Open Access Open Access  Restricted Access Subscription or Fee Access

Mathematical Modeling of the Membrane Concentration of Whey by the State Space Method


(*) Corresponding author


Authors' affiliations


DOI: https://doi.org/10.15866/iremos.v13i4.18643

Abstract


In this paper, the development of a mathematical model for the membrane concentration process and the methods for determining the design parameters of the pilot membrane (ultra-filtration) device based on tubular membrane filters are studied. The state space method has been used to compile the state and control matrices, including coefficients that have been obtained taking into account the structure of transfer functions. The experimental studies have allowed carrying out a parametric identification of the mathematical model of the membrane concentration process of whey in the membrane (ultra-filtration) device with tubular membranes. The authors have developed a set of interrelated mathematical models that make it possible to evaluate the dynamics of the membrane concentration process of whey, taking into account its technological parameters and the design peculiarities of the membrane device. The authors have carried out software implementation of the set of models and have developed methods for calculating the rational values of the design parameters of a pilot device. The main parameters of the mathematical models include high prediction accuracy (the discrepancy between experimental values and values obtained using the model does not exceed 7.8%) and simplicity of implementation in most modern software products. The effectiveness of the methods for calculating the design parameters of the membrane device is determined by their versatility in the design of pilot membrane plants based on tubular membrane filters.
Copyright © 2020 Praise Worthy Prize - All rights reserved.

Keywords


Mathematical Model; State Space Method; Calculation Method; Ultra-Filtration; Whey

Full Text:

PDF


References


G. V. Averin, A. V. Zvyagintseva, and A. A. Shvetsova, On the Approaches to Predicative Modeling of Complex Systems. Scientific Statements, Economy Series, Computer Science, Vol. 1(Issue 45): 140–148, 2018.

T. I. Kasatkina, E. V. Grechishnikov, V. E. Didrikh, and A. S. Solovev, Mathematical Modeling Methods and Algorithms for Analyzing Systems and Processing Information for Studying the Dynamics of Complex, in Newsletter of the Voronezh Institute of the Federal Penitentiary Service of Russia, Vol. 4 (2017, pp. 48–58).

P. Ghorai, S. Pandey, and S. Majhi, State Space Approach for Identification of Real-Time Plant Dynamics, in 2017 Indian Control Conference (ICC), pp. 28–32, Guwahati, India, Jan. 2017.
https://doi.org/10.1109/indiancc.2017.7846447

D. H. Owens, State Space Models, in Iterative Learning Control (Springer London, 2016, pp. 55–86).

C. Pozna and R.-E. Precup, An Approach to the Design of Nonlinear State-Space Control Systems, Studies in Informatics and Control, Vol. 27(Issue 1): 5-14, Mar. 2018.
https://doi.org/10.24846/v27i1y201801

D. Pal and H. K. Pillai, Multidimensional behaviors: The state-space paradigm, Systems & Control Letters, Vol. 95: 27–34, Sep. 2016.
https://doi.org/10.1016/j.sysconle.2016.02.012

A. Svensson and T. B. Schön, A flexible state–space model for learning nonlinear dynamical systems, Automatica, Vol. 80: 189–199, Jun. 2017.
https://doi.org/10.1016/j.automatica.2017.02.030

P. Tatjewski, Offset-free nonlinear Model Predictive Control with state-space process models, Archives of Control Sciences, Vol. 27(Issue 4): 595–615, Dec. 2017.
https://doi.org/10.1515/acsc-2017-0035

H. Li and J. Zhang, Improved PID design using new state space predictive functional control optimization based structure, Chemometrics and Intelligent Laboratory Systems, Vol. 151: 95–102, Feb. 2016.
https://doi.org/10.1016/j.chemolab.2015.12.007

K. Lu, W. Zhou, G. Zeng, and W. Du, Design of PID controller based on a self-adaptive state-space predictive functional control using extremal optimization method, Journal of the Franklin Institute, Vol. 355(Issue 5): 2197–2220, Mar. 2018.
https://doi.org/10.1016/j.jfranklin.2017.12.034

Y. Yao and W. Zheng-xin, A motion simulation for Dual-arm robot based on the state-space method, in 2017 29th Chinese Control And Decision Conference (CCDC), pp. 4939–4943, Chongqing, China, May 2017.
https://doi.org/10.1109/ccdc.2017.7979370

