Automation and Remote Control

, Volume 76, Issue 12, pp 2124–2142 | Cite as

Compensation of polyharmonic disturbance of state and output of a linear plant with delay in the control channel

  • A. A. Pyrkin
  • A. A. Bobtsov
  • V. O. Nikiforov
  • S. A. Kolyubin
  • A. A. Vedyakov
  • O. I. Borisov
  • V. S. Gromov
Linear Systems


A new adaptive algorithm to compensate the unknown a priori multisinusoidal disturbance affecting the plant state and the measured output was proposed. It was intended for the plants that can be unstable, have time delay in the control channel and arbitrary relative degree of the model, as well as be nonminimal-phase, which is much superior to the existing counterparts.


Remote Control Control Channel Exponential Convergence Input Delay Adaptive Observer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Gaiduk, A.R., Design of Nonlinear Selectively Invariant Systems Based on the Controllable Jordan Form, Autom. Remote Control, 2013, vol. 74, no. 7, pp. 1061–1071.CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Gajduk, A.R. and Plaksienko, E.A., Control of Nonlinear Plants with Compensated Uncertain Perturbation, Mekhatronika, Avtomatiz., Upravlen., 2013, no. 1, pp. 2–8.Google Scholar
  3. 3.
    Nikiforov, V.O., Nonlinear Control System with Compensation of the External Deterministic Perturbations, J. Comput. Syst. Sci. Int., 1997, vol. 36, no. 4, pp. 564–568.MathSciNetzbMATHGoogle Scholar
  4. 4.
    Nikiforov, V.O., Robust Output Control of a Linear Object, Autom. Remote Control, 1998, vol. 59, no. 9, part 1, pp. 1274–1283.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Nikiforov, V.O., Observers of External Deterministic Disturbances. I. Objects with Known Parameters, Autom. Remote Control, 2004, vol. 65, no. 10, pp. 1531–1541.CrossRefMathSciNetzbMATHGoogle Scholar
  6. 6.
    Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.CrossRefMathSciNetzbMATHGoogle Scholar
  7. 7.
    Bodson, M. and Douglas, S.C., Adaptive Algorithms for the Rejection of Periodic Disturbances with Unknown Frequencies, Automatica, 1997, vol. 33, pp. 2213–2221.CrossRefMathSciNetzbMATHGoogle Scholar
  8. 8.
    Marino, R., Santosuosso, G., and Tomei, P., Adaptive Stabilization of Linear Systems with Outputs Affected by Unknown Sinusoidal Disturbances, inProc. Eur. Control Conf., Kos, Greece, 2007, pp. 129–134.Google Scholar
  9. 9.
    Marino, R., Santosuosso, G., and Tomei, P., Regulation of Linear Systems with Unknown Additive Sinusoidal Sensor Disturbances, in Proc. 17th World Congr. IFAC, Seoul, Korea, 2008.Google Scholar
  10. 10.
    Marino, R. and Tomei, P., Adaptive Regulator for Uncertain Linear Minimum Phase Systems with Unknown Undermodeled Exosystems, in Proc 17th World Congr. IFAC, Seoul, Korea, 2008.Google Scholar
  11. 11.
    Guretskii, Kh., Analiz i sintez sistem upravleniya s zapazdyvaniem (Analysis and Design of the Delay Control Systems), Moscow: Mashinostroenie, 1973.Google Scholar
  12. 12.
    Eremin, E.L. and Telichenko, D.A., Algorithms of the Adaptive Control-delay System in the Circuit with Extended Error and Reference Leader, Mekhatronika, Avtomatiz., Upravlen., 2006, no. 6, pp. 9–16.Google Scholar
  13. 13.
    Kir’yanen, A.I., Ustoichivost’ sistem s posledeistviem i ikh prilozheniya (Stability of Systems with Memory and Their Application), St. Petersburg: S.-Peterburg. Gos. Univ., 1994.Google Scholar
  14. 14.
