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Scalable Non-dimensional Model Predictive Control of Liquid Level in Generally Shaped Tanks Using RBF Neural Network

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  • Intelligent Control and Applications
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Abstract

This paper focuses on developing and analyzing a concept of a fully scalable control method applicable to highly nonlinear systems with dynamics varying over the whole working area. The approach is demonstrated on control of liquid level in non-trivial shaped tanks. Non-dimensionalised quantities were used for the development of general geometric model systems of the liquid accumulation in the tanks. Then, training sets were obtained from simulations of the model systems and used for training radial basis function neural network (RBFNN) models. These RBFNNs were implemented in controllers using model predictive control (MPC) method. Both the models and controllers are scalable and applicable in industry or nature. A tentative set of conditions and rules was defined to transfer the solution to practical situations.

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Abbreviations

h :

liquid height

h max :

maximum liquid height

V :

volume of liquid

V max :

maximum volume of liquid = total volume of the tank

t :

time

t max :

filling/emptying time of tank

A :

accumulation (dV/dt)

A max :

maximum accumulation

G :

volume element (dV/dh)

a :

fractional accumulation

a min :

minimum fractional accumulation

a max :

maximum fractional accumulation

d ms :

shape denominator

k q :

time scaling factor

q in :

inlet flow

q out :

outlet flow

q of :

function of overflow

q b :

function of bottom

y :

output vector of model

u :

input vector of model

Θ NN :

parameters of NN, where

c :

are centers

Σ :

are norms

w o :

are output weights

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Funding

Authors are thankful to the support of Tomas Bata University in Zlín, Czech Republic. The work of Jan Antos and Marek Kubalcik was supported by two projects of Internal grant agency of the Tomas Bata University in Zlín, contract numbers: IGA/FAI/2014/009 and IGA/CebiaTech/2015/026. The work of Jan Antos and Ivo Kuritka was supported by two projects funded by the Ministry of Education, Youth and Sports of the Czech Republic, project numbers: LO1504 and RP/CPS/2020/006.

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Authors and Affiliations

  1. Centre of Polymer Systems, Tomas Bata University in Zlín, tř. Tomáše Bati 5678, 760 01, Zlín, Czech Republic

    Jan Antos & Ivo Kuritka

  2. Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stránémi 4511, 760 05, Zlín, Czech Republic

    Marek Kubalcik

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  1. Jan Antos
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Corresponding author

Correspondence to Jan Antos.

Additional information

Jan Antos received his Ph.D. degree in Automatic Control and Informatics from Tomas Bata University in 2019. His research interests include predictive control, computer science, artificial intelligence, system identification, process control, and measurement.

Marek Kubalcik received his Ph.D. degree in Technical Cybernetics from Brno University of Technology in 2000. His research interests include multivariable control, adaptive control, self-tuning controllers, system identification, and predictive control.

Ivo Kuritka received his Ph.D. degree in technology of macromolecular compounds from Tomas Bata University in 2005. His research interests include nanomaterials, chemistry, spectroscopy, process control, and measurements.

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Antos, J., Kubalcik, M. & Kuritka, I. Scalable Non-dimensional Model Predictive Control of Liquid Level in Generally Shaped Tanks Using RBF Neural Network. Int. J. Control Autom. Syst. 20, 1041–1050 (2022). https://doi.org/10.1007/s12555-020-0904-9

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