# Research of optimal fast-acting systems of automatic control on laboratory bench

### Abstract

*Purpose. This paper presents a laboratory bench for research of optimal and quasi-optimal automatic control system in respect of its operation speed. Laboratory bench consists of thermal unit and software and hardware suite which includes VIPA System 200 V and HMI/SCADA logic controller and Zenon Supervisor 7.0 system. Thermal unit is described by differential equation of second order pursuing the control channel “amperage in electric heating unit power converter – air temperature inside thermal unit.” Differential equation coefficients depend on screen position and centrifugal blower rotation frequency. Methodology. Reported the methodology of synthesis and results of calculation of optimal relay hypothesis for thermal unit control through the chosen channel. Were demonstrated the results of experiment in transition of thermal unit from various initial states to final states. Was shown the possibility of implementing optimal control system in respect of its operation speed in real time scale by means of software development by including algorithms for transcendence set of simultaneous equations into it or by means of development of predicative model of thermal unit. Results. Were specified conditions for application of quasi-optimal relay control hypothesis in respect of its operation speed. Reported the methodology of synthesis and results of calculation of the length of the first control interval depending on the predetermined value of readjustment. Were demonstrated the results of modeling of quasi-optimal automatic control system in respect of its operation speed in Simulink of Matlab app. Was established functional relation of the length of the first control interval depending on the predetermined value of readjustment for implementing of quasi-optimal automatic control system in real time scale with application of basic operational units of programmed logic controller.*

### References

Pritchenko O.V. (2010), “The concept of the incentives of small-sized laboratory stands”, Schokvartalniy naukovo-virobnichiy zhurnal “Elektromehanichni i energozberigayuchi sistemi”, Kremenchuk: KDPU, Vol. 2., pp. 56-61.

Pontryagin L.S. (1998) Primenenie printsipa maksimuma v optimalnom upravlenii. [The application of the maximum principle in optimal control], Nauka, Moscow, Russia.

Triputen N.M. and Boyko O. (2014) “Development of a fuzzy regulator for controlling a thermal object based on a logic programmable controller” , Materiali XI mizhnarodnoyi konferentsiyi Problemi rozvitku vprovadzhennya Informatsiynih tehnologiy v naukovu ta innovatsiynu sferu osviti [Materials of the XI International Conference Problems of the development of the introduction of information technologies in the scientific and innovative sphere of education], Dnipropetrovsk, NGU, November 25, 2014, pp.24-25.

Shishov O.V. (2015) Elementyi sistem avtomatizatsii. Kontrolleryi, operatornyie paneli, moduli udalyonnogo dostupa: laboratornyiy praktikum [Elements of automation systems. Controllers, operator panels, remote access modules: laboratory practice], Direkt-Media, Moscow, Russia – Berlin, Germany.

Rajib Mall. (2006), Real-time Systems: Theory and Practice. IGI Global.

Scherbakov A. and Gubkina V. (2013) “Fuzzy Logic Systems”, The 8th International Forum for Students and Young Researches WIDENING OUR HORIXONS, April 11-12, Volume 2,p.78.

Belikov D. and Nechay N. (2014) “Extreme Control System for a Thermal Object”, The 9th International Forum for Students and Young Researches WIDENING OUR HORIXONS, April 3-4, Volume 2, p.92.

Triputen N.M. and Belikov D.V. (2014), “Identification of the thermal object”, Materiali XI mizhnarodnoyi konferentsiyi Problemi rozvitku vprovadzhennya Informatsiynih tehnologiy v naukovu ta innovatsiynu sferu osviti [Materials of the XI International Conference Problems of the development of the introduction of information technologies in the scientific and innovative sphere of education], Dnipropetrovsk, NGU, November 25, 2014, pp.18-19.

Kachan Yu.G. (1990) “The development of a control unit for the process control system for large-scale chipping”, Metallurgicheskaya i gornorudnaya promyishlennost, Vol.3, pp.64-66.

Kuznetsov V.V. (2017) “Algorithm of recognition in tasks of increasing the energy efficiency of induction motors operating in conditions of low-quality electric power”, Vestnik Natsionalnogo tehnicheskogo universiteta "Harkovskiy politehnicheskiy institut", Vol.27, no. 1249, pp. 95-98.

Voronov V.A. (1982), “Method of describing technological situations and its use in process management”, Obogaschenie rud, Vol.2, pp.31-35.

Voronov V.A. (1984), “One-dimensional numerical coding of situations in the automated control of technological processes ”, Obogaschenie rud, Vol.4, pp.38-41.

Beshta D.O. (2001), “α-algebra in the problems of control of technological processes”, Naukovyy visnyk NHA Ukrayiny, Vol. 2, pp.80-83.

Gmurman V.E. (2004), Rukovodstvo k resheniyu zadach po teorii veroyatnostey i matematicheskoy statistike [A guide to solving problems in probability theory and mathematical statistics],Vyisshaya shkola, Moscow, Russia.