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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
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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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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

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+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

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+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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