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.
Similar content being viewed by others
References
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.
Gajduk, A.R. and Plaksienko, E.A., Control of Nonlinear Plants with Compensated Uncertain Perturbation, Mekhatronika, Avtomatiz., Upravlen., 2013, no. 1, pp. 2–8.
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.
Nikiforov, V.O., Robust Output Control of a Linear Object, Autom. Remote Control, 1998, vol. 59, no. 9, part 1, pp. 1274–1283.
Nikiforov, V.O., Observers of External Deterministic Disturbances. I. Objects with Known Parameters, Autom. Remote Control, 2004, vol. 65, no. 10, pp. 1531–1541.
Tsykunov, A.M., Robust Control Algorithms with Compensation of Bounded Perturbations, Autom. Remote Control, 2007, vol. 68, no. 7, pp. 1213–1224.
Bodson, M. and Douglas, S.C., Adaptive Algorithms for the Rejection of Periodic Disturbances with Unknown Frequencies, Automatica, 1997, vol. 33, pp. 2213–2221.
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.
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.
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.
Guretskii, Kh., Analiz i sintez sistem upravleniya s zapazdyvaniem (Analysis and Design of the Delay Control Systems), Moscow: Mashinostroenie, 1973.
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.
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.
Rezvan, V., Absolyutnaya ustoichivost’ avtomaticheskikh sistem s zapazdyvaniem (Absolute Stability of the Automatic Delay Systems), Moscow: Nauka, 1997.
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.
Tsykunov, A.M., Adaptivnoe upravlenie obektami s posledeistviem (Adaptive Control of Plants with Memory), Moscow: Nauka, 1984.
Tsykunov, A.M., Velocity Gradient Algorithms for Delay Systems, Autom. Remote Control, 1987, vol. 48, no. 3, part 2, pp. 353–360.
Tsykunov, A.M., Tracking Systems for Linear Plants with Delayed Control, Mekhatronika, Avtomatiz., Upravlen., 2010, no. 3, pp. 9–14.
Tsypkin, Y.Z., Stability of Systems with Retarding Feedback, Autom. Telemekh., 1946, vol. 7, nos. 2, 3, pp. 107–129.
Yanushevskii, R.T., Upravlenie obektami s zapazdyvaniem (Control of Delay Plants), Moscow: Nauka, 1987.
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.
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.
Kristic, M., Delay Compensation for Nonlinear, Adaptive, and PDE Systems, Boston: Birkhauser, 2009.
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.
Manitius, A.Z. and Olbrot, A.W., Finite Spectrum Assignment for Systems with Delays, IEEE Trans. Autom. Control, 1979, vol. 24, pp. 541–553.
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.
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.
Richard, J.P., Time-delay Systems: An Overview of Some Recent Advances and Open Problems, Automatica, 2003, vol. 39, pp. 1667–1694.
Smith, O.J.M., A Controller to Overcome Dead Time, ISA, 1959, vol. 6, pp. 28–33.
Vassilyev, S.N. and Kurdyukov, A.P., 70 let teorii invariantnosti (Seventy Years of the Invariance Theory), Moscow: LKI, 2008.
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.
Tsykunov, A.M., Adaptivnoe i robastnoe upravlenie dinamicheskimi obektami po vykhodu (Adaptive and Robust Output Control of Dynamic Plants), Moscow: Fizmatlit, 2009.
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.
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.
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.
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.
Kuo, S.M. and Morgan, D., Active Noise Control Systems: Algorithms and DSP Implementations, Hoboken: Wiley, 1995.
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.
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.
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.
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.
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.
Nikiforov, V.O., Adaptive Servocompensation of Input Disturbances, in Proc. 13th IFAC World Congr., San-Francisco, USA, 1996. pp. 175–180.
Nikiforov, V.O., Adaptive Non-Linear Tracking with Complete Compensation of Unknown Disturbances, Eur. J. Control, 1998, vol. 4, no. 2, pp. 132–139.
Ioannou, P.A. and Sun, J., Robust Adaptive Control, Upper Saddle River: Prentice Hall, 1996.
Khalil, H., Nonlinear Systems, Upper Saddle River: Prentice Hall, 2002, 3rd. ed.
Author information
Authors and Affiliations
Corresponding author
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
About this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117915120036