Skip to main content
Log in

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

  • Linear Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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.

    MathSciNet  MATH  Google Scholar 

  4. Nikiforov, V.O., Robust Output Control of a Linear Object, Autom. Remote Control, 1998, vol. 59, no. 9, part 1, pp. 1274–1283.

    MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  6. Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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. Guretskii, Kh., Analiz i sintez sistem upravleniya s zapazdyvaniem (Analysis and Design of the Delay Control Systems), Moscow: Mashinostroenie, 1973.

    Google Scholar 

  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. 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. Rezvan, V., Absolyutnaya ustoichivost’ avtomaticheskikh sistem s zapazdyvaniem (Absolute Stability of the Automatic Delay Systems), Moscow: Nauka, 1997.

    Google Scholar 

  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. Tsykunov, A.M., Adaptivnoe upravlenie obektami s posledeistviem (Adaptive Control of Plants with Memory), Moscow: Nauka, 1984.

    Google Scholar 

  17. Tsykunov, A.M., Velocity Gradient Algorithms for Delay Systems, Autom. Remote Control, 1987, vol. 48, no. 3, part 2, pp. 353–360.

    MathSciNet  MATH  Google Scholar 

  18. Tsykunov, A.M., Tracking Systems for Linear Plants with Delayed Control, Mekhatronika, Avtomatiz., Upravlen., 2010, no. 3, pp. 9–14.

    Google Scholar 

  19. Tsypkin, Y.Z., Stability of Systems with Retarding Feedback, Autom. Telemekh., 1946, vol. 7, nos. 2, 3, pp. 107–129.

    Google Scholar 

  20. Yanushevskii, R.T., Upravlenie obektami s zapazdyvaniem (Control of Delay Plants), Moscow: Nauka, 1987.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  23. Kristic, M., Delay Compensation for Nonlinear, Adaptive, and PDE Systems, Boston: Birkhauser, 2009.

    Book  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  28. Richard, J.P., Time-delay Systems: An Overview of Some Recent Advances and Open Problems, Automatica, 2003, vol. 39, pp. 1667–1694.

    Article  MathSciNet  MATH  Google Scholar 

  29. Smith, O.J.M., A Controller to Overcome Dead Time, ISA, 1959, vol. 6, pp. 28–33.

    Google Scholar 

  30. Vassilyev, S.N. and Kurdyukov, A.P., 70 let teorii invariantnosti (Seventy Years of the Invariance Theory), Moscow: LKI, 2008.

    Google Scholar 

  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. 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. 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. 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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  37. Kuo, S.M. and Morgan, D., Active Noise Control Systems: Algorithms and DSP Implementations, Hoboken: Wiley, 1995.

    Google Scholar 

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. Nikiforov, V.O., Adaptive Non-Linear Tracking with Complete Compensation of Unknown Disturbances, Eur. J. Control, 1998, vol. 4, no. 2, pp. 132–139.

    Article  MATH  Google Scholar 

  45. Ioannou, P.A. and Sun, J., Robust Adaptive Control, Upper Saddle River: Prentice Hall, 1996.

    MATH  Google Scholar 

  46. Khalil, H., Nonlinear Systems, Upper Saddle River: Prentice Hall, 2002, 3rd. ed.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Pyrkin.

Additional information

Original Russian Text © A.A. Pyrkin, A.A. Bobtsov, V.O. Nikiforov, S.A. Kolyubin, A.A. Vedyakov, O.I. Borisov, V.S. Gromov, 2015, published in Avtomatika i Telemekhanika, 2015, No. 12, pp. 43–64.

This paper was recommended for publication by A.L. Fradkov, a member of the Editorial Board

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pyrkin, A.A., Bobtsov, A.A., Nikiforov, V.O. et al. Compensation of polyharmonic disturbance of state and output of a linear plant with delay in the control channel. Autom Remote Control 76, 2124–2142 (2015). https://doi.org/10.1134/S0005117915120036

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117915120036

Keywords

Navigation