ANALYSIS AND DATA PROCESSING SYSTEMS

This article presents the results of the study of various transient modes of the pumping unit of an oil pumping station, in particular, the stator currents of the drive motor and the speed characteristic of its rotor rotation. The characteristics of the pumping unit can change quite significantly during operation. This is due to the fact that the parameters of the pumped oil change almost continuously, physical wear of the parts of the pumping unit also occurs, and the impeller is especially susceptible to wear. The input and output variables of this object are, respectively, the time and the angular velocity of rotation of its rotor. The combination of the above factors has a significant impact on the change in the speed of rotation of the rotor during operation, which can adversely affect the operation of the system as a whole. In order to eliminate the influence of external factors on the operation of the pumping unit, the relationship between the input and output variables was described by an ordinary differential equation with constant coefficients. The purpose of this work is to illustrate the possibilities and "technology" of applying the sensitivity algorithm for estimating the parameters of a given equation and to show that the proposed method and the numerical algorithm that implements it allow us to quite successfully solve the problem under consideration and they are suitable for solving many similar applied problems related to estimation of parameters of ordinary differential equations.Based on the results of the work, the proposed method and the numerical algorithm that implements it have shown their efficiency and can be further used to automate real control objects in various fields of science and technology.

1. Eykhoff P. System identification: parameter and state estimation. London, John Wiley and Sons, 1974. 555 p. (Russ. ed.: Eikkhoff P. Osnovy identifikatsii sistem upravleniya: otsenivanie parametrov i sostoyaniya. Мoscow, Мir Publ., 1975. 680 p.).

2. Yurevich E.I. Teoriya avtomaticheskogo upravleniya [Theory of automatic control]. 4th ed., rev. St. Petersburg, BHV-Petersburg Publ., 2016. 560 p.

3. Vasin V.V. Ob ustoichivom vychislenii proizvodnoi v prostranstve C(−∞,∞) [The stable evaluation of a derivative in space C(−∞, ∞)]. Zhurnal vychislitel'noi matematiki i matematicheskoi fiziki = USSR Computational Mathematics and Mathematical Physics, 1973, vol. 13, no. 6, pp. 1383–1389. (In Russian).

4. Tikhonov A.N., Arsenin V.Ya. Metody resheniya nekorrektnykh zadach [Methods for solving ill-posed problems]. 2nd ed. Moscow, Nauka Publ., 1979. 286 p.

5. Fikhtengol'ts G.M. Osnovy matematicheskogo analiza. V 2 ch. Ch. 1 [Fundamentals of mathematical analysis. Pt. 1]. St. Petersburg, Lan' Publ., 2001. 440 p.

6. Maistrenko A.V., Svetlakov A.A. Kosvennoe izmerenie raskhoda zhidkosti perekachivaemoi nasosnymi agregatami [The indirect measurement of oil flow rate, delivered with a pump unit]. Doklady TUSUR = Proceedings of TUSUR University, 2014, no. 4 (34), pp. 215–220.

7. Maistrenko A.V., Svetlakov A.A., Starovoitov N.V. Tsifrovoe differentsirovanie signalov v real'nom masshtabe vremeni s primeneniem skol'zyashchei kvadratichnoi approksimatsii [Digital differentiation of signals in real time with moving square approximation]. Omskii nauchnyi vestnik = Omsk Scientific Bulletin, 2006, no. 7 (43), pp. 110–113.

8. Maistrenko A.V., Svetlakov A.A., Starovoitov N.V. Tsifrovoe differentsirovanie signalov na osnove skol'zyashchei kvadratichnoi approksimatsii i ego primenenie v sinteze PID-regulyatorov approksimatsii [Digital differentiation signals based on moving quadratic approximation and its application in the synthesis of PID-regulators]. Omskii nauchnyi vestnik = Omsk Scientific Bulletin, 2016, no. 1 (145), pp. 73–77.

9. Jabo V.V., Uvarov V.V. Gidravlika i nasosy [Hydraulics and pumps]. 2nd ed., rev. Moscow, Energoatomizdat, 1984. 327 p.

10. Tikhonov A.N. O nekorrektnykh zadachakh lineinoi algebry i ustoichivom metode ikh resheniya [On incorrect problems of linear algebra and a stable method for their solution]. Doklady Akademii nauk SSSR, 1965, vol. 163, no. 3, pp. 591–594. (In Russian).

11. Maistrenko A.V., Svetlakov A.A., Starovoitov N.V. Regulyarizatsiya prosteishego algoritma tsifrovogo differentsirovaniya signalov [Regularization of the elementary algorithm of digital differentiation of signals]. Nauchnyi vestnik Novosibirskogo gosudarstvennogo tekhnicheskogo universiteta = Science Bulletin of the Novosibirsk State Technical University, 2006, no. 4 (25), pp. 53–65.

12. Maistrenko A.V., Svetlakov A.A., Starovoitov N.V. Tsifrovoe differentsirovanie izmeryaemykh signalov s primeneniem integral'nykh uravnenii V. Vol'terra i ego regulyarizatsiya [Digital differentiation of measured signals with application of the integrated equations of V. Volterra and its regularization]. Omskii nauchnyi vestnik = Omsk Scientific Bulletin, 2013, no. 2 (120), pp. 308–312.

13. Tomovic? R., Vukobratovic? M. Obshchaya teoriya chuvstvitel'nosti [General sensitivity theory]. Moscow, Sovetskoe radio Publ., 1972. 240 p. (In Russian).

14. Il'in V.A. Osnovy matematicheskogo analiza. V 2 ch. Ch. 1 [Fundamentals of mathematical analysis. In 2 pt. Pt. 1]. Moscow, Fizmatlit Publ., 2005. 648 p.

15. Cruceanu S. Regularisation pour les problemes a operateurs monotones et la methode de Galerkine. Commentationes Mathematicae Universitatis Carolinae, 1971, vol. 12, no. 1, pp. 1–13. (In French).