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An Approach to Model Validation for Model Predictive Control Based on Dvurecenska’s Metric

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CONTROLO 2020 (CONTROLO 2020)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 695))

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Abstract

In this paper, Dvurecenska’s validation metric is proposed as a criterion for selecting a suitable model to be used by a Dynamic Matrix Control algorithm. As part of the work developed in this paper, it is analyzed how this algorithm performs when using different models. Besides, a comparison between the validation of these model results is performed. Additionally to the above metrics, the Theil Inequality Coefficient index and the FIT index are employed too. This paper was developed on a simulated plant based on Clarke’s benchmark, which is controlled with a Dynamic Matrix Control. As a result, it can be seen that Dvurecenska’s metric accomplishes its objective and in some cases, gives better validation criteria than the other metrics analyzed.

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Authors and Affiliations

  1. Escola Politécnica, University of São Paulo, São Paulo, SP, Brazil

    Victor D. Reyes Dreke, Manuel A. Pérez Serrano & Claudio Garcia

Authors
  1. Victor D. Reyes Dreke
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  2. Manuel A. Pérez Serrano
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  3. Claudio Garcia
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Corresponding author

Correspondence to Victor D. Reyes Dreke .

Editor information

Editors and Affiliations

  1. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Bragança, Portugal

    José Alexandre Gonçalves

  2. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Bragança, Portugal

    Manuel Braz-César

  3. Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Bragança, Bragança, Portugal

    João Paulo Coelho

Appendix A. Table Containing the Non-parametric Models

Appendix A. Table Containing the Non-parametric Models

Model no.

Polynomials of the discrete-time model

885

\( A\left( z \right) = 1 - 2.578z^{ - 1} + 2.29z^{ - 2} - 0.7021z^{ - 3} \)

\( {\text{B}}\left( {\text{z}} \right) = - 0.02791 z^{ - 10} + 0.01409 z^{ - 11} + 0.01942 z^{ - 12} + 0.00409 z^{ - 13} + 7.161e^{ - 05} z^{ - 14} \)

\( \begin{aligned} {\text{C}}\left( {\text{z}} \right) = & 1 + 0.9756z^{ - 1} + 0.5274z^{ - 2} + 0.3529 z^{ - 3} + 0.2562 z^{ - 4} + 0.3491z^{ - 5} \\ & + 0.06699z^{ - 6} + 0.7827z^{ - 7} + 0.9114z^{ - 8} + 0.3458z^{ - 9} + 0.04423z^{ - 10} \\ \end{aligned} \)

2443

\( A\left( z \right) = 1 - 1.669z^{ - 1} + 0.7425z^{ - 2} \)

\( {\text{B}}\left( {\text{z}} \right) = - 0.04885 z^{ - 1} + 0.1219 z^{ - 2} \)

\( \begin{aligned} {\text{C}}\left( {\text{z}} \right) = & 1 - 1.051z^{ - 1} + 0.2701z^{ - 2} + 0.01785 z^{ - 3} - 0.02654 z^{ - 4} + 0.008613z^{ - 5} \\ & - 0.006509z^{ - 6} + 0.02535z^{ - 7} - 0.02804z^{ - 8} - 0.008055z^{ - 9} + 0.03944z^{ - 10} \\ \end{aligned} \)

4669

\( {\text{B}}\left( {\text{z}} \right) = 0.1422z^{ - 1} - 0.2996z^{ - 2} + 0.18z^{ - 3} \)

\( {\text{F}}\left( {\text{z}} \right) = 1 - 2.651z^{ - 1} + 2.438z^{ - 2} - 0.7637z^{ - 3} \)

4720

\( \begin{aligned} {\text{B}}\left( {\text{z}} \right) = & 0.05462z^{ - 1} - 0.1254z^{ - 2} - 0.03513z^{ - 3} + 0.4091 z^{ - 4} - 0.4717z^{ - 5} \\ & + 0.1479z^{ - 6} + 0.4263z^{ - 7} - 1.143z^{ - 8} + 1.17z^{ - 9} - 0.4311z^{ - 10} \\ \end{aligned} \)

\( {\text{F}}\left( {\text{z}} \right) = 1 - 2.893z^{ - 1} + 2.767z^{ - 2} - 0.605z^{ - 3} - 0.4237 z^{ - 4} + 0.1569z^{ - 5} \)

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Reyes Dreke, V.D., Pérez Serrano, M.A., Garcia, C. (2021). An Approach to Model Validation for Model Predictive Control Based on Dvurecenska’s Metric. In: Gonçalves, J.A., Braz-César, M., Coelho, J.P. (eds) CONTROLO 2020. CONTROLO 2020. Lecture Notes in Electrical Engineering, vol 695. Springer, Cham. https://doi.org/10.1007/978-3-030-58653-9_10

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