DOI: 10.17586/2226-1494-2018-18-3-384-391


ADAPTIVE ROBUST DISTURBANCE COMPENSATION IN LINEAR SYSTEMS WITH DELAY

A. V. Paramonov


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For citation: Paramonov A.V. Adaptive robust disturbance compensation in linear systems with delay. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 3, pp. 384–391 (in Russian). doi: 10.17586/2226-1494-2018-18-3-384-391

Abstract
 Subject of Research. The paper considers the problem of disturbance compensation for the class of linear time-invariant plants with known parameters and delay.Method. The disturbance is presented as a sum of irregular and regular components. An irregular component is treated as an unknown bounded time function. A regular component is described as unmeasurable output of linear autonomous model (exosystem) with known order and unknown parameters. The problem is resolved with the use of parametrized representation of disturbance designed by means of exosystem state observer and predictor of this state that finally allows applying certainty equivalence principle. In order to remove undesirable influence of delay, a modified adaptation algorithm is created. The algorithm is based on augmentation of the plant state vector and generates advanced adjustable parameters for control. Robust modification of adaptive algorithm is used for keeping stability of closed-loop system in the presence of irregular disturbance. As distinct from widespread approaches the proposed algorithm does not require identification of disturbance parameters and gives the possibility to discard from the control system such restrictions as adaptation gain margin and time delay margin. Main Results. Simulation results obtained in MATLAB/Simulink environment are presented to demonstrate the performance of the proposed approach. The results illustrate the boundedness of all signals in the closed-loop system in the presence of external disturbance. It is shown that the proposed idea enables keeping system stability for different values of input delay. Practical Relevance. Thealgorithm of adaptive compensation is recommended for application in such problems as: the problem of control for active vibration protection devices wherein several dominating harmonics can be taken from the spectrum of vibration signal, control problems of robotic systems with periodical behavior, the problems of ship roll compensation, control problems of space plants in the presence of uncontrollable rotation.

Keywords: adaptive robust control, disturbance compensation, delayed system, internal model

Acknowledgements. This work was partially financially supported by the Government of the Russian Federation (grant 074-U01), the Russian Ministry of Education and Science (project 14.Z50.31.0031).

References
 
  1. Basturk H.I., Krstic M. State derivative feedback for adaptive cancellation of unmatched disturbances in unknown strict-feedback LTI systems. Automatica, 2014, vol. 50, no. 10, pp. 2539–2545. doi: 10.1016/j.automatica.2014.08.002
  2. Bodson M., Douglas S.C. Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequencies. Automatica, 1997, vol. 33, pp. 2213–2221. doi: 10.1016/S0005-1098(97)00149-0
  3. Marino R., Santosuosso G.L., Tomei P. Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency. Automatica, 2003, vol. 39, no. 10, pp. 1755–1761. doi: 10.1016/S0005-1098(03)00170-5
  4. Nikiforov V.O. Adaptive servocompensation of input disturbances. Proc. 13th IFAC World Congress. San-Francisco, USA, 1996, pp. 175–180.
  5. Nikiforov V.O. Nonlinear control system with compensation of external deterministic perturbations. Journal of Computer and Systems Sciences International, 1997, vol. 36, no. 4, pp. 564–568.
  6. Nikiforov V.O. Nonlinear servocompensation of unknown external disturbances. Automatica, 2001, vol. 37, no. 10, pp. 1647–1653. doi: 10.1016/S0005-1098(01)00117-0
  7. Nikiforov V.O. Adaptive non-linear tracking with complete compensation of unknown disturbances. European Journal of Control, 1998, vol. 4, no. 2, pp. 132–139. doi: 10.1016/S0947-3580(98)70107-4
  8. Nikiforov V.O. Adaptive and Robust Control with Perturbations Compensation. St. Petersburg, Nauka Publ., 2003, 282 p. (in Russian)
  9. Francis D.A., Wonham W.N. The internal model principle for linear multivariable regulators. Applied Mathematics and Optimization, 1975, vol. 2, no. 4, pp. 170–194. doi: 10.1007/BF01447855
  10. Johnson C.D. Accommodation of external disturbances in linear regulator and servomechanism problems. IEEE Transactions on Automatic Control, 1971, vol. 16, no. 6, pp. 635–644. doi: 10.1109/TAC.1971.1099830
  11. Pyrkin A., Smyshlyaev A., Bekiaris-Liberis N., Krstic M. Rejection of sinusoidal disturbance of unknown frequency for linear system with input delay. American Control Conference. Baltimore, USA, 2010, pp. 5688–5693.
  12. Basturk H.I., Krstic M. Adaptive sinusoidal disturbance cancellation for unknown LTI systems despite input delay. Automatica, 2015, vol. 58, pp. 131–138. doi: 10.1016/j.automatica.2015.05.013
  13. Bobtsov A.A., Pyrkin A.A. The compensation of a harmonic perturbation under conditions of a delay in control. Journal of Computer and Systems Sciences International, 2008, vol. 47, no. 4, pp. 513–517. doi: 10.1134/S1064230708040035
  14. Gerasimov D.N., Nikiforov V.O., Paramonov A.V. Adaptive disturbance compensation in delayed linear systems: internal model approach. Proc. IEEE Conference on Control Applications. Sydney, Australia, 2015, pp. 1692–1696. doi: 10.1109/CCA.2015.7320853
  15. Pyrkin A.A., Bobtsov A.A. Adaptive controller for linear system with input delay and output disturbance. IEEE Transactions on Automatic Control, 2015, art. 7358095. doi: 10.1109/TAC.2015.2509428
  16. Narendra K.S., Annaswamy A.M. Stable Adaptive Systems. Prentice-Hall, 1989,494 p.
  17. Annaswamy A., Jang J., Lavretsky E. Stability margins for adaptive controllers in the presence of time-delay. AIAA Guidance, Navigation, and Control Conference and Exhibit. Honolulu, Hawaii, 2008, art. 2008-6659. doi: 10.2514/6.2008-6659
  18. GerasimovD.N., Paramonov A.V., Nikiforov V.O. Algorithm of multiharmonic disturbance compensation in linear systems with arbitrary delay: internal model approach. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, vol. 16, no. 6, pp. 1023–1030. (in Russian) doi: 10.17586/2226-1494-2016-16-6-1023-1030
  19. Gerasimov D.N., Paramonov A.V., Nikiforov V.O. Adaptive disturbance compensation in linear systems with input arbitrary delay: internal model approach. Proc. 8th Int. Congress on Ultra Modern Telecommunications and Control Systems and Workshops, ICUMT. Lisbon, Portugal, 2016, pp. 304–309. doi: 10.1109/ICUMT.2016.7765376
  20. Ioannou P.A., Kokotovic P.V. Instability analysis and improvement of robustness of adaptive control. Automatica, 1984, vol. 20, no. 5, pp. 583–594. doi: 10.1016/0005-1098(84)90009-8
  21. Richard J.-P. Time-delay systems: an overview of some recent advances and open problems. Automatica, 2003, vol. 39, no. 10, pp. 1667–1694. doi: 10.1016/S0005-1098(03)00167-5
  22. Nikiforov V.O. Observers of external deterministic disturbances. I. Objects with known parameters. Automation and Remote Control, 2004, vol. 65, no. 10, pp. 1531–1541. doi: 10.1023/B:AURC.0000044264.74470.48


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