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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

Figures

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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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The phase-plane solution paths of the system for large initial states
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Time history of the three controllers as well as the corresponding error responses and error rate responses
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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
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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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