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TECHNICAL PAPERS

Design of Continuous Time Controllers Having Almost Minimum Time Response

[+] Author and Article Information
M. Kalyon

ME Department, KFUPM PO Box 1382, Dharan 31261, Saudi Arabiae-mail: kalyon@kfupm.edu.sa

J. Dyn. Sys., Meas., Control 124(2), 252-260 (May 10, 2002) (9 pages) doi:10.1115/1.1468862 History: Received March 26, 2000; Online May 10, 2002
Copyright © 2002 by ASME
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References

Bonger,  I., and Kazda,  O. F., 1954, “An Investigation of the Switching Criteria for Higher Order Contactor Servomechanisms,” AIEE Transactions, 73, pp. 118–127.
Kalman,  R. E., 1955, “Analysis and Design Principles of Second and Higher Order Saturating Servomechanisms,” AIEE Transactions, 74, pp. 102–118.
Lewis,  J. B., 1953, “The Use of Nonlinear Feedback to Improve the Transient Response of a Servomechanism,” Trans. AIEE, 71, pp. 449–453.
McDonald,  D. C., 1952, “Multiple Mode Operation of Servomechanisms,” Rev. Sci. Instrum., 23, pp. 22–30.
Rauch, L. L., and Howe, R. M., 1956, “A Servo with Linear Operation in a Region about the Optimum Discontinuous Switching Curve,” reprinted from the Proc. Symp. on Nonlinear Circuit Analysis, Polytechnic Inst. of Brooklyn, NY.
Workman, M. L., 1987, “Adaptive Proximate Time-Optimal Control: Continuous Time Case,” Proc. 1987 American Control Conference, Minneapolis, MN, pp. 589–594.
Workman M. L., 1987, “Adaptive Proximate Time-Optimal Servomechanisms,” Ph.D. thesis, Stanford University.
Pao,  L. Y., and Franklin,  G. F., 1993, “Proximate Time-Optimal Control of Third-Order Servomechanisms,” IEEE Trans. Autom. Control, 38, pp. 560–580.
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Wu,  S-T., 1999, “Time-Optimal Control and High-Gain Linear State Feedback,” Int. J. Control, 72, pp. 764–772.
McDonald D. C., 1953, “Intentional Nonlinearization of Servomechanisms,” Proc. Symp. on Nonlinear Circuit Analysis, Polytechnic Inst. of Brooklyn, NY, pp. 402–411.
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Kalyon, M., 1993, “Continuous Proximate Time-Optimal Control of Servomechanisms,” Ph.D. thesis, University of Michigan.
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La Salle, J., and Lefschetz, S., 1961, Stability by Liapunov’s Direct Method: with Applications, Academic Press, New York.
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Figures

Grahic Jump Location
The phase-plane solution paths of the system for large initial states
Grahic Jump Location
Time history of the three controllers as well as the corresponding error responses and error rate responses
Grahic Jump Location
The CPTO controller state trajectories: (a) the phase-plane solution paths and the boundaries of the unsaturated controller region; (b) and (c) time history of the CPTO controller (u), the error (x1), and the error rate (x2) for the initial conditions x(0)=[1 0]T and x(0)=[0 −2]T, respectively
Grahic Jump Location
The CPTO controller state trajectories: (a) The phase-plane solution paths, and the boundaries of the unsaturated controller region, and the boundaries of the recoverable set; (b) and (c) time history of the CPTO controller (u), the error (x1), and the error rate (x2) for the initial conditions x(0)=[00.95]T and x(0)=[−0.5 1.6]T, respectively.
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(a) A portion of the switching surface together with the switching curve; (b) the corresponding portion of the slab together with the sets defining behavior of CPTO controller
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Error state trajectory in 3-D using the CPTO controller: (a), (b), and (c) trajectory projections on x1−x2,x1−x3, and x2−x3 planes, respectively; (d) side view
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(a) Time response of the error state (x1,x2,x3); (b) time history of the CPTO controller, the switching surface function x1−X1, and the switching curve function x2−X2
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(I) Time response of the Ideal Time Optimal Controller; (II) time response of three CPTO Controllers, namely, u1,u2, and u3; (III) zoomed portions of (II)

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