K. Yovchev, K. Delchev, and E. Krastev, State Space Constrained Iterative Learning Control for Robotic Manipulators: State Space Constrained Iterative Learning Control for Manipulators, Asian Journal of Control, Vol. 20(Issue 3): 1145–1150, May 2018.
https://doi.org/10.1002/asjc.1680

J. P. Noël and J. Schoukens, Grey-box state-space identification of nonlinear mechanical vibrations, International Journal of Control, Vol. 91(Issue 5): 1118–1139, May 2018.
https://doi.org/10.1080/00207179.2017.1308557

Y. A. Sizy, E. G. Chaika, and A. N. Ushakov, The State Space Method in the Study and Analysis of Torsional Vibrations of the Rotational Drive, Newsletter of Mechanical Engineering, Vol. 2: 3-7, 2017.

E. Sariyildiz, G. Chen, and H. Yu, Robust Trajectory Tracking Control of Multimass Resonant Systems in State Space, IEEE Transactions on Industrial Electronics, Vol. 64(Issue 12: 9366–9377, Dec. 2017.
https://doi.org/10.1109/tie.2017.2708001

K. Oprzedkiewicz and E. Gawin, A non integer order, state space model for one dimensional heat transfer process, Archives of Control Sciences, Vol. 26(Issue 2): 261–275, Jun. 2016.
https://doi.org/10.1515/acsc-2016-0015

M. Ławryńczuk, Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation, ISA transactions, Vol. 67: 476–495, Mar. 2017.
https://doi.org/10.1016/j.isatra.2017.01.016

T. Zou, S. Wu, and R. Zhang, Improved state space model predictive fault-tolerant control for injection molding batch processes with partial actuator faults using GA optimization, ISA Transactions, Vol. 73: 147–153, Feb. 2018.
https://doi.org/10.1016/j.isatra.2017.12.022

D. B. Fedosenkov, A. A. Simikova, and B. A. Fedosenkov, Investigation of multidimensional control systems in the state space and wavelet medium, IOP Conference Series: Materials Science and Engineering, Vol. 354: 012004, May 2018.
https://doi.org/10.1088/1757-899x/354/1/012004

A. V. Chernov and A. V. Semenov, Mathematical Models of Dynamic Tracking Systems in the State Space with Nonlinearities of Phase Coordinates, Newsletter of Aerospace Defense.
Vol. 2(Issue 14): 89–95, 2017

K. V. Shapovalova, V. Y. Kapitan, A. G. Makarov, Y. A. Shevchenko, and K. V. Nefedov, Methods of Canonical and Multi-Canonical Sampling of the State Space of Vector Models, Far Eastern Mathematical Journal, Vol. 1(Issue 17): 124–130, 2017.

V. A. Yesakov, V. G. Dudko, and A. A. Shlopak, On a Method for Solving the Problems of the Synthesis of Optimal Observers of Perfect Order in a State Space, Problems of Modern Science and Education, Vol. 35(Issue 117): 9–15, 2017.

A. E. Stefankin, Intensification of the Whey Processing Process in the Membrane Device with a Hydrodynamic Insert, PhD dissertation, Kemerovo, 2017.

A. E. Stefankin and R. V. Kotlyarov, The apparatus for membrane filtration, Patent RF 152198, Jan. 21, 2014.

Lakhdari, F., Input Control of Photovoltaic Fed DC-DC Converter Based on a Dual Modeling Approach, (2020) International Review of Electrical Engineering (IREE), 15 (1), pp. 9-20.
https://doi.org/10.15866/iree.v15i1.17482

Kamoun, S., Kamoun, M., A New Parametric Estimation Algorithm for Large-Scale Systems Described by State-Space Mathematical Models, (2018) International Journal on Engineering Applications (IREA), 6 (6), pp. 202-210.
https://doi.org/10.15866/irea.v6i6.16998

Alkurawy, L., Saleh, M., Fatah, I., Saleh, A., Modeling and Identification of Human Heart System, (2019) International Journal on Engineering Applications (IREA), 7 (4), pp. 130-136.
https://doi.org/10.15866/irea.v7i4.17807


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize