Study of Dynamic Modes of Current Stabilization Systems of Powerful Electromagnets with Pulse-Width Modulation

This study is devoted to the consideration of a method for assessing the stability of systems with pulse-width modulation, based on the linearization of its equivalent system with pulse-width modulation. An approximate study of the dynamic modes of operation of systems with pulse-width modulation, taking into account the stability for the system of automatic control of the supply current of electromagnets under the conditions of external and internal interference, is carried out. Variants of execution of schemes of pulse-width regulators for the power supply of an electromagnet based on a unipolar and bipolar element with pulse-width modulation are presented. The possibility of linearization of systems with pulse-width modulation for the subsequent detailed assessment of the stability of such systems is shown. The prospects of using functional differential equations for stability analysis of automatic systems with pulse-width modulation are shown. The frequency characteristics of an equivalent pulse system are analyzed using the example of a current stabilization system of high-power electromagnets with a pulse-width regulator, taking into account the replacement of the latitude modulation by the amplitude one. Based on the analysis of the resulting transfer function, which is a stable linearized equivalent open system, the ways of evaluating the stability of the original system with pulse-width modulation using the Nyquist stability criterion are proposed. The conclusion is made about the advantage of a system with PWM, in relation to a system with AIM, in terms of stability, and recommendations are given for the use of the obtained data in the analysis oftransients in such systems.

1. Yakubovich V. A. About pulsed control systems with latitudinal modulation, Dokl. Academy of Sciences of the USSR,1968, vol. 180, pp. 283—285 (in Russian).

2. Vorotnikov V. I., Martyshenko Yu. G. To Problem of Partial Stability of Nonlinear Discrete-Time Systems, Mekhatronika, Avtomatizatsiya, Upravlenie, 2017, vol. 18, no. 6, pp. 371—375 (in Russian).

3. Dikusar Yu. G., Kuznetsova N. I. The study of the absolute sustainability of nonlinear discrete automatic control systems, Energy Installations and Technologies, 2017, no. 3, pp. 20—25 (in Russian).

4. Fa ld in N. V. , Feof ilov S. V. , Koz yr A. V. On a method of linearization of control systems operating in PWM, Izvestiya Tulgu. Technical Science, 2016, vol. 12, no. 4, pp. 61—64 (in Russian).

5. Abramov S. S. Assessment of the stability of the latitude and pulse system by the method of approximate analysis, Bulletin of TSTU, 2010, vol. 16, no. 3, pp. 528—532 (in Russian).

6. Helig A. Kh., Churilov A. N. Frequency methods in the theory of stability of control systems with pulse modulation, Automatic. and Telemeh., 2006, vol. 11, no. 11, pp. 60—76 (in Russian).

7. Mouton H. du T., Cox S. M., McGrath B., Risbo L., Putzeys B. Small-Signal Analysis of Naturally-Sampled SingleEdge PWM Control Loops, Power Electronics IEEE Transactions on,2018, vol. 33, no. 11, pp. 51—64.

8. He Sh., Chunjiang Q., Yunlei Z. Analysis of a Chain of Integrators with Pulse-Width-Modulation Controller, American Control Conference (ACC),2020, pp. 3653—3658

9. Bordry F., Dupaquier A. High Current, Low Voltage Power Converters for LHC. Present development Directions, Proc. of the EPAC-96,1996, vol. 3, pp. 2314.

10. Tsapkin Ya. Z. Theory of nonlinear impulse systems, Moscow, Nauka, 1973. 416 p (in Russian).

11. Urman E. L. On the transfer function of the DC motor controlled by a change in excitation voltage, Avtomat. and Telemeh., 1958, vol. 6, no. 19, pp. 609—613 (in Russian).

12. Zhits M. Z. Transient processes in DC, Moscow, Energia, 1974, 112 p. (in Russian).

13. Merkel B., Thirumalai K., Tarlton J. E., Sch fer V. M., Balance C., Harty T. P., Lucas D. M. Magnetic field stabilization system for atomic physics experiments, The Review of scientific instruments, 2019, vol. 90, iss. 4, pp. 044702.

14. Zhang Z., Han H., Zhao Q., Ye L. Stability Analysis of Pulse-Width-Modulated Feedback Systems with Time-Varying Delays, Mathematical Problems in Engineering,2014, Vol. 2014, Article ID 686389, 7 p.

15. Andean P. E. Analysis of pulse duration sampled data systems with linear elements, IRE Trans. Automat. Contr., 1960. Sept., vol. 9, pp. 17—22.

16. Nease R. E. Analysis and design of non linear sampled date control systems, Mars. Inst.Techn. Cambridge W. A. D.C., Techn. note, 1957, June, pp. 57—162.

17. Lur’e M. S. Research the possibility of linearization of systems with pulse modulation (PWM), LPI works, 1976, no. 355, pp. 28—32 (in Russian).

18. Kovachin S. A, Lur’e M. S. Approximate study of the dynamic modes of automatic control systems with pulse modulation, Automation of production: Interunion. Sat, 1979, vol. 2, pp. 67—76 (in Russian).