic-Disturbance Rejection and Set-Point Tracking With Application to a Peristaltic Pump,” Proceedings of the European Control Conference , Groningen, The Netherlands, pp. 202–208.
12
Ryu, Y. S., and Longman, R. W., 1994, “Use of Anti-Reset Windup in Integral Control Based Learning and Repetitive Control,” Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics , Vol. 3 , pp. 2617–2622.
13
Francis, B. A., and Wonham, W. M., 1975, “The Internal Model Principle for Linear Multivariable Regulators,” Appl. Math. Optim., 2 , pp. 170–194.  [CrossRef]
14
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 (2), pp. 353–358.
15
Tomizuka, M., 1987, “Zero Phase Error Tracking Algorithm for Digital Control,” ASME J. Dyn. Syst., Meas., Control, 109 (1), pp. 65–68.
16
Meserve, W. E., and Torng, H. C., 1961, “Investigation of Periodic Modes of Sample-Data Control Systems Containing a Saturating Element,” ASME. J. Basic Eng., D83 (1), pp. 77–81.
17
Rönnbäck, S., 1993, “Linear Control of Systems With Actuator Constraints,” Ph.D. thesis, Luleå University of Technology, Sweden.
18
Chen, Ch. L., and Chiu, G. T., 2008, “Spatially Periodic Disturbance Rejection With Spatially Sampled Robust Repetitive Control,” ASME J. Dyn. Syst., Meas., Control, 130 (2), pp. 77–81.

Figures

Grahic Jump Location
+Repetitive controller with saturating actuator
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Repetitive controller with saturating actuator
Figure 1

Repetitive controller with saturating actuator

Grahic Jump Location
+Alternative drawing of Fig. 1
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Alternative drawing of Fig. 1
Figure 2

Alternative drawing of Fig. 1

Grahic Jump Location
+Effect of a saturating actuator on the closed loop response of a repetitive controller
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Effect of a saturating actuator on the closed loop response of a repetitive controller
Figure 3

Effect of a saturating actuator on the closed loop response of a repetitive controller

Grahic Jump Location
+Detuned internal model with antiwindup compensator
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Detuned internal model with antiwindup compensator
Figure 4

Detuned internal model with antiwindup compensator

Grahic Jump Location
+Block diagram manipulation of system in Fig. 4
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Block diagram manipulation of system in Fig. 4
Figure 5

Block diagram manipulation of system in Fig. 4

Grahic Jump Location
+The effect of the nonlinearity is represented by a fictitious disturbance δ(k)
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The effect of the nonlinearity is represented by a fictitious disturbance δ(k)
Figure 6

The effect of the nonlinearity is represented by a fictitious disturbance δ(k)

Grahic Jump Location
+Repetitive controller with antiwindup compensator
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Repetitive controller with antiwindup compensator
Figure 7

Repetitive controller with antiwindup compensator

Grahic Jump Location
+Repetitive controller with antiwindup compensator and F(z−1)=0
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Repetitive controller with antiwindup compensator and F(z−1)=0
Figure 8

Repetitive controller with antiwindup compensator and F(z−1)=0

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