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Research Papers

Improved Internal Model Control-Proportional-Integral- Derivative Fractional-Order Multiloop Controller Design for Non Integer Order Multivariable Systems

[+] Author and Article Information
Tassadit Chekari

Laboratoire de Conception et Conduite des
Systèmes de Production (L2CSP),
Mouloud Mammeri University,
Tizi Ouzou 15000, Algeria
e-mail: tassadit.chekari@gmail.com

Rachid Mansouri

Professor
Laboratoire de Conception et Conduite des
Systèmes de Production (L2CSP),
Mouloud Mammeri University,
Tizi Ouzou 15000, Algeria
e-mail: rachid_mansouri_ummto@yahoo.fr

Maamar Bettayeb

Professor
Electrical and Computer Engineering Department,
University of Sharjah,
Sharjah 27272, United Arab Emirates;
Center of Excellence in Intelligent Engineering
Systems (CEIES),
King Abdulaziz University,
Jeddah 21589, Saudi Arabia
e-mail: maamar@sharjah.ac.ae

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received December 13, 2017; final manuscript received August 16, 2018; published online September 26, 2018. Assoc. Editor: Yongchun Fang.

J. Dyn. Sys., Meas., Control 141(1), 011014 (Sep 26, 2018) (11 pages) Paper No: DS-17-1617; doi: 10.1115/1.4041353 History: Received December 13, 2017; Revised August 16, 2018

This paper is aimed to propose a multiloop control scheme for fractional order multi-input multi-output (FO-MIMO) systems. It is an extension of the FO-multiloop controller design method developed for integer order multivariable systems to FO-MIMO ones. The interactions among the control loops are considered as disturbances and a two degrees-of-freedom (2DOF) paradigm is used to deal with the process outputs performance and the interactions reduction effect, separately. The proposed controller design method is simple, in relation with the desired closed-loop specifications and a tuning parameter. It presents an interest in controlling complex MIMO systems since fractional order models (FO-models) represent some real processes better than integer order ones and high order systems can be approximated by FO-models. Two examples are considered and compared with other existing methods to evaluate the proposed controller.

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Figures

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Fig. 1

Internal model control and conventional feedback structures

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Fig. 2

Proposed 2DOFs-IMC multiloop control scheme

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Fig. 3

Enhanced multiloop control scheme

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Fig. 4

Magnitude diagrams of sFO(s) and tFO(s) for different values of the parameter μ

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Fig. 5

Step response of g(s) for different values of the parameter μ:0<μ<1: (a) perturbed step response and (b) step response with noise

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Fig. 6

Step Response of g(s) (β=1.5) for different values of the parameter μ:1<μ<2: (a) perturbed step response and (b) step response with noise

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Fig. 7

Magnitude diagrams of s(s) and t(s) for different values of τt

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Fig. 8

Control scheme of the FO-decoupling controller

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Fig. 9

Closed-loop responses to sequential step changes in set-points

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Fig. 10

Controls evolution

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Fig. 11

Closed-loop output responses to sequential disturbances changes

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Fig. 12

Closed-loop output responses with variations on diagonal gains: (a) proposed method and (b) decoupling method

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Fig. 13

Closed-loop output responses with variations on off-diagonal gains: (a) proposed method and (b) decoupling method

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Fig. 14

Closed-loop output responses with noise

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Fig. 15

Closed-loop output responses to sequential set-point changes

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Fig. 16

Closed-loop output responses to sequential disturbances changes with the proposed controller

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Fig. 17

Closed-loop output responses to sequential disturbances changes with the dRI controller

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Fig. 18

Closed-loop output responses with noise, proposed controller

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Fig. 19

Closed-loop output responses with noise, dRI controller

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Fig. 20

Step responses with process gains variations, proposed controller

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Fig. 21

Step responses with process gains variations, dRI controller

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Fig. 22

Step responses with time delays process variations, proposed controller

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Fig. 23

Step responses with process time delay variations, dRI controller

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