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	A new algorithm for the identification of sinusoidal signal frequency with constant parameters</div>

Nguyen Khac Tung, Vlasov Sergey M., Pyrkin Anton Alexandrovich, Ivan V. Popkov

2022 , VOLUME 22, NUMBER 1 ( january-february )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Editor-in-Chief

Nikiforov
Vladimir O.
D.Sc., Prof.

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doi: 10.17586/2226-1494-2022-22-1-18-24

A new algorithm for the identification of sinusoidal signal frequency with constant parameters

K. Nguyen, S. M. Vlasov, A. A. Pyrkin, I. V. Popkov

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Article in Russian

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Nguyen Kh.T., Vlasov S.M., Pyrkin A.A., Popkov I.V. A new algorithm for the identification of sinusoidal signal frequency with constant parameters. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2022, vol. 22, no. 1, pp. 18–24 (in Russian). doi: 10.17586/2226-1494-2022-22-1-18-24

Abstract

The paper presents a solution for identifying the frequency of a sinusoidal signal with constant parameters. The issue can be relevant for compensation of disturbances, control of dynamic objects, and other tasks. The authors propose a method to improve the quality of the estimation of the sinusoidal signal frequency and to ensure exponential convergence to zero of the estimation errors. At the first stage, the sinusoidal signal is presented as an output signal of a linear generator of finite dimension. The signal parameters (amplitude, phase, and frequency) are unknown. At the second stage, the Jordan form of the matrix and the delay operator are applied to parameterize the sinusoidal signal. After a series of special transformations, the simplest equation is obtained containing product of one frequency-dependent unknown parameter and a known function of time. To find the unknown parameter, the authors used the methods of gradient descent and least squares. A new algorithm for the parametrization of a sinusoidal signal is presented. The solution is based on transforming the signal model to a linear regression equation. The problem is solved using gradient descent and least squares tuning methods based on a linear regression equation obtained by parametrizing a sinusoidal signal. The results involve the analysis of the capabilities of the proposed estimation method using computer modeling in the Matlab environment (Simulink). The results confirmed the convergence of the frequency estimation errors to the true values. The developed method can be effectively applied to a wide class of tasks related to compensating or suppressing disturbances described by sinusoidal or multisinusoidal signals, for example, to control a surface vessel with compensation of sinusoidal disturbances.

Keywords: sinusoidal signal, identification, Jordan form of the matrix, linear regression model

