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Sliding-Mode Control of Phase Shift for Two-Rotor Vibration Setup

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Interactive Collaborative Robotics (ICR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14214))

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Abstract

This paper successfully developed and studied a phase shift control system for a two-rotor vibration mechatronic setup, aiming to maintain the desired revolving speed of the rotors. The sliding mode motion was achieved by utilizing a relay controller in the phase loop, while PI controllers were employed in the velocity control loops. Through numerical study and simulations using the parameters of the Mechatronic Vibration Setup SV-2M, the effectiveness of the proposed velocity and phase shift control laws was demonstrated. The possibility of sliding mode occurrence in the phase shift loop was examined through analytical and numerical analysis, confirming its presence. The relationship between the relative degree of the transfer function of the plant and the possibility of the occurrence of a sliding mode is analyzed based on the locus of a perturbed relay system approach. Simulation results indicated that sliding mode motion appeared after a finite transient time and showcased the dynamical properties of the closed-loop system. In conclusion, the findings of this study validate the efficacy of the phase shift control system in achieving the desired rotor speed and demonstrate the feasibility of implementing sliding mode motion in the mechatronic setup.

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References

  1. Pati, C.S., Kala, R.: Vision-based robot following using PID control. Technologies 5(2), 34 (2017)

    Article  Google Scholar 

  2. Aggogeri, F., Borboni, A., Merlo, A., Pellegrini, N., Ricatto, R.: Vibration damping analysis of lightweight structures in machine tools. Materials 10(3), 297 (2017)

    Article  Google Scholar 

  3. Tomchin, D.A., Fradkov, A.L.: Control of rotor passing through the resonance zone on the basis of the high-speed gradient method. J. Mach. Manuf. Reliab. 5(55), 66–71 (2005)

    Google Scholar 

  4. Nonlinear problems of oscillation theory and control theory. Vibration Mechanics: In: Beletsky, V.V., Indeytsev, D.A., Fradkov, A.L. (eds.) Nauka, SPb (2009). (in Russian)

    Google Scholar 

  5. Panovko, G., Shokin, A.E.: Experimental analysis of the oscillations of two-mass system with self-synchronizing unbalance vibration exciters. Vibroengineering Procedia 18(3), 8–13 (2018)

    Article  Google Scholar 

  6. Fradkov, A.L., Tomchina, O.P., Andrievsky, B., Boikov, V.I.: Control of phase shift in two-rotor vibration units. IEEE Trans. Control Syst. Technol. 29(3), 1316–1323 (2021)

    Article  Google Scholar 

  7. Zaitceva, I., Andrievsky, B.: Methods of intelligent control in mechatronics and robotic engineering: a survey. Electronics 11(15) (2022)

    Google Scholar 

  8. Gouskov, A., Panovko, G., Shokhin, A.: To the issue of control resonant oscillations of a vibrating machine with two self-synchronizing inertial exciters. In: Sapountzakis, E.J., Banerjee, M., Biswas, P., Inan, E. (eds.) Proc. 14th Int. Conf. on Vibration Problems 2019, LNME, pp. 515–526. Springer, Singapure (2021)

    Google Scholar 

  9. Fradkov, A., Tomchina, O., Galitskaya, V., Gorlatov, D.: Multiple controlled synchronization for 3-rotor vibration unit with varying payload. In: 5th IFAC Workshop on Periodic Control Systems, pp. 5–10. Elsevier, Amsterdam (2013)

    Google Scholar 

  10. Andrievsky, B., Boikov, V.I., Fradkov, A.L., Seifullaev, R.E.: Mechatronic laboratory setup for study of controlled nonlinear vibrations. In: 6th IFAC Workshop on Periodic Control Systems, pp. 1–6. Elsevier, Amsterdam (2010)

    Google Scholar 

  11. Fradkov, A., Gorlatov, D., Tomchina, O., Tomchin, D.: Control of oscillations in vibration machines: start up and passage through resonance. Chaos 26(11), 116310 (2016)

    Article  MathSciNet  Google Scholar 

  12. Zaitceva, I., Andrievsky, B.: Real-time reinforcement learning of vibration machine PI-controller. In: 6th Scientific School Dynamics of Complex Networks and their Applications, pp. 307–311. IEEE, New York (2022)

    Google Scholar 

  13. Andrievsky, B., Zaitceva, I.: Symmetrical control law for chaotization of platform vibration. Symmetry 14(11) (2022)

    Google Scholar 

  14. Zaitceva, I., Kuznetsov, N.V., Andrievsky, B.: Approach to identifying areas of uncontrolled oscillations in human-machine systems. In: International Russian Smart Industry Conference, pp. 196–201. IEEE, New York (2023)

    Google Scholar 

  15. Andrievsky, B., Zaitceva, I., Barkana, I.: Passification-based robust phase-shift control for two-rotor vibration machine. Electronics 12(4), 1006 (2023)

    Article  Google Scholar 

  16. Blekhman, I.I., Yaroshevich, N.P.: Multiple modes of vibration maintenance of rotation of unbalanced rotors. Proceedings of the Academy of Sciences of the USSR. Machine Science 6, 62–67 (1986). (in Russian)

    Google Scholar 

  17. Blekhman, I.I.: Vibrational Mechanics. Phys.-math. lit, Moscow (1994). (in Russian)

    MATH  Google Scholar 

  18. Blekhman, I.I., Fradkov, A.L. (eds.): Control of Mechatronic Vibrational Units. Nauka, St.Petersburg (2001). (in Russian)

    Google Scholar 

  19. Li, L., Chen, X.: Multi-frequency vibration synchronization and stability of the nonlinear screening system. IEEE Access 7, 171032–171045 (2019)

    Article  Google Scholar 

  20. Jia, L., Wang, C., Liu, Z.: Multifrequency controlled synchronization of four inductor motors by the fixed frequency ratio method in a vibration system. Sci. Rep. 13, 2467 (2023)

    Article  Google Scholar 

  21. Zou, M., Fang, P., Hou, Y., Wang, Y., Hou, D., Peng, H.: Synchronization analysis of two eccentric rotors with double-frequency excitation considering sliding mode control. J. Commu. Nonlin. Sci. Numeri. Simul. 92, 105458 (2021)

    Google Scholar 

  22. Andrievsky, B.R., Blekhman, I.I., Blekhman, L.I., Boikov, V.I., Vasil’kov, V.B., Fradkov, A.L.: Education and research mechatronic complex for studying vibration devices and processes. Prob. Mecha. Eng. Reliab. Machi. 4, 90–97 (2016). (in Russian)

    Google Scholar 

  23. Boikov, V.I., Andrievsky, B., Shiegin, V.V.: Experimental study of unbalanced rotors synchronization of the mechatronic vibration setup. Cybernetics and Physics 5(1), 5–11 (2016)

    Google Scholar 

  24. Tomchin, D.A., Fradkov, A.L.: Control of passage through a resonance area during the start of a two-rotor vibration machine. J. Machi. Manuf. Reliabi. 36(4), 380–385 (2007)

    Article  Google Scholar 

  25. Andrievsky, B., Fradkov, A.L., Tomchina, O.P., Boikov, V.I.: Angular velocity and phase shift control of mechatronic vibration setup. In: 8th IFAC Symposium on Mechatronic Systems, pp. 436–441. Elsevier, Amsterdam (2019)

    Google Scholar 

  26. Blekhman, I.I.: Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications. World Scientific, Singapore (2000)

    Google Scholar 

  27. Blekhman, I.I.: Synchronization in Nature and Technology: Theory and Applications. ASME Press, New York (1988)

    Google Scholar 

  28. Khalil, H.K., Strangas, E.G., Jurkovic, S.: Speed Observer and reduced nonlinear model for sensorless control of induction motors. IEEE Trans. Control Syst. Technol. 17(2), 327–339 (2009)

    Article  Google Scholar 

  29. Joshi, B., Chandorkar, M.: Two-motor single-inverter field-oriented induction machine drive dynamic performance. Sadhana 39(2), 391–407 (2014)

    Article  Google Scholar 

  30. Giri, F.: AC Electric Motors Control: Advanced Design Techniques and Applications. John Wiley & Sons, Ltd., Chichester, UK (2013)

    Google Scholar 

  31. Ljung, L.: System Identification: Theory for the User. Prentice Hall, Upper Saddle River, NJ, USA (1999)

    MATH  Google Scholar 

  32. Fradkov, A.L., Miroshnik, I.V., Nikiforov, V.: Nonlinear and Adaptive Control of Complex Systems. Kluwer, Dordrecht (1999)

    Book  MATH  Google Scholar 

  33. Fradkov, A.L.: Adaptive control in large-scale systems. Nauka, Moscow (1990). (in Russian)

    MATH  Google Scholar 

  34. Andrievsky, B., Fradkov, A.: Implicit model reference adaptive controller based on feedback kalman-yakubovich lemma. In: IEEE Conference on Control Applications, pp. 1171–1174. IEEE, Glasgow (1994)

    Google Scholar 

  35. Andrievskii, B.R., Fradkov, A.: Method of passification in adaptive control, estimation, and synchronization. Autom. Remote. Control. 67(11), 1699–1731 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  36. Landau, J.D.: Adaptive control systems. the model reference approach. Dekker, New York, NY (1979)

    Google Scholar 

  37. Boiko, I.: Analysis of modes of oscillations in a relay feedback system. In: American Control Conference, pp. 1253–1258. IEEE, Boston (2004)

    Google Scholar 

  38. Fradkov, A.: Passification of linear systems with respect to given output. In: 47th IEEE Conference on Decision and Control, pp. 646–651. IEEE, Mexico (2008)

    Google Scholar 

  39. Boiko, I.: Discontinuous Control Systems. Frequency-Domain Analysis and Design. Birkhäuser, Boston (2009)

    MATH  Google Scholar 

  40. Boiko, I.M., Kuznetsov, N.V., Mokaev, R.N., Akimova, E.D.: On asymmetric periodic solutions in relay feedback systems. J. Franklin Inst. 358(1), 363–383 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  41. Boiko, I.: Input-output analysis of limit cycling relay feedback control systems. In: American Control Conference, pp. 542–546. IEEE, San Diego (1999)

    Google Scholar 

  42. Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. Control 58(6), 1247–1263 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  43. Bartolini, G., Levant, A., Pisano, A., Usai, E.: Adaptive second-order sliding mode control with uncertainty compensation. Int. J. Control 89(9), 1747–1758 (2016)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported in part by the St. Petersburg State University grant Pure ID 75207094, by the Leading Scientific Schools of the Russian Federation, project NSh-4196.2022.1.1.

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Authors and Affiliations

  1. Department of Applied Cybernetics, Faculty of Mathematics and Mechanics, St. Petersburg State University, 28, Universitetsky Pr., Stary Peterhof, St. Petersburg, 198504, Russia

    Nikolay Kuznetsov, Boris Andrievsky, Iuliia Zaitceva & Elizaveta Akimova

  2. Institute for Problems in Mechanical Engineering of Russian Academy of Sciences, 61, Bol‘Shoy Prospect V.O., St. Petersburg, 199178, Russia

    Nikolay Kuznetsov, Boris Andrievsky & Iuliia Zaitceva

  3. Department of Automatic Control Systems, St. Petersburg, Electrotechnical University “LETI”, 5, Professora Popova St., St. Petersburg, 197376, Russia

    Iuliia Zaitceva

Authors
  1. Nikolay Kuznetsov
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  2. Boris Andrievsky
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  3. Iuliia Zaitceva
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  4. Elizaveta Akimova
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Corresponding author

Correspondence to Iuliia Zaitceva .

Editor information

Editors and Affiliations

  1. St. Petersburg Federal Research Center of the Russian Academy of Sciences, St. Petersburg, Russia

    Andrey Ronzhin

  2. Institute of Control Systems of Ministry of Science and Education of the Republic of Azerbaijan, Baku, Azerbaijan

    Aminagha Sadigov

  3. V.A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia

    Roman Meshcheryakov

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Kuznetsov, N., Andrievsky, B., Zaitceva, I., Akimova, E. (2023). Sliding-Mode Control of Phase Shift for Two-Rotor Vibration Setup. In: Ronzhin, A., Sadigov, A., Meshcheryakov, R. (eds) Interactive Collaborative Robotics. ICR 2023. Lecture Notes in Computer Science(), vol 14214. Springer, Cham. https://doi.org/10.1007/978-3-031-43111-1_20

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  • DOI: https://doi.org/10.1007/978-3-031-43111-1_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43110-4

  • Online ISBN: 978-3-031-43111-1

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