Research Papers

Cyclic Control: Problem Formulation and Stability Analysis

[+] Author and Article Information
Yongsoon Eun

Daegu Gyeongbuk Institute of Science and Technology,
Daegu, Republic of Korea
e-mail: yeun@dgist.ac.kr

Eric M. Gross

Xerox Research Center Webster,
Xerox Corporation,
Webster, NY 14850
e-mail: eric.gross@xerox.com

Pierre T. Kabamba

Department of Aerospace Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: kabamba@umich.edu

Semyon M. Meerkov

Department of Electrical Engineering and Computer Science,
University of Michigan,
Ann Arbor, MI 48109
e-mail: smm@umich.edu

Amor A. Menezes

California Institute for Quantitative Biosciences,
University of California,
Berkeley, Berkeley, CA 94720
e-mail: amenezes@berkeley.edu

Hamid R. Ossareh

Department of Electrical Engineering and Computer Science,
University of Michigan,
Ann Arbor, MI 48109
e-mail: hamido@umich.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL. Manuscript received April 22, 2012; final manuscript received March 19, 2013; published online June 27, 2013. Assoc. Editor: YangQuan Chen.

J. Dyn. Sys., Meas., Control 135(5), 051012 (Jun 27, 2013) (9 pages) Paper No: DS-12-1117; doi: 10.1115/1.4024201 History: Received April 22, 2012; Revised March 19, 2013

This paper considers the problem of controlling rotating machinery with actuators and sensors fixed in inertial space. Such a problem arises in control of charging and fusing stages in the xerographic process, drilling and milling machines, and turbo machinery. If a rotating device is represented as a set of discrete wedges, the resulting system can be conceptualized as a set of plants (wedges) with a single actuator and sensor. In such architecture, each plant can be controlled only intermittently, in a stroboscopic manner. This leads to the problem of cyclic control (CC) considered in this paper. Specifically, the problem of stabilizability in CC architecture is considered, and the resulting stabilizability conditions are compared with those in the usual, permanently acting control (PAC). In this regard, it is shown that the domain of asymptotic stability under CC is an open disc in the open left half plane (OLHP), rather than the OLHP itself, and the controller gains that place the closed loop poles at the desired locations under CC are N times larger than those under PAC, where N is the number of wedges. The results are applied to temperature stabilization of the fusing stage of a xerographic process.

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Grahic Jump Location
Fig. 1

Rotating device modeled by N wedges, where the sensor and actuator are located at different wedges. This paper considers the case where the sensor and actuator are located at the same wedge.

Grahic Jump Location
Fig. 2

Switching representation of a CC system, where the sensor and actuator are located at the same plant

Grahic Jump Location
Fig. 7

Example 5: an eigenvalue of Φe and Φ∧e

Grahic Jump Location
Fig. 9

The gain vectors k1, k10, and k20 in controller (33)

Grahic Jump Location
Fig. 10

The gain vectors l1, l10, and l20 in controller (33)



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