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Technical Briefs

First Order Controller for Time Delay System

[+] Author and Article Information
Kaouther Laabidi

Rihem Farkh1

Mekki Ksouri1

Research unit on Systems Analysis and Control, National School Engineering of Tunis, BP, 37, Le Belvedere, 1002 Tunis, TunisiaMekki.Ksour@insat.rnu.tn

1

Corresponding author.

J. Dyn. Sys., Meas., Control 133(5), 054502 (Aug 05, 2011) (5 pages) doi:10.1115/1.4003798 History: Received December 20, 2009; Revised January 15, 2011; Published August 05, 2011; Online August 05, 2011

In this paper, we consider the control of time delay system by first order controller. By Using the Hermite-Biehler theorem, which is applicable to quasipolynomials, we seek a stability region of the controller for first order delay systems.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Closed-loop control of a time delay system

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Figure 2

Representation of the curves of f(z) and of g(z) (case: x1<x1u)

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Figure 3

Representation of the curves of f(z) and of g(z) (case: x1=x1u)

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Figure 4

Representation of the curves of f(z) and of g(z) (case: x1>x1u)

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Figure 5

Plots of δi(z) and a(z)

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Figure 6

Controller stability domain in (x1,x2) plane for x3=0.3. The step response of the closed-loop system with some first order controllers is shown in Fig. 7.

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Figure 7

Time response of the closed-loop system (case: x3=0.3). For x3=0 we find this stability region as shown in the following figure.

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Figure 8

Controller stability domain in (x1,x2) plane for x3=0. The step response of the closed-loop system with some first order controllers is shown in Fig. 7.

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Figure 9

Time response of the closed-loop system (case: x3=0)

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