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Fuzzy Model Predictive Control: Complexity Reduction for Implementation in Industrial Systems

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Abstract

In this paper, a new fuzzy logic-based control-design technique is presented. The method aims at reducing the complexity of Takagi-Sugeno Fuzzy systems via the reduction of fuzzy rules. This reduction is obtained by finding a function basis via the Functional Principal Component Analysis, and then the model is used for Model Predictive Control (MPC). This procedure is systematic, and eventually leads to feasible low-cost microcontroller-based implementations, which has become a generic need in the era of IoT. In order to validate the results, two experimental setups have been controlled using these principles. The first of these, a mechanical pendulum, presents nonlinear dynamics that suggests the use of linear discrete models at specific operating points. In the second, a pilot plant implementing an industrial process with a chemical reactor and a heat exchanger, presents nonlinear multivariate dynamics that are successfully handled with the Fuzzy MPC Controller.

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Abbreviations

N :

Dimension of the original space

R :

Dimension of the new reduced subspace

\({\varvec{C}}\) :

\(\{c_{il}\},\; i = 1,\ldots,n; l = 1,\ldots,L\), with \(c_{il}\in {\mathbb {R}}\)

\(\bar{{\varvec{C}}}\) :

\(\{\bar{c_{i}}\},\; i = 1,\ldots,n\), with \(\bar{c_{i}}=\displaystyle \frac{\sum _{l=1}^{L}c_{il}}{L}\)

\(\varGamma\) :

\(\{\gamma _{ij}\}, i = 1,ldots,n; j = 1,ldots,N\), with \(\gamma _{ij}\in {\mathbb {R}}\)

\(\lambda _{i}\) :

Eigenvalues

v :

Variability index \(\in [0,1]\)

\(h_{j}({\varvec{x}})\) :

Consequent functions

\(\alpha _{j}({\varvec{x}})=\displaystyle \frac{{\bar{\mu }}_{j}({\varvec{x}}) }{\sum _{j=1}^{N}{\bar{\mu }}_{j}({\varvec{x}})}\) :

Antecedent functions

\(\theta ({\varvec{x}}),\xi ({\varvec{x}}), \delta _{i}(x)\) :

Functions \(\in L^{2}[0,X]\)

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Acknowledgements

The authors would like to acknowledge the VI Plan of Research and Transfer of the University of Seville (VI PPIT-US) for funding this work and also the Ministry of Economy and Competitiveness of Spain for the financial support under Grants DPI2016-78338-R and DPI2016-75294-C2-2-R.

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Authors and Affiliations

  1. Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla, Seville, Spain

    Juan M. Escaño & C. Bordons

  2. Nimbus Research Centre, Cork Institute of Technology, Cork, Ireland

    K. Witheephanich

  3. Departamento de Ingeniería, Universidad Loyola Andalucía, Seville, Spain

    F. Gómez-Estern

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  1. Juan M. Escaño
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  2. C. Bordons
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  3. K. Witheephanich
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  4. F. Gómez-Estern
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Correspondence to Juan M. Escaño.

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Escaño, J.M., Bordons, C., Witheephanich, K. et al. Fuzzy Model Predictive Control: Complexity Reduction for Implementation in Industrial Systems. Int. J. Fuzzy Syst. 21, 2008–2020 (2019). https://doi.org/10.1007/s40815-019-00693-z

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