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11
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vol 67 / November, 2024
Article

DOI 10.17586/0021-3454-2016-59-7-517-523

UDC 681.51

ADAPTIVE CONTROL OF UNCERTAIN SYSTEMS UNDER CONDITIONS OF MEASUREMENTS WITH DYNAMIC QUANTIZER

A. A. Margun
ITMO University, Saint Petersburg, 197101, Russian Federation; Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Saint Petersburg, 199178, Russian Federation; Associate professor; Scientific Researcher


I. B. Furtat
ITMO University, Saint Petersburg, 197101, Russian Federation; Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, Saint Petersburg, 199178, Russian Federation; Full Professor; Head of Department, Chief Researcher


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Abstract. An adaptive algorithm of control over linear system with parametric uncertainties under external disturbances and output measurements with dynamic quantizer is presented. The output characteristic of the dynamic quantizer is supposed to be close to the characteristic of static quantizer. Coefficients of the used control model of the object are assumed to belong to a bounded set, and the transfer function numerator is Hurwitz polynomial. The control algorithm is synthesized on the base of the consecutive compensator method proposed by A. A. Bobtsov. The proposed heuristic algorithm for adjustment of integral-type controller parameters and quantization step is based on the use of Kharitonov polynomials. The developed control system provides convergence of tracking error to the bounded region. The efficiency of the proposed method is confirmed by results of computer simulation for an object under the control of the third order with relative degree equal to three. 
Keywords: adaptive control, quantization, disturbances, consecutive compensator, uncertain systems

References:
  1. Golding L.S., Schultheiss P.M.M. Proc. IEEE, 1967, no. 3(55), pp. 293–297.
  2. Goodman D.J., Gersho A. Trans. on Communication, 1974, no. 8(COM-22), pp. 1037–1045.
  3. Zierhofer C.M. IEEE Trans. on Circuits Systems II, 2000, no. 5(47), pp. 408–415.
  4. Venayagamoorthy G.K., Zha W. IEEE Trans. on Industry, 2007, no. 1(43), pp. 238–244.
  5. Furtat I.B. Izv. vuzov. Priborostroenie, 2013, no. 1(56), pp. 26–31. (in Russ.)
  6. Widrow B. Transaction on AIEE, 1961, no. 2(79), pp. 555–567.
  7. Gray R.M., Neuhoff D.L. IEEE Transaction on Information Theory, 1988, no. 44, pp. 2325–2383.
  8. Delchamps D.F. System Control Letters, 1989, no. 13, pp. 365–372.
  9. Fu M., Xie L. IEEE Transactions on Automatic Control, 2005, no. 11(50), pp. 1698–1711.
  10. Margun A., Furtat I. Proc. of the 1st IFAC Conference on Modeling, Identification and Control of Nonlinear Systems (MICNON-2015), St. Petersburg, June 24–26, 2015, pр. 853–857.
  11. Bobtsov A.A. Journal of Computer and Systems Sciences International, 2003, no. 2, pp. 93–97. (in Russ.)
  12. Margun A., Furtat I. Proc. of the 20th Intern. Conf. on Methods and Models in Automation and Robotics, MMAR 2015, Międzyzdroje, Poland, August 24–27, 2015, рp. 341–346.
  13. Brockett R.W., Liberzon D. IEEE Trans. on Automatic Control, 2000, no. 45, pp. 1279–1289.
  14. Bobtsov A.A, Nagovitsina A.G. Automation and Remote Control, 2003, no. 8, pp. 82–95. (in Russ.)
  15. Kharitonov V.L. J. of Difference Equations and Applications, 1979, no. 11(14), pp. 1483.