An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers

This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order Pl lambda D mu controllers. It is based on determining a set of global stability regions in the (k p , K i , K d )-space corresponding to the fractional orders...

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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 52; no. 10; pp. 1964 - 1969
Main Author: Hamamci, S.E.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Computer science; control theory; systems
Control system synthesis
Control systems
Control theory. Systems
Controllers
Delay effects
Delay systems
Design engineering
Differential equations
Electrical equipment industry
Exact sciences and technology
Fractional-order PID controller
fractional-order systems
Gain
gain and phase margins
Industrial control
Open loop systems
Proportional integral derivative
Stability
stabilization
System theory
Three-term control
Time delay
stabilization
Gain margin
Control synthesis
fractional-order systems
Delay system
gain and phase margins
time delay
Stability region
Fractional derivative
Global stabilization
Fractional-order PID controller
Delay time
Phase margin
Differential integral proportional control
ISSN:0018-9286, 1558-2523
Online Access:Get full text
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Description
Summary:This technical note presents a solution to the problem of stabilizing a given fractional-order system with time delay using fractional-order Pl lambda D mu controllers. It is based on determining a set of global stability regions in the (k p , K i , K d )-space corresponding to the fractional orders lambda and mu in the range of (0, 2) and then choosing the biggest global stability region in this set. This method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements. The algorithm is simple and has reliable result which is illustrated by an example, and, hence, is practically useful in the analysis and design of fractional-order control systems.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.906243