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This work addresses the challenge of simulating and tuning commercial PID controllers for industrial applications, whose algorithm and parameters could be unknown or partially known. The contributions are: 1) the proposal of a validation step of the PID controller model before its tuning, which consists of evaluating, through model simulation and comparison with real data, how well this selected PID controller model reproduces the observed behavior of the actual PID controller; and 2) the proposal of the usage of a grey-box model structure, made up of a white-box model, consisting of a general commercial PID algorithm containing the known parameters of the PID to be modeled, connected to a black-box model, which captures dynamics not modeled by the white-box model. This structure, applied as a model of a commercial PID controller, is the main novelty of this work, since, based on the literature review and the authors’ experience, it has not been used before for this purpose. Several black-box model structures were evaluated to be used as part of the grey box structure, with promising results obtained with an ANFIS model.

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Open Loop Validation and Grey Box Modelling of PID Controllers with Algorithm and Parameters Partially Known

  • 章节

  • 发表日期：

    2026年

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  • Carlos Alberto García Vázquez,
  • Ana Isabel González Santos,
  • Daniel Tudor Cotfas,
  • Petru Adrian Cotfas,
  • Bernardo Yaser León Ávila,
  • Osmel Pérez Baluja

摘要

This work addresses the challenge of simulating and tuning commercial PID controllers for industrial applications, whose algorithm and parameters could be unknown or partially known. The contributions are: 1) the proposal of a validation step of the PID controller model before its tuning, which consists of evaluating, through model simulation and comparison with real data, how well this selected PID controller model reproduces the observed behavior of the actual PID controller; and 2) the proposal of the usage of a grey-box model structure, made up of a white-box model, consisting of a general commercial PID algorithm containing the known parameters of the PID to be modeled, connected to a black-box model, which captures dynamics not modeled by the white-box model. This structure, applied as a model of a commercial PID controller, is the main novelty of this work, since, based on the literature review and the authors’ experience, it has not been used before for this purpose. Several black-box model structures were evaluated to be used as part of the grey box structure, with promising results obtained with an ANFIS model.