    Rezvan, V., Absolyutnaya ustoichivost’ avtomaticheskikh sistem s zapazdyvaniem (Absolute Stability of the Automatic Delay Systems), Moscow: Nauka, 1997.Google Scholar
  15. 15.
    Furtat, I.B. and Tsykunov, A.M., Adaptive Output Control of the Delay Plant, Izv. Vyssh. Uchebn. Zaved., Priborostr., 2005, no. 7, pp. 15–19.Google Scholar
  16. 16.
    Tsykunov, A.M., Adaptivnoe upravlenie obektami s posledeistviem (Adaptive Control of Plants with Memory), Moscow: Nauka, 1984.Google Scholar
  17. 17.
    Tsykunov, A.M., Velocity Gradient Algorithms for Delay Systems, Autom. Remote Control, 1987, vol. 48, no. 3, part 2, pp. 353–360.MathSciNetzbMATHGoogle Scholar
  18. 18.
    Tsykunov, A.M., Tracking Systems for Linear Plants with Delayed Control, Mekhatronika, Avtomatiz., Upravlen., 2010, no. 3, pp. 9–14.Google Scholar
  19. 19.
    Tsypkin, Y.Z., Stability of Systems with Retarding Feedback, Autom. Telemekh., 1946, vol. 7, nos. 2, 3, pp. 107–129.Google Scholar
  20. 20.
    Yanushevskii, R.T., Upravlenie obektami s zapazdyvaniem (Control of Delay Plants), Moscow: Nauka, 1987.Google Scholar
  21. 21.
    Gu, K. and Niculescu, S.I., Survey on Recent Results in The Stability and Control of Time-delay Systems, Trans. ASME, 2003, vol. 125, pp. 158–165.CrossRefGoogle Scholar
  22. 22.
    Kristic, M. and Smyshlyaev, A., Backstepping Boundary Bontrol for First-Order Hyperbolic PDEs and Application to Systems with Actuator and Sensor Delays, Syst. Control Lett., 2008, vol. 57, pp. 750–758.CrossRefGoogle Scholar
  23. 23.
    Kristic, M., Delay Compensation for Nonlinear, Adaptive, and PDE Systems, Boston: Birkhauser, 2009.CrossRefGoogle Scholar
  24. 24.
    Kwon, W.H. and Pearson, A.E., Feedback Stabilization of Linear Systems with Delayed Control, IEEE Trans. Autom. Control, 1980, vol. 25, pp. 266–269.CrossRefMathSciNetzbMATHGoogle Scholar
  25. 25.
    Manitius, A.Z. and Olbrot, A.W., Finite Spectrum Assignment for Systems with Delays, IEEE Trans. Autom. Control, 1979, vol. 24, pp. 541–553.CrossRefMathSciNetzbMATHGoogle Scholar
  26. 26.
    Mazenc, F., Mondie, S., and Francisco, R., Global Asymptotic Stabilization of Feedforward Systems with Delay at the Input, IEEE Trans. Autom. Control, 2004, vol. 49, pp. 844–850.CrossRefMathSciNetGoogle Scholar
  27. 27.
    Olbrot, A.W., Stabilizability, Detectability, and Spectrum Assignment for Linear Autonomous Systems with General Time Delays, IEEE Trans. Autom. Control, 1978, vol. 23, pp. 887–890.CrossRefMathSciNetzbMATHGoogle Scholar
  28. 28.
    Richard, J.P., Time-delay Systems: An Overview of Some Recent Advances and Open Problems, Automatica, 2003, vol. 39, pp. 1667–1694.CrossRefMathSciNetzbMATHGoogle Scholar
  29. 29.
    Smith, O.J.M., A Controller to Overcome Dead Time, ISA, 1959, vol. 6, pp. 28–33.Google Scholar
  30. 30.
    Vassilyev, S.N. and Kurdyukov, A.P., 70 let teorii invariantnosti (Seventy Years of the Invariance Theory), Moscow: LKI, 2008.Google Scholar
  31. 31.
    Kopylova, L.G. and Tararykin, S.V., Compensation of Harmonic Perturbations of the Load Moment in the Electromechanical Tracking Systems and Elements of Controller Structural Optimization, in Vest. Ivanov. Gos. Energet. Univ., 2012, no. 6, pp. 44–51.Google Scholar
  32. 32.
    Tsykunov, A.M., Adaptivnoe i robastnoe upravlenie dinamicheskimi obektami po vykhodu (Adaptive and Robust Output Control of Dynamic Plants), Moscow: Fizmatlit, 2009.Google Scholar
  33. 33.
