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.
Issue Section:
Technical Brief
References
1.
Visioli
, A.
, 2006
, Practical PID Control
, Springer-Verlag
, London
.2.
Åström
, K.
, and Hägglund
, T.
, 1995
, PID Controllers: Theory, Design, and Tuning
, The Instrumentation, Systems, and Automation Society
, Research Triangle Park, NJ
.3.
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
.10.1016/0005-1098(94)90048-54.
Zaccarian
, L.
, and Teel
, A.
, 2011
, Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation
, Princeton University Press
, Princeton, NJ
.5.
Goodwin
, G.
, Graebe
, S.
, and Salgado
, M.
, 2001
, Control System Design
, Prentice Hall
, Englewood Cliffs, NJ
.6.
Golnaraghi
, F.
, and Kuo
, B.
, 2010
, Automatic Control Systems
, 9th ed., John Wiley & Sons
, Hoboken, NJ
.7.
Berstein
, D.
, and Michel
, A.
, 1995
, “A Chronological Bibliography on Saturating Actuators
,” Int. J. Robust Nonlinear Control
, 5
(5
), pp. 375
–380
.10.1002/rnc.45900505028.
Saberi
, A.
, and Stoorvogel
, A.
, 1999
, Control of Linear Systems with Regulation and Input Constraints
, Springer
, New York
.9.
Hu
, T.
, and Lin
, Z.
, 2001
, Control Systems with Actuator Saturation: Analysis and Design, Birkhäuser, Boston, MA.10.
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
.11.
Skorokhod
, A.
, 1989
, Asymptotic Methods in the Theory of Stochastic Differential Equations, American Mathematical Society, Providence, RI
.12.
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.13.
Shein
, L.
, 1998
, Electrophotography and Development Physics
, Springer-Verlag
, New York
.14.
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.Copyright © 2014 by ASME
You do not currently have access to this content.