Technical Brief

Noise Induced Loss of Tracking in Systems With Saturating Actuators and Antiwindup

[+] Author and Article Information
Yongsoon Eun

Information and Communication Engineering,
Daegu Gyeongbuk Institute of Science and Technology,
Daegu, South Korea
e-mail: yeun@dgist.ac.kr

Eric S. Hamby

Xerox Research Center Webster,
Webster, NY 14580
e-mail: eric.hamby@xerox.com

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 4, 2012; final manuscript received February 28, 2014; published online May 28, 2014. Assoc. Editor: Jiong Tang.

J. Dyn. Sys., Meas., Control 136(5), 054501 (May 28, 2014) (6 pages) Paper No: DS-12-1405; doi: 10.1115/1.4027163 History: Received December 04, 2012; Revised February 28, 2014

This technical note is devoted to a recently discovered phenomenon that takes place in feedback systems with saturating actuators, proportional-integral (PI) control, and antiwindup. Namely, in such systems, measurement noise induces steady-state error in step tracking, which is incompatible with the standard error coefficients. We quantify this phenomenon using stochastic averaging theory and show that the noise induced loss of tracking occurs only if antiwindup is present. An indicator that predicts this phenomenon is derived, and a rule-of-thumb, based on this indicator, is formulated. An illustration using a digital printing device is provided.

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Visioli, A., 2006, Practical PID Control, Springer-Verlag, London.
Åström, K., and Hägglund, T., 1995, PID Controllers: Theory, Design, and Tuning, The Instrumentation, Systems, and Automation Society, Research Triangle Park, NJ.
Kothare, M., Campo, P., Morari, M., and Nett, C., 1994, “A Unified Framework for the Study of Anti-Windup Designs,” Automatica, 30(12), pp. 1869–1883. [CrossRef]
Zaccarian, L., and Teel, A., 2011, Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation, Princeton University Press, Princeton, NJ.
Goodwin, G., Graebe, S., and Salgado, M., 2001, Control System Design, Prentice Hall, Englewood Cliffs, NJ.
Golnaraghi, F., and Kuo, B., 2010, Automatic Control Systems, 9th ed., John Wiley & Sons, Hoboken, NJ.
Berstein, D., and Michel, A., 1995, “A Chronological Bibliography on Saturating Actuators,” Int. J. Robust Nonlinear Control, 5(5), pp. 375–380. [CrossRef]
Saberi, A., and Stoorvogel, A., 1999, Control of Linear Systems with Regulation and Input Constraints, Springer, New York.
Hu, T., and Lin, Z., 2001, Control Systems with Actuator Saturation: Analysis and Design, Birkhäuser, Boston, MA.
Ching, S., Eun, Y., Gökçek, C., Kabamba, P., and Meerkov, S., 2011, Quasilinear Control: Performance Analysis and Design of Feedback Systems with Nonlinear Sensors and Actuators, Cambridge University Press, Cambridge, UK.
Skorokhod, A., 1989, Asymptotic Methods in the Theory of Stochastic Differential Equations, American Mathematical Society, Providence, RI.
Hamby, E., and Gross, E., 2004, “A Control-Oriented Survey of Xerographic Systems: Basic Concepts to New Frontiers,” Proceedings of the American Control Conference, Boston, MA.
Shein, L., 1998, Electrophotography and Development Physics, Springer-Verlag, New York.
Hamby, E., et al. , 2007, “System for Active Toner Concentration Target Adjustments and Method to Maintain Development Performance,” U.S. Patent No. 7,228,080.


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Fig. 1

Block diagram of motivating example

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Fig. 2

Step responses of the system in Fig. 1

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Fig. 3

SISO feedback system with PI-like control and antiwindup

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Fig. 4

Averaged version of system in Fig. 3

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Fig. 5

hαβ(u¯;Kpσn) and satαβ(u¯) with α = −1 and β = 2 for Kpσn = 0.5, 1, and 2

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Fig. 6

Responses of the original and averaged systems for the motivating example

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Fig. 7

Plot of hαβ(u¯;Kpσn) for α = −1, β = 2, and Kpσn = 0.2

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Fig. 8

TC control responses

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Fig. 9

TC control response with the revised controller and sensor (Kp = 0.61 and σn = 0.006)

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Fig. 10

Step responses of the system similar to Fig. 1 with antiwindup implementation of Ref. [5]



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