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Formalization of Requirements for Locked-Loop Control Systems for Their Numerical Optimization

  • Vadim ZhmudEmail author
  • Galina Frantsuzova
  • Lubomir Dimitrov
  • Jaroslav Nosek
Conference paper
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 199)

Abstract

Methods of designing regulators for locked systems have been studied and developed for more than half a century. Recently, due to the development of computing and software, numerical optimization methods have come to the fore. These methods allow you to effectively calculate the controller for a known mathematical model of a particular object. The developer can get positive such calculations even without sufficiently deep knowledge of the theory of regulation. The greatest difficulty lies in the fact that the requirements for the optimization result, formulated in a technical language understandable to the developer, are transformed into formal requirements that can be taken over by the software that performs these calculations. In this article, these requirements are formulated and systematically set out on the basis of a long experience in the development of these methods and their use for a wide variety of different management tasks.

Keywords

Control theory Optimization Numerical modeling Cost functions Objective functions Transient processes Regulator Controllers 

References

  1. 1.
  2. 2.
    Ang, K.H., Chong, G., Li, Y.: PID control system analysis, design, and technology. IEEE Trans. Control Syst. Technol. 4(13), 559–576 (2005)Google Scholar
  3. 3.
    Skogestad, S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 13(4), 291–309 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wang, Q.-G., Zhang, Z., Astrom, K.J., Chek, L.S.: Guaranteed dominant pole placement with PID controllers. J. Process Control 2(19), 349–352 (2009)CrossRefGoogle Scholar
  5. 5.
    Shmaliy, Y.: Continuous-Time Systems. Springer, Dordrecht (2007)CrossRefGoogle Scholar
  6. 6.
    Ichikawa, A., Katayama, H.: Linear Time Varying Systems and Sampled Data Systems. Springer, London (2001)zbMATHGoogle Scholar
  7. 7.
    Amato, F.: Robust Control of Linear Systems Subject to Uncertain Time-Varying Parameters. Springer, Berlin (2006)zbMATHGoogle Scholar
  8. 8.
    Berdnikov, V.P.: Algorithm of determination of non-stationary nonlinear systems full stability areas. Russ. Technol. J. 5(6), 55–72 (2017)Google Scholar
  9. 9.
    Berdnikov, V.P.: Modified algorithm of determination of non-stationary nonlinear systems full stability areas. Russ. Technol. J. 6(3), 39–53 (2018)Google Scholar
  10. 10.
    Sastry, S.: Nonlinear Systems: Analysis, Stability, and Control, p. 668. Springer, New York (1999)CrossRefGoogle Scholar
  11. 11.
    Merlet, J.: Parallel Robots. Solid Mechanics and its Applications, p. 394. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  12. 12.
    Wang, J., Gosselin, C.M.: A new approach for the dynamic analysis of parallel manipulators. Multibody Syst. Dyn. 2(3), 317–334 (1998)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Briot, S., Khalil, W.: Dynamics of Parallel Robots: From Rigid Bodies to Flexible Elements. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  14. 14.
    Zhang, Y., Luo, J., Hauser, K.: Samplingbased motion planning with dynamic intermediate state objectives: application to throwing. In: 2012 IEEE International Conference on Robotics and Automation (ICRA), pp. 2551–2556 (2012)Google Scholar
  15. 15.
    Mori, W., Ueda, J., Ogasawara, T.: 1-DOF dynamic pitching robot that independently controls velocity, angular velocity, and direction of a ball: contact models and motion planning. In: Proceedings of the IEEE, ICRA 2009, pp. 1655–1661 (2009)Google Scholar
  16. 16.
    Senoo, T. Namiki, A., Ishikawa M.: Highspeed throwing motion based on kinetic chain approach. In: Proceedings of the IEEE/RSJ, IROS 2008, pp. 3206–3211 (2008)Google Scholar
  17. 17.
    Kober, J., Wilhelm, A., Oztop, E., Peters, J.: Reinforcement learning to adjust parametrized motor primitives to new situations. Auton. Robots 33(4), 361–379 (2012)CrossRefGoogle Scholar
  18. 18.
