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Research Papers

Robust Fixed Low-Order Controller for Uncertain Decoupled MIMO Systems

[+] Author and Article Information
Maher Ben Hariz

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20 Laboratoire Analyse,
Conception et Commande des Systémes,
BP 37 Le Belvedére 1002, Tunis, Tunisie
e-mail: maherbenhariz@gmail.com

Faouzi Bouani

Université de Tunis El Manar,
Ecole Nationale d'Ingénieurs de Tunis,
LR11ES20 Laboratoire Analyse,
Conception et Commande des Systémes,
BP 37 Le Belvedére 1002, Tunis, Tunisie
e-mail: bouani.faouzi@yahoo.fr

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 11, 2016; final manuscript received May 26, 2017; published online September 8, 2017. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 140(2), 021001 (Sep 08, 2017) (14 pages) Paper No: DS-16-1022; doi: 10.1115/1.4037329 History: Received January 11, 2016; Revised May 26, 2017

The design of a robust fixed low-order controller for uncertain decoupled multi-input multi-output (MIMO) systems is proposed in this paper. The simplified decoupling is used as a decoupling system technique. In this work, the real system behavior is described by a linear model with parametric uncertainties. The main objective of the control law is to satisfy, in presence of model uncertainties, some step response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a min–max nonconvex optimization problem. The resolution of this kind of problems using standard methods can generate a local solution. Thus, we propose, in this paper, the use of the generalized geometric programming (GGP) which is a global optimization method. Simulation results and a comparison study between the presented approach, a proportional integral (PI) controller, and a local optimization method are given in order to shed light the efficiency of the proposed controller.

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Figures

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Fig. 1

TITO process representation

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Fig. 2

Decoupling scheme for TITO processes

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Fig. 3

Block diagram of the simplified decoupling

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Fig. 4

A feedback control system

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Fig. 5

Evolution of the first output and set point for the three models using the GGP method

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Fig. 6

Evolution of the second output and set point for the three models using the GGP method

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Fig. 7

Evolution of control signals for the three models using the GGP method

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Fig. 8

Evolution of the first output and set point for the three models using a local optimization method

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Fig. 9

Evolution of the second output and set point for the three models using a local optimization method

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Fig. 10

Evolution of control signals for the three models using a local optimization method

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Fig. 11

Response curve for Ziegler–Nichols first method

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Fig. 12

Evolution of the first output and set point for the three models using the PI controller

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Fig. 13

Evolution of the second output and set point for the three models using the PI controller

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Fig. 14

Evolution of the control signals for the three models using the PI controller

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Fig. 15

Evolution of the first output and set point for the three models using the GGP method

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Fig. 16

Evolution of the second output and set point for the three models using the GGP method

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Fig. 17

Evolution of the third output and set point for the three models using the GGP method

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Fig. 18

Evolution of control signals for the three models using the GGP method

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