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Application of Mathematical Models to Estimate the Water Level Stability in a Two-Tank System in Series with Service Demand Variations

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12949))

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Abstract

In this research work, a two-tank system in series was developed. In this system, water flows from the first tank to the second. Opening variations were present in the inlet valve, while the opening flow was fixed in the outlet valve. Using differential equations, the Jacobian matrix and eigenvalues, it was possible to analyze the stability of the system and obtain the equilibrium points. To estimate the adequate water levels, a linear and nonlinear model were implemented. Both models were able to estimate in real time the tanks water levels, identifying the system equilibrium points, this ensured the service demand. A simulation process was applied to evaluate the model’s behavior over time. This simulation was performed using the Simulink tool of Matlab. Both linear and nonlinear models obtained similar results. Results analysis suggested the use of the linear model to implement the control system, since its transfer functions compositions are less complex and more efficient to deploy.

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Authors and Affiliations

  1. Universidad Nacional de Jaen, Jr. Cuzco N° 250, Pueblo Libre, Jaén, Cajamarca, Peru

    Nilthon Arce & José Piedra

  2. Universidad Nacional de Piura, Urb. Miraflores s/n, Castilla, Piura, Peru

    Eder Escobar, Luis Aguilar & Flabio Gutierrez

  3. Universidad Católica de Trujillo, Panamericana Norte Km. 555, Moche, Trujillo, La Libertad, Peru

    Edwar Lujan

Authors
  1. Nilthon Arce
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  2. José Piedra
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  3. Eder Escobar
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  4. Edwar Lujan
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  5. Luis Aguilar
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  6. Flabio Gutierrez
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Corresponding author

Correspondence to Flabio Gutierrez .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Arce, N., Piedra, J., Escobar, E., Lujan, E., Aguilar, L., Gutierrez, F. (2021). Application of Mathematical Models to Estimate the Water Level Stability in a Two-Tank System in Series with Service Demand Variations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_35

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  • DOI: https://doi.org/10.1007/978-3-030-86653-2_35

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

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