    Khalil, H., Saberi, A.: Adaptive stabilization of a class of nonlinear systems using high-gain feedback. IEEE Trans. Autom. Control 32(11), 1031–1035 (1987)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Qian, C., Lin, W.: Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm. IEEE Trans. Automat. Control. 47(10), 1710–1715 (2002)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Marino, R., Tomei, P.: Output regulation for linear minimum phase systems with unknown order exosystem. IEEE Trans. Autom. Control 52, 2000–2005 (2007)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Marino, R., Tomei, P.: Global estimation of unknown frequencies. IEEE Trans. Autom. Control 47, 1324–1328 (2002)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Bobtsov, A.: New approach to the problem of globally convergent frequency estimator. Int. J. Adapt. Control Signal Process. 22(3), 306–317 (2008)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhmud, V., Liapidevskiy, A., Prokhorenko, E.: The design of the feedback systems by means of the modeling and optimization in the program VisSim 5.0/6. In: Proceedings of the IASTED International Conference on Modelling, Identification and Control, AsiaMIC 2010, Phuket, Thailand, 24–26 November 2010, pp. 27–32 (2010)Google Scholar
  24. 24.
    Zhmud, V., Yadrishnikov, O., Poloshchuk, A., Zavorin, A.: Modern key technologies in automatics: structures and numerical optimization of regulators. In: Proceedings of the 2012 7th International Forum on Strategic Technology, IFOST 2012, Tomsk, Russia (2012)Google Scholar
  25. 25.
    Zhmud, V., Yadrishnikov, O.: Numerical optimization of PID-regulators using the improper moving detector in cost function. In: Proceedings of the 8-th International Forum on Strategic Technology 2013, (IFOST-2013), vol. II, Ulaanbaatar, Mongolia, 28 June–1 July, pp. 265–270 (2013)Google Scholar
  26. 26.
    Zhmud, V., Zavorin, A.: Method of designing energy-efficient controllers for complex objects with partially unknown model. In: Proceedings of the XVI International Conference the Control and Modeling in Complex Systems, Samara, Russia, 30 June–3 July 2014, pp. 557–567 (2014)Google Scholar
  27. 27.
    Zhmud, V., Dimitrov, L.: Designing of complete multi-channel PD-regulators by numerical optimization with simulation. In: Proceedings of 2015 International Siberian Conference on Control and Communications, SIBCON 2015 (2015)Google Scholar
  28. 28.
    Zhmud, V., Yadrishnikov, O., Semibalamut, V.: Control of the objects with a single output and with two or more input channels of influence. WIT Trans. Model. Simul. 59, 147–156 (2015). https://www.witpress.comGoogle Scholar
  29. 29.
    Zhmud, V., Dimitrov, L.: Investigation of the causes of noise in the result of multiple digital derivations of signals researches with mathematical modeling. In: 11th International IEEE Scientific and Technical Conference on Dynamics of Systems, Mechanisms and Machines (Dynamics), Omsk, Russia, 14–16 November 2017 (2017)Google Scholar
  30. 30.
    Zhmud, V., Dimitrov, L., Roth, H.: New approach to numerical optimization of a controller for feedback system. In: 2nd International Conference on Applied Mechanics, Electronics and Mechatronics Engineering (AMEME), Beijing, 22–23 October 2017. Destech Publicat Inc. (2017)Google Scholar
  31. 31.
    Zhmud, V., Zavorin, A.: Compensation of the sources of unwanted direction of the transient process in the control of oscillatory object. Autom. Softw. Eng. (3) (2013). http://jurnal.nips.ru/sites/default/files/ASE-3-2013-3.pdf
  32. 32.
    Ivoilov, A., Zhmud, V., Trubin, V., Roth, H.: Using the numerical optimization method for tuning the regulator coefficients of the two-wheeled balancing robot. In: 2018 IEEE Proceedings of the 14th International Scientific-Technical Conference APEIE—44894, Novosibirsk, Russia, pp. 228–236 (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Novosibirsk State Technical UniversityNovosibirskRussia
  2. 2.Faculty of Mechanical EngineeringTechnical University of SofiaSofiaBulgaria
  3. 3.Technical University of LiberecLiberecCzech Republic

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