    Pyrkin, A., Smyshlyaev, A., Bekiaris-Liberis, N., and Krstic, M., Rejection of Sinusoidal Disturbance of Unknown Frequency for Linear System with Input Delay, in Am. Control Conf., Baltimore, USA, 2010.Google Scholar
  34. 34.
    Pyrkin, A., Smyshlyaev, A., Bekiaris-Liberis, N., and Krstic, M., Output Control Algorithm for Unstable Plant with Input Delay and Cancellation of Unknown Biased Harmonic Disturbance, in Time Delay Syst., Prague, Czech Republic, 2010.Google Scholar
  35. 35.
    Aranovskii, S.V., Bobtsov, A.A., and Pyrkin, A.A., Adaptive Observer of an Unknown Sinusoidal Output Disturbance for Linear Plants, Autom. Remote Control, 2009, vol. 70, no. 11, pp. 1862–1870.CrossRefMathSciNetzbMATHGoogle Scholar
  36. 36.
    Bobtsov, A.A. and Pyrkin, A.A., Cancellation of Unknown Multiharmonic Disturbance for Nonlinear Plant with Input Delay, Int. J. Adaptive Control Signal Proc., 2012, vol. 26, no. 4, pp. 302–315.CrossRefMathSciNetzbMATHGoogle Scholar
  37. 37.
    Kuo, S.M. and Morgan, D., Active Noise Control Systems: Algorithms and DSP Implementations, Hoboken: Wiley, 1995.Google Scholar
  38. 38.
    Aranovskiy, S., Adaptive Attenuation of Disturbance Formed as a Sum of Sinusoidal Signals Applied to a Benchmark Problem, in 2013 Eur. Control Conf. (ECC), Zurich, Switzerland, 2013, pp. 2879–2884.Google Scholar
  39. 39.
    Aranovskiy, S. and Freidovich, L.B., Adaptive Compensation of Disturbances Formed as Sums of Sinusoidal Signals with Application to an Active Vibration Control Benchmark, Eur. J. Control, 2013, vol. 19, no. 4, pp. 253–265.CrossRefMathSciNetzbMATHGoogle Scholar
  40. 40.
    Landau, I.D., Castellanos, S.A., Airimitoaie, T.B., and Buche, G., Benchmark on Adaptive Regulation-Rejection of Unknown/Time-varying Multiple Narrow Band Disturbances, Eur. J. Control, 2013, vol. 19, no. 4, pp. 237–252.CrossRefMathSciNetzbMATHGoogle Scholar
  41. 41.
    Bobtsov, A.A., Kolyubin, S.A., and Pyrkin, A.A., Compensation of Unknown Multi-harmonic Disturbances in Nonlinear Plants with Delayed Control, Autom. Remote Control, 2010, vol. 71, no. 11, pp. 2383–2394.CrossRefMathSciNetzbMATHGoogle Scholar
  42. 42.
    Pyrkin, A.A., Adaptive Algorithm to Compensate Parametrically Uncertain Biased Disturbance of a Linear Plant with Delay in the Control Channel, Autom. Remote Control, 2010, vol. 71, no. 8, pp. 1562–1577.CrossRefMathSciNetzbMATHGoogle Scholar
  43. 43.
    Nikiforov, V.O., Adaptive Servocompensation of Input Disturbances, in Proc. 13th IFAC World Congr., San-Francisco, USA, 1996. pp. 175–180.Google Scholar
  44. 44.
    Nikiforov, V.O., Adaptive Non-Linear Tracking with Complete Compensation of Unknown Disturbances, Eur. J. Control, 1998, vol. 4, no. 2, pp. 132–139.CrossRefzbMATHGoogle Scholar
  45. 45.
    Ioannou, P.A. and Sun, J., Robust Adaptive Control, Upper Saddle River: Prentice Hall, 1996.zbMATHGoogle Scholar
  46. 46.
    Khalil, H., Nonlinear Systems, Upper Saddle River: Prentice Hall, 2002, 3rd. ed.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • A. A. Pyrkin
    • 1
    • 2
  • A. A. Bobtsov
    • 1
    • 2
  • V. O. Nikiforov
    • 2
  • S. A. Kolyubin
    • 2
  • A. A. Vedyakov
    • 2
  • O. I. Borisov
    • 2
  • V. S. Gromov
    • 2
  1. 1.Hangzhou Dianzi UniversityHangzhouChina
  2. 2.St. Petersburg National Research University of Information Technologies, Mechanics, and OpticsSt. PetersburgRussia

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