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.

Issue Section:
Technical Briefs
Keywords:
delays, polynomials, stability
Topics:
Control equipment, Delays, Stability, Theorems (Mathematics), Time delay systems

References

1.
Niculescu
,
S. I.
,
Delay Effects on Stability
(
Springer
,
London
, 2001).
2.
Gu
,
K.
,
Kharitonov
,
V.
, and
Chen
,
J.
, 2003,
Stability of Time-Delay Systems
,
Birkhauser
,
Boston, MA
.
3.
Gorecki
,
H.
,
Fuksa
,
S.
,
Grabowski
,
P.
, 1993, and
Korytowski
,
A.
, 1989,
Analysis and Synthesis of Time Delay Systems
,
Wiley
,
New York
, p.
369
.
4.
Hale
,
J. K.
, and
Lunel
,
S. M. V.
, 1993,
Introduction to Functional Differential Equations
,
Springer-Verlag
,
New York
.
5.
Richard
,
J. P.
, 2003, “
Time-Delay Systems: An Overview of Some Recent Advances and Open Problems
,”
Automatica
,
39
, pp.
1667
–
1694
.
Crossref
Search ADS
 
6.
Silva
,
G. J.
,
Datta
,
A.
, and
Bhattacharyya
,
S. P.
, 2005,
PID Controllers for Time Delay Systems
,
Springer
,
London
.
7.
Tantaris
,
R. N.
,
Keel
,
L. H.
, and
Bhattacharyy
,
S. P.
, 2002, “
Stabilization of Continuous Time System by First Order Controller
,”
Proceedings of the 10th Mediterranean Conference on Control and Automation—MED2002
,
Lisbon, Portugal
, July 9–12.
8.
Tantaris
,
R. N.
,
Keel
,
L. H.
, and
Bhattacharyy
,
S. P.
, 2003, “
Stabilization of Discrete-Time Systems by First-Order Controllers
,”
IEEE Trans. Automat. Cont.
,
48
, pp.
858
–
860
.
Crossref
Search ADS
 
9.
Farkh
,
R.
,
Laabidi
,
K.
, and
Ksouri
,
M.
, 2009, “
PI Control for Second Order Delay System with Tuning Parameter Optimization
,”
Int. J. Electr. Electron. Eng.
,
3
, pp.
1
–
7
.
10.
Farkh
,
R.
,
Laabidi
,
K.
, and
Ksouri
,
M.
, 2009, “
Computation of All Stabilizing PID Gains for Second Order Delay System
,”
Math. Probl. Eng.
,
2009
, pp.
1
–
17
.
Crossref
Search ADS
 
11.
Farkh
,
R.
,
Laabidi
,
K.
, and
Ksouri
,
M.
, 2009, “
Robust Stabilization for Uncertain Second Order Time-Lag System
,”
Mediterr. J. Meas. Control
,
5
(
4
), pp.
138
–
145
.
12.
Farkh
,
R.
,
Laabidi
,
K.
, and
Ksouri
,
M.
, 2011, “
Robust PI/PID Controller for Interval First Order System With Time Delay
,”
Int. J. Model. Identif. Control
,
13
(1/2), pp.
67
–
77
.
Crossref
Search ADS
 
13.
Keunsik
,
K. Y
, and
Chol
,
K.
, 2006, “
The Entire Set of First Order Controllers Guaranteed Stability and Gain/Phase Margins for a LTI Plant with Time Delay
,”
SICE-ICASE International Joint Conference 2006
,
Bexco, Busan, Korea
, October 18–21.
14.
Tantaris
,
R. N.
,
Keel
,
L. H.
, and
Bhattacharyy
,
S. P.
, 2003, “
Gain/Phase Margin Design with First order Controllers
,”
Proceedings of the American Control Conference
,
Denver, Colorado
, Vol.
5
, pp.
3937
–
3942
.
15.
Tantaris
,
R. N.
,
Keel
,
L. H.
, and
Bhattacharyya
,
S. P.
, 2003, “
H∞ design with first order controllers
,”
Proceedings of the 2003 IEEE Conference on Decision and Control
,
Maui, HI
, December 9–12.
16.
Keel
,
L. H.
, and
Bhattacharyy
,
S. P.
, 2005, “
Direct Synthesis of First Order Controllers from Frequency Response Measurements
,”
American Control Conference
,
Portland, OR
, June 8–10.
17.
Saadaoui
,
K.
,
Elmadssia
,
S.
, and
Benrejeb
,
M.
, 2008, “
Stabilizing First-Order Controllers for n-th Order All Pole Plants with Time Delay
,”
16th Mediterranean Conference on Control and Automation Congress Centre
,
Ajaccio, France
, June 25–27.
18.
Tan
,
N.
, 2003, “
Computation of Stabilizing Lag/Lead Controller Parameters
,”
Comput. Electr. Eng.
,
29
, pp.
835
–
849
.
Crossref
Search ADS
 
19.
Bhattacharyya
,
S. P.
,
Chapellat
,
H.
,
Keel
,
L. H.
, 1995,
Robust Control: The Parametric Approach
,
Prentice-Hall
,
Upper Saddle River, NJ
.
Copyright © 2011
 by American Society of Mechanical Engineers
You do not currently have access to this content.