References

Pyrkin A.A., Bobtsov A.A., Efimov D., Zolghadri A. Frequency estimation for periodical signal with noise in finite time. Proc. of the 50^th IEEE Conference on Decision and Control and European Control Conference(CDC-ECC), 2011, pp. 3646–3651. https://doi.org/10.1109/CDC.2011.6160655
Aranovskiy S., Bobtsov A., Ortega R., Pyrkin A. Improved transients in multiple frequencies estimation via dynamic regressor extension and mixing. IFAC-PapersOnLine, 2016, vol. 49, no. 13, pp. 99–104. https://doi.org/10.1016/j.ifacol.2016.07.934
Bobtsov A., Lyamin A., Romasheva D. Algorithm of parameters’ identification of polyharmonic function. IFAC Proceedings Volumes, 2002, vol. 35, no. 1, pp. 439–443. https://doi.org/10.3182/20020721-6-ES-1901.01059
Marino R., Tomei R. Global estimation of n unknown frequencies. IEEE Transactions on Automatic Control, 2002, vol. 47, no. 8, pp. 1324–1328. https://doi.org/10.1109/TAC.2002.800761
Bodson M., Douglas S.C. Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency. Automatica, 1997, vol. 33, no. 12, pp. 2213–2221.https://doi.org/10.1016/S0005-1098(97)00149-0
Khac T., Vlasov S.M., Iureva R.A. Estimating the Frequency of the Sinusoidal Signal using the Parameterization based on the Delay Operators. Proc. of the 18^th International Conference on Informatics in Control, Automation and Robotics (ICINCO), 2021, pp. 656–660. https://doi.org/10.5220/0010536506560660
Sevasteeva E.S., Chernov V.A., Bobtsov A.A. Algorithm for increasing the speed of sinusoidal signal frequency identification. Journal of Instrument Engineering, 2019, vol. 62, no. 9,pp. 767–771. (in Russian). https://doi.org/10.17586/0021-3454-2019-62-9-767-771
Pyrkin A.A., Bobtsov A.A., Nikiforov V.O., Kolyubin S.A., Vedyakov A.A., Borisov O.I., Gromov V.S.Compensation of polyharmonic disturbance of state and output of a linear plant with delay in the control channel. Automation and Remote Control, 2015, vol. 76, no. 12, pp. 2124–2142.https://doi.org/10.1134/S0005117915120036
Bobtsov A.A., Pyrkin A.A.Compensation of unknown sinusoidal disturbances in linear plants of arbitrary relative degree. Automation and Remote Control,2009,vol. 70, no. 3,pp. 449–456.
Bobtsov A.A., Kolyubin S.A., Pyrkin A.A.Compensation of unknown multi-harmonic disturbances in nonlinear plants with delayed control. Automation and Remote Control, 2010, vol. 71, no. 11, pp. 2383–2394.https://doi.org/10.1134/S000511791011010X
Vlasov S., Margun A., Kirsanova A., Vakhvianova P. Adaptive controller for uncertain multi-agent system under disturbances. Proc. of the 16^th International Conference on Informatics in Control, Automation and Robotics(ICINCO), 2019, vol. 2, pp. 198–205.https://doi.org/10.5220/0007827701980205
Vlasov S.M., Borisov O.I., Gromov V.S., Pyrkin A.A., Bobtsov A.A. Algorithms of adaptive and robust output control for a robotic prototype of a surface vessel. Mekhatronika, Avtomatizatsiya, Upravlenie, 2016, vol. 17, no. 1, pp. 18–25. (in Russian). https://doi.org/10.17587/mau.17.18-25
Vlasov S.M., Borisov O.I., Gromov V.S., Pyrkin A.A., Bobtsov A.A. Robust system of dynamic positioning for robotized model of surface craft. Journal of Instrument Engineering,2015, vol. 58, no. 9, pp. 713–719. (in Russian). https://doi.org/10.17586/0021-3454-2015-58-9-713-719
Hsu L., Ortega R., Damm G. A globally convergent frequency estimator. IEEE Transactions on Automatic Control, 1999, vol. 44, no. 4, pp. 698–713. https://doi.org/10.1109/9.754808
Hou M. Amplitude and frequency estimator of a sinusoid. IEEE Transactions on Automatic Control, 2005, vol. 50, no. 6, pp. 855–858. https://doi.org/10.1109/TAC.2005.849244
Lee S.W., Lim J.S., Baek S., Sung K.M. Time-varying signal frequency estimation by VFF Kalman filtering. Signal Processing, 1999, vol. 77, no. 3, pp. 343–347. https://doi.org/10.1016/S0165-1684(99)00085-7
Karimi-Ghartemani M.,Ziarani A.K.A nonlinear time-frequency analysis method. IEEE Transactions on Signal Processing, 2004, vol. 52, no. 6, pp. 1585–1595. https://doi.org/10.1109/TSP.2004.827155
Fedele G., Ferrise A. A frequency-locked-loop filter for biased multi-sinusoidal estimation. IEEE Transactions on Signal Processing, 2014, vol. 62, no. 5, pp. 1125–1134. https://doi.org/10.1109/TSP.2014.2300057
Hall S., Wereley N. Performance of higher harmonic control algorithms for helicopter vibration reduction. Journal of Guidance, Control, and Dynamics, 1993, vol. 16, no. 4, pp. 793–797. https://doi.org/10.2514/3.21085
Nikiforov V.O. Adaptive servomechanism controller with an implicit reference model.International Journal of Control, 1997, vol. 68, no. 2, pp