RESEARCH OF THE DYNAMIC PROPERTIES OF THE COMPENSATOR OF CROSS-CONNECTIONS OF THE AUTONOMOUS CONTROL SYSTEM
DOI:
https://doi.org/10.31471/1993-9981-2022-2(49)-74-88Keywords:
муфельна піч, перехресні зв’язки, компенсатор, передавальні функції, декомпозиція, z-перетворення, оцінка, точність.Abstract
Muffle furnaces are used to heat various small products to a given temperature. A design feature of muffle furnaces is the presence of a muffle, which is made of heat-resistant material and delimits the working space of the furnace and the heated sample.
Modern muffle furnaces are universal heating devices that are used both for laboratory research and for heating small products.
Muffle furnace unit of periodic action. Heating processes in a muffle furnace proceed in three stages - heating the furnace to a certain temperature, operating mode and cooling. The first two stages must be performed in automatic mode and ensure the necessary accuracy of temperature maintenance during the implementation of the second stage.
This work considers a muffle furnace with two heaters (thena), which have two independent power sources, which causes two channels of transmission of influences "thena power-temperature in the furnace". Studies have shown that between the inputs and outputs of the object (muffle furnace) there are not only direct, but also cross connections, the presence of which greatly complicates the process of controlling the temperature regime in the muffle furnace. In order to eliminate the negative effect of cross-connections, a compensator was synthesized in the work and its dynamic properties were investigated.
The matrix transfer function of the compensator was obtained and its elements were found in the form of a ratio of two polynomials, the order of which is determined by the order of the transfer functions of the object.
Since the transfer functions of the muffle furnace have a high order, a decomposition method has been developed, which makes it possible to present the corresponding transfer functions in the form of a parallel connection of typical links of the first and second order. The decomposition made greatly simplifies the transition from the continuous model to its discrete representation in terms of the z-transformation.
Downloads
References
Horbiychuk M. I., Lazoriv N. T., Lazoriv A. M. Avtonomna systema avtomatychnoho keruvannya temperaturnym rezhymom mufelʹnoyi pechi. Informatsiyni tekhnolohiyi v osviti, tekhnitsi ta promyslovosti: materialy nauk.-prakt. konf., (m. Ivano-Frankivsʹk, 13 zhovt., 2022.) Ivano-Frankivsʹk, 2022. S. 42 – 44.
URL: https://drive.google.com/file/d/1WqQ2msGllAbwQ4WsE-Yruxd1keUxCTad/view. [in Ukrainian]
Shtifzon O. Y., Novikov V. P., Bunʹ V. P. Teoriya avtomatychnoho upravlinnya: navchalʹnyy posibnyk. K.: KPI im. I. Sikorsʹkoho. 2020. 144 s. [in Ukrainian]
Levin J. J. On the matrix Riccati equation. Proc. Amer. Math. Soc., 10. 1959. Pp. 519–524.
Ray W. Advanced Process Control. New York: McGraw-Hill Book, Company, 1981. 368 p
Kuster George E. H-infinity Norm Calculation via a State Space Formulation. URL: https://vtechworks.lib.vt.edu/bitstream/handle/10919/49544/Kuster_GE_T_2013.pdf?isAllowed=y&sequence=1 (Дата звернення 26.09.2022)
Gaiduk A.R. Synthesis of control systems of multivariable objects. Journal of Computer and Systems Sciences International. 1998. Vol. 37, N 1. P. 5–13.
Gaiduk A.R., Vershinin Y.A., Jawaid A. A method of synthesis of a multivariable system with decoupled and interconnected channels // Proceedings of the 2003 IEEE International Symposium on Intelligent Control. Houston, TX, 2003. P. 548–552.
Gorbiychuk M. I., Povarchuk D. D., Humeniuk T. V., Lazoriv N. T. Development of the imitation model of the two-stage separation process of oil. Earsten-European Journal of Enterprise Technologies. 2018. -№ ½ (92). Р. 20 – 27. [in Ukrainian]
Isermann R. Digital Control Systems. Berlin: Springer-Vtrlag, 1980. 541 p.
Goodwin G. C., Graebe S. F., Saldago M. E. Control Systems Design. Prentice Hall, 2000. 944 p.
Tou Julius T. Digital and Sampled-data Control Systems. New York: McGraw-Hill Book Company, INC, 1960. 694 p.
Horbiychuk M. I., Lazoriv N. T. Dyskretyzatsiya matematychnykh modeley liniynykh obʺyektiv keruvannya. Journal Věda a perspektivy. 2022. № 1: P. 241-254. [in Ukrainian]
Horbiychuk M. I., Pistun YE. P. Chyslovi metody i modelyuvannya na EOM: navch. posibnyk. Ivano-Frankivsʹk: IFNTUNH, 2010. 409 s. [in Ukrainian]
.png)
