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Research Papers

Spatially Periodic Disturbance Rejection With Spatially Sampled Robust Repetitive Control

[+] Author and Article Information
Cheng-Lun Chen

Department of Electrical Engineering, National Chung Hsing University, Taichung, Taiwan 40227, Republic of China

George T.-C. Chiu

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Dyn. Sys., Meas., Control 130(2), 021002 (Feb 29, 2008) (11 pages) doi:10.1115/1.2837306 History: Received July 18, 2005; Revised July 18, 2007; Published February 29, 2008

Repetitive controllers have been shown to be effective for tracking periodic reference commands or for rejecting periodic disturbances. Typical repetitive controllers are synthesized in temporal domain where the periods of the reference or disturbance signals are assumed to be known and stationary. For periodic references and disturbances with varying periods, researchers usually resort to adaptive and robust control approaches. For rotational motion systems where the disturbances or reference signals are spatially periodic (i.e., periodic with respect to angular displacement), the temporal period of the disturbance and reference signals will be inversely proportional to the rotational speed and vary accordingly. Motivating by reducing halftone banding for laser printers, we propose a design framework for synthesizing spatially sampled repetitive controller by reformulating a linear time-invariant system subject to spatially periodic disturbances using angular displacement as the independent variable. The resulting nonlinear system can be represented as a quasi-linear parameter-varying (quasi-LPV) system with the angular velocity as one of the varying state-dependent parameters. An LPV self-gain–scheduling controller that includes a spatially sampled repetitive control can be designed to take into consideration bounded model uncertainty and input nonlinearity, such as actuator saturation. Using the signal from an optical encoder pulse as a triggering interrupt, experimental results verified the effectiveness of the proposed approach in rejecting spatially periodic disturbances that cannot be compensated with fixed period temporal repetitive controllers.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

LPV gain-scheduling control system with repetitive controller

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Figure 2

LPV gain-scheduling control system with repetitive controller, anti-windup scheme, and sensor/actuator dynamics

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Figure 3

Experimental setup for the closed-loop control of a typical 600dpi monochrome laser printer

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Figure 4

Output multiplicative uncertainties for the experimental platform approximated using a second- or third-order transfer function. The solid line is the magnitude of a first-order filter that upper bounds the uncertainties.

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Figure 5

Parameter variation set and the selected (convex) polytope, which bounds the set

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Figure 6

The parameter-dependent performance weighting W1 and uncertainty weighting W2

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Figure 7

NP, RS, and RP curves for the four vertex closed-loop systems

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Figure 8

Histories of drum angular velocity, motor input voltage, and the three varying parameters with respect to drum angular position

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Figure 9

Frequency spectra of the velocity signals for the open-loop and closed-loop systems. Spectra for the closed-loop system are divided into four, with each corresponding to signals measured from each ten-revolution interval (psd stands for power spectrum density).

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Figure 10

Frequency spectra of the velocity signals for the closed-loop system using fixed period temporal repetitive control

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