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Multi-objective PID Controller Tuning for Multi-model Control of Nonlinear Systems

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Abstract

Multi-model approaches for non-linear control usually consist in partitioning the operating space of a given non-linear process, in such a way, it is possible to approximate a local linear model for each partition. That allows using standard control and tuning techniques for each local linear model. After that, a global controller merging the set of local controllers is defined to control the original non-linear process. This global controller merges the local controllers, given that a single controller will exhibit different trade-offs in its performance in different operating regions; therefore, a single controller could exhibit a deficient performance in the overall operating space. In this paper, we exploit this fact from a multi-objective optimisation point of view, to tune a single controller using a parametric multi-model, looking for a suitable controller with a preferable trade-off along with the overall operating space.

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Notes

  1. A maximisation problem can be converted to a minimisation problem. For each of the objectives that have to be maximised, the transformation: \(\max J_i({\varvec{x}}) = -\min (-J_i({\varvec{x}}))\) could be applied.

  2. Available at: https://es.mathworks.com/matlabcentral/fileexchange/65145.

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Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), and the Fundação Araucária (FAPPR)—Brazil—Finance Codes: 310079/2019-5-PQ2, 4408164/2021-2-Univ and 51432/2018-PPP.

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Author notes

  1. Gilberto Reynoso-Meza, Jesús Carrillo-Ahumada, Victor Henrique Alves Ribeiro and Tainara Marques contributed equally to this work.

Authors and Affiliations

  1. PPGEPS, Pontifícia Universidade Católica do Paraná, Imaculada Conceição 1155, Curitiba, PR, 80215-901, Brazil

    Gilberto Reynoso-Meza & Tainara Marques

  2. Universidad del Papaloapan, Circuito Central 200, Tuxtepec, 68301, Oaxaca, Mexico

    Jesús Carrillo-Ahumada

  3. Silex, Amazonas Marcondes 448, Curitiba, PR, 80035-230, Brazil

    Victor Henrique Alves Ribeiro

Authors
  1. Gilberto Reynoso-Meza
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  2. Jesús Carrillo-Ahumada
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  4. Tainara Marques
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Correspondence to Gilberto Reynoso-Meza.

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Reynoso-Meza, G., Carrillo-Ahumada, J., Alves Ribeiro, V.H. et al. Multi-objective PID Controller Tuning for Multi-model Control of Nonlinear Systems. SN COMPUT. SCI. 3, 351 (2022). https://doi.org/10.1007/s42979-022-01236-4

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