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Research Papers

Internal Model Control–Proportional Integral Derivative–Fractional-Order Filter Controllers Design for Unstable Delay Systems

[+] Author and Article Information
Kahina Titouche

L2CSP Laboratory,
Mouloud Mammeri University,
Tizi-Ouzou 15000, Algeria
e-mail: titouche.kahina@gmail.com

Rachid Mansouri

L2CSP Laboratory,
Mouloud Mammeri University,
Tizi-Ouzou 15000, Algeria
e-mail: rachid_mansouri_ummto@yahoo.fr

Maamar Bettayeb

Center of Excellence in Intelligent
Engineering Systems,
University of Sharjah,
Sharjah, UAE;
Center of Excellence in Intelligent
Engineering Systems,
King Abdulaziz University,
Jaddah, Saudi Arabia
e-mail: maamar@sharjah.ac.ae

Ubaid M. Al-Saggaf

Center of Excellence in Intelligent
Engineering Systems,
King Abdulaziz University,
Jeddah 21146, Saudi Arabia
e-mail: usaggaf@kau.edu.sa

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 15, 2014; final manuscript received November 23, 2015; published online December 23, 2015. Assoc. Editor: M. Porfiri.

J. Dyn. Sys., Meas., Control 138(2), 021006 (Dec 23, 2015) (10 pages) Paper No: DS-14-1416; doi: 10.1115/1.4032131 History: Received October 15, 2014; Revised November 23, 2015

An analytical design for proportional integral derivative (PID) controller cascaded with a fractional-order filter is proposed for first-order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) paradigm. A two degrees-of-freedom (2DOF) control structure is used to improve the performance of the closed-loop system. In the 2DOF control structure, an integer order controller is used to stabilize the inner-loop, and a fractional-order controller for the stabilized system is employed to improve the performance of the closed-loop system. The Walton–Marshall's method, which is applicable to quasi-polynomials, is then used to establish the internal stability condition of the closed-loop system (the fractional part of the controller in particular) and to seek the set of stabilizing proportional (P) or proportional-derivative (PD) controller parameters.

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References

Figures

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Fig. 1

IMC and conventional feedback control structures

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Fig. 3

KM and Km of UFOPTD with G0 = 1 and T = 1

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Fig. 2

Two degrees-of-freedom control structure

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Fig. 4

b̂ of UFOPTD with G0 = 1 and T = 1

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Fig. 7

Closed-loop step response for θ=1.2 and τc=3, with disturbance

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Fig. 8

Closed-loop step response for θ=1.2 and τc=3, with white noise added to the output signal

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Fig. 9

Closed-loop step response with 10% loop-gain variation for θ=1.2 and τc=3

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Fig. 10

Closed-loop step response with 10% time constant variation for θ=1.2 and τc=3

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Fig. 11

Closed-loop step response with 10% dead time variation for θ=1.2 and τc=3

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Fig. 14

Closed-loop step responses with loop-gain variation: proposed method

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Fig. 15

Closed-loop step responses with loop-gain variation: method proposed in Ref. [35]

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Fig. 16

Closed-loop step responses with loop-gain variation: method proposed in Ref. [34]

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Fig. 17

Closed-loop step responses with time constant variation: proposed method

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Fig. 18

Closed-loop step responses with time constant variation: method proposed in Ref. [35]

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Fig. 19

Closed-loop step responses with time constant variation: method proposed in Ref. [34]

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Fig. 20

Closed-loop step responses with dead time variation: proposed method

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Fig. 12

Closed-loop step responses with θ=0.4 and τc=1

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Fig. 13

Closed-loop step responses with noise where θ=0.4 and τc=1

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Fig. 21

Closed-loop step responses with dead time variation: method proposed in Ref. [35]

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Fig. 22

Closed-loop step responses with dead time variation: method proposed in Ref. [34]

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