Application of the Surveillance Device in the Control System for an Electromechanical System with Distributed Parameters in its Mechanical Part

A system with distributed parameters in its mechanical part is considered. Examples of such a system are given. The reason for taking into account the distribution of parameters in such systems is indicated. Existing methods of research and calculation of control systems are considered. The boundary value problem for a system with distributed parameters is presented. The use of a surveillance device as one of the ways to implement a control system for a system with distributed parameters is proposed. The necessity of using a closed control system and the complexity of its implementation are demonstrated. A block diagram of the control method being developed is presented. Also, transfer functions describing a system with distributed parameters are given; the mathematical calculation of the surveillance device is given as well. A method for implementing a closed control system along an intermediate coordinate for an electromechanical system with distributed parameters in the mechanical part using a surveillance device has been obtained. The surveillance device is in feedback and restores the output speed without measuring it directly. A general view of the transfer function is determined for the surveillance device. The advantages and disadvantages of the transfer function of the surveillance device and a graphical view of a simple implementation of the surveillance device with a dedicated auxiliary device in feedback are presented. An approximation that is used for systems with distributed parameters is described. Approximation conclusions are obtained. According to the parameters of the experimental installation, approximated transfer functions of the mechanical part of the system with distributed parameters without a surveillance device and with a surveillance device are obtained. The LACH of the mechanical part of the system with distributed parameters with a surveillance device and without a surveillance device for an experimental installation for the simplest case is presented, as well as a method for implementing a closed control system along an intermediate coordinate for an electromechanical system with distributed parameters in the mechanical part using a surveillance device.

1. Zames G., Kallman R. (1970) On Spectral Mapping, Higher Order Circle Criteria and Periodically Varying System. IEEE Transactions on Automatic Control, 15 (6), 649–652. https://doi.org/10.1109/tac.1970.1099587.

2. Jagannathan S. (2006) Neural Network Control of Nonlinear Discrete-Time Systems. CRC Press. 622. https://doi.org/10.1201/9781420015454.

3. Rassudov L. N., Myadzel V. N. (1987) Electric Drives with Distributed Parameters of Electromechanical Elements. Leningrad, Energoatomizdat Publ. 144 (in Russian).

4. Brocket R. W. (1966) The Status of Stability Theory for Deterministic Systems. IEEE Transactions on Automatic Control, 11 (3), 596–606. https://doi.org/10.1109/tac.1966.1098354.

5. Ortega R., Tarallo M. (2003) Almost Periodic Equations and Conditions of Ambrosetti – Prodi Type. Mathematical Proceedings of the Cambridge Philosophical Society, 135 (2), 239–254. https://doi.org/10.1017/s0305004103006662.

6. Butkovsky A. G. (1975) Control Methods for Systems with Distributed Parameters. Moscow, Nauka Publ. 230 (in Russian).

7. Doetsch G. (1971) Guide to the Practical Application of the Laplace Transform and Z-Transform. Mоscow, Nauka Publ. 288 (in Russian).

8. Bakhvalov N. S., Zhidkov N. P., Gobelkov G. M. (1987) Numerical Methods. Moscow, Nauka Publ. 632 (in Russian).

9. Butenin N. V. (1991) Introduction to the Theory of Nonlinear Oscillations. Moscow, Nauka Publ. 256 (in Russian).

10. Nagendga K. S., Taylor J. H. (1973) Frequency Domain Criteria for Absolute Stability. Academic Press, N. Y. and London. 358.

11. Corduneanu C. (1973) Integral Equations and Stability of Feedback Systems. Acad. Press, N. Y. 357.

12. Terekhov V. M. (1966) Accounting for the Elasticity of Long Ropes in the Dynamics of the Electric Drive of Lifts. Elektpichestvo [Electricity], (11), 60–65 (in Russian).

13. Willems J. C. (1968) On the Asymptotic Stability of the Null Solution on Linear Differential Equations with Periodic Coefficients. IEEE Transactions on Automatic Control, 13 (1), 65–72. https://doi.org/10.1109/tac.1968.1098793.

14. Vamvoudakis K. G., Jagannathan S. (eds). (2016) Control of Complex Systems. Theory and Applications. Butterworth-Heinemann. 386. https://doi.org/10.1016/C2015-0-02422-4.

15. Kuzovkov N. T. (1976) Modal Control and Monitoring Devices. Moscow, Mashinostroenie Publ. 184 (in Russian).

16. Korneev A. P., Lenevsky G. S. (2005) Involvement of State Observers in Systems with Distributed Parameters. Informatsionnye Tekhnologii, Energetika i Ekonomika: Vaterialy II Mezhregional'noi Nauch.-Tekhn. Konf., Smolensk, 13–14 Aprelya 2005 g. [Information Technologies, Energy and Economics: Proceedings of the II Interregional Scientific and Technical Conference, Smolensk, April 13–14, 2005]. Smolensk, MPEI (TU), 40–44 (in Russian).

17. Korneev A. P. (2017) A New Method for Approximating the Mechanical Section of a Non-Stationary Electromechanical System with Distributed Parameters. Nauka Nastoyashchego i Budushchego: Sb. Materialov v Nauch.-Prakt. Konf. s Mezhdunar. Uchastiem, Sankt-Peterburg, 17–18 Marta 2017 g. [Science of the Present and Future: Collection of Materials of the V Scientific and Practical Conference with International Participation, St. Petersburg, March 17–18, 2017]. St. Petersburg, “LETI” ETU, 168–170 (in Russian).

18. Tolochko O. I. (2004) Analysis and Synthesis of Electromechanical Systems under Observation. Donetsk, Nord-Press Publ. 298 (in Ukrainian).

19. Karneyev A. P., Lenevsky G. S. (2011) Development of a Stand for Research of Systems with the Distributed Parameters. Journal of the Technical University of Gabrovo, 41, 32–35.

20. Jagannathan S., Hao Xu (2016) Optimal Networked Control Systems with MATLAB. CRC Press. 386. https://doi.org/10.1201/b19390.

21. German-Galkin S. G. (2001) Computer Modeling of Semiconductor Systems in MATLAB 6.0. St. Petersburg, Korona Print Publ. 320 (in Russian).

22. Korneev A.P., Lenevsky G. S. (2015) The Program of “Calculation of the Distribution of Resonant Frequencies at Different Positions and Different Weights of the Load”. Application Republic of Belarus No С20150095 (in Russian).