ALGORITHM OF MULTIHARMONIC DISTURBANCE COMPENSATION IN LINEAR SYSTEMS WITH ARBITRARY DELAY: INTERNAL MODEL APPROACH
Read the full article
For citation: Gerasimov D.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. doi: 10.17586/2226-1494-2016-16-6-1023-1030
Subject of Research. The problem of multiharmonic disturbance compensation for the class of linear time-invariant plants with known parameters and delay is considered. Method. The disturbance is presented 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 enables 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. As distinct from widespread approaches, the proposed algorithm does not require identification of disturbance parameters and gives the possibility to remove 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 proposed approach. Results illustrate the boundness of all signals in the closed-loop system and complete compensation of harmonic signal. It is shown that the proposed idea makes it possible to increase the adaptation gain for different delays without system stability loss. Practical Relevance. The algorithm of adaptive compensation is recommended for the use 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; the problems of control of robotics systems with periodical behavior; the problems of ship roll compensation; the problems of space plants control in the presence of uncontrollable rotation.
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) and the Russian Federation President Grant No.14.Y3116.9281-НШ.
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. Adaptivnoe i Robastnoe Upravlenie s Kompensatsiei Vozmushchenii [Adaptive and Robust Control with Perturbations Compensation]. St. Petersburg, Nauka Publ., 2003, 282 p.
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. 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
17. 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
18. 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