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Journal of Dynamic Systems, Measurement, and Control | Volume 129 | Issue 2 | Technical Brief
TECHNICAL BRIEFS

On Fractional-Order QFT Controllers

[+] Author and Article Information
P. S. V. Nataraj

Systems and Control Engineering Group, Indian Institute of Technology Bombay, Mumbai - 400076, IndiaNataraj@ee.iitb.ac.in

Sachin Tharewal

Systems and Control Engineering Group, Indian Institute of Technology Bombay, Mumbai - 400076, Indiatharewal@iitb.ac.in

J. Dyn. Sys., Meas., Control 129(2), 212-218 (Jul 25, 2006) (7 pages) doi:10.1115/1.2432361 History: Received March 25, 2005; Revised July 25, 2006
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We propose the synthesis of robust fractional-order controllers using the principles of quantitative feedback theory (QFT). The resulting controllers are called as fractional-order QFT controllers. To demonstrate the synthesis method, we synthesize proportional-integral-derivative (PID) and more general types of fractional-order QFT controllers for a fractional-order plant, a DC motor, and a multistage flash desalination process.
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Figures

Grahic Jump Location
+Example 4.1 Closed-loop step responses corresponding to (a)PDβ controller designed by Podlubny (1) (dashed line) and (b)PDβ controller designed with proposed method (solid line)
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Example 4.1 Closed-loop step responses corresponding to (a)PDβ controller designed by Podlubny (1) (dashed line) and (b)PDβ controller designed with proposed method (solid line)
Figure 1

Example 4.1 Closed-loop step responses corresponding to (a)PDβ controller designed by Podlubny (1) (dashed line) and (b)PDβ controller designed with proposed method (solid line)

Grahic Jump Location
+Example 4.2. Plots of the nominal loop transmission functions corresponding to (a) the integer-order QFT controller synthesized by Chen (32) (marked with ▵) and (b) the fractional-order QFT controller synthesized with the proposed algorithm (marked with *)
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Example 4.2. Plots of the nominal loop transmission functions corresponding to (a) the integer-order QFT controller synthesized by Chen (32) (marked with ▵) and (b) the fractional-order QFT controller synthesized with the proposed algorithm (marked with *)
Figure 2

Example 4.2. Plots of the nominal loop transmission functions corresponding to (a) the integer-order QFT controller synthesized by Chen (32) (marked with ▵) and (b) the fractional-order QFT controller synthesized with the proposed algorithm (marked with *)

Grahic Jump Location
+Example 4.2. Magnitude plots corresponding to (a) the integer-order QFT controller synthesized by Chen in (32) (marked as GB) and (b) the fractional-order QFT controller synthesized by proposed algorithm (marked as GA)
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Example 4.2. Magnitude plots corresponding to (a) the integer-order QFT controller synthesized by Chen in (32) (marked as GB) and (b) the fractional-order QFT controller synthesized by proposed algorithm (marked as GA)
Figure 3

Example 4.2. Magnitude plots corresponding to (a) the integer-order QFT controller synthesized by Chen in (32) (marked as GB) and (b) the fractional-order QFT controller synthesized by proposed algorithm (marked as GA)

Grahic Jump Location
+Example 4.3. Closed-loop step responses corresponding to the fractional-order controller 48, prefilter 49, and sample plants from the plant family 46
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Example 4.3. Closed-loop step responses corresponding to the fractional-order controller 48, prefilter 49, and sample plants from the plant family 46
Figure 4

Example 4.3. Closed-loop step responses corresponding to the fractional-order controller 48, prefilter 49, and sample plants from the plant family 46

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