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Research Papers

A Systematic Determination Approach of Model's Base Using Gap Metric for Nonlinear Systems

[+] Author and Article Information
Ali Zribi

Department of Electrical Engineering,
National Engineering School of Sfax,
B. P. 1173,
Sfax 3038, Tunisia
e-mail: ali_zribi@yahoo.fr

Mohamed Chtourou

Professor
Department of Electrical Engineering,
National Engineering School of Sfax,
B. P. 1173,
Sfax 3038, Tunisia
e-mail: Mohamed.Chtourou@enis.rnu.tn

Mohamed Djemal

Professor
Department of Electrical Engineering,
National Engineering School of Sfax,
B. P. 1173,
Sfax 3038, Tunisia
e-mail: Mohamed.Djemel@enis.rnu.tn

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 9, 2014; final manuscript received November 25, 2015; published online January 13, 2016. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 138(3), 031008 (Jan 13, 2016) (7 pages) Paper No: DS-14-1280; doi: 10.1115/1.4032222 History: Received July 09, 2014; Revised November 25, 2015

This paper proposes a novel gap metric based fuzzy decomposition approach resulting in a reduced model bank that provides enough information to design controllers. It requires, first, the determination of the model base. For this, the number of initial models is obtained via fuzzy c-means (FCM) algorithm. Then, a gap metric based method which aims to get a reduced model bank is developed. Based on the linear models bank, a set of linear controllers are designed and combined into a global controller for setpoint tracking control.

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References

Figures

Grahic Jump Location
Fig. 1

The evolution of the reduced model numbers with respect to the threshold values (for different initial local models numbers)

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Fig. 2

Dendrogram for the first example

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Fig. 5

Calculated gap metrics using models 2 and 5 (dotted—δ2 and solid—δ5)

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Fig. 14

Closed-loop response of TITO system using two models (dotted—setpoint; solid—with models 2–4; and dashed—with models 6–1)

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Fig. 6

The evolution of the reduced model numbers with respect to the threshold values (for different initial local models numbers)

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Fig. 7

Dendrogram for the second example

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Fig. 8

Closed-loop responses and control inputs moves of CSTR using two models (dotted—setpoint; solid—with models 2–6; and dashed—with models 4–10)

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Fig. 3

Closed-loop responses and control inputs evolutions of CSTR using two models (dotted—setpoint; solid—with models 2–5; and dashed—with models 1–7)

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Fig. 4

Closed-loop responses and control inputs moves of CSTR using two models (dotted—setpoint; solid—with models 1–5; and dashed—with models 2–7)

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Fig. 13

Closed-loop response of TITO system using three models (2, 5, and 3)

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Fig. 9

Calculated gap metrics using models 4 and 10 (dotted—δ4 and solid—δ10)

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Fig. 10

Closed-loop responses and control inputs moves of CSTR using two models (dotted—setpoint; solid—with models 2–4; and dashed—with models 6–10)

Grahic Jump Location
Fig. 11

The evolution of the reduced model numbers with respect to the threshold values (for different initial local models numbers)

Grahic Jump Location
Fig. 12

Dendrogram for the third example

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