Abstract

The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. A sugar syrup cooler was chosen as an object of modeling. The mathematical model of the cooler is formalized by a set of perfect reactors. The simulation results showed that the mathematical model adequately describes the main regularities of the process, the deviation of the calculated data from the regulations did not exceed 10%. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.

Keywords

Mathematical modeling, dynamic systems, sugar syrup cooler, MathWorks Simulink™

REFERENCES

1. Berk Z. Food Process Engineering and Technology: Second Edition. New York: Academic Press, 2013. 720 p.
2. Van Boekel M. Kinetic Modeling Reactions in Foods. Florida : CRC Press, 2009. 767 p.
3. Harriot P. Chemical Reactor Design. New York: Marcel Dekker, 2003. 99 p.
4. MathWorks. Available at: http://matlab.ru/. (accessed 02 October 2017).
5. Herman R. Solving Differential Equations Using SIMULINK. Published by R.L. Herman, 2016. 87 p.
6. Gray M.A. Introduction to the Simulation of Dynamics Using Simulink. Boca Raton, Florida : CRC Press 2011. 308 p.
7. Duffy D.G. Transform Methods for Solving Partial Differential Equations, Second Edition. Boca Raton, Florida : CRC Press, 2004. 728 p.
8. Wong M.W. Partial differential equations: topics in fourier analysis. Boca Raton; London; New York: CRC Press, 2013. 184 p.
9. Ozana S. and Pies M. Using Simulink S-Functions with Finite Difference Method Applied for Heat Exchangers. Proceedings of the 13th WSEAS International Conference on SYSTEMS. Greece, Rodos, 2009, p. 210–215.
10. Mazzia A. and Mazzia F. High-order transverse schemes for the numerical solution of PDEs. Journal of Computational and Applied Mathematics, 1997, vol. 82, no. 1–2, pp. 299–311. DOI: https://doi.org/10.1016/S0377-0427(97)00090-3.
11. LeVeque R.J. Finite Difference Methods For Ordinary and Partial Differential Equations. Philadelphia: SIAM, 2007. 339 p.
12. Moler C.B. Numerical Computing with MATLAB. Philadelphia: SIAM, 2004. 336 p.
13. Hunt A.B.R., Lipsman R.L., Rosenberg J.M., et al. A Guide to MATLAB: for Beginners and Experienced Users. Cambridge: Cambridge University Press, 2006. 302 p.
14. Dragilev A.I., Khromeenkov V.M., and Chernov M.E. Tekhnologicheskoe oborudovanie: khlebopekarnoe, makaronnoe i konditerskoe [Technological equipment: bakery, macaroni and confectionery]. St. Petersburg: Lan Publ., 2016. 430 p. (In Russ.).
15. Dragilev A.I. and Rub M.D. Sbornik zadach po raschetu tekhnologicheskogo oborudovaniya konditerskogo proizvodstva [Problem book on confectionery technological equipment calculation]. Moscow: DeLi Print Publ., 2005. 244 p. (In Russ.).
16. Salov V.S. and Nazarenko S.V. Temperatura kipeniya i vyazkost' sakharnykh rastvorov [Boiling point and viscosity of sugar solutions]. News institutes of higher Education. Food technology, 1999, nos 2–3, pp. 69–71. (In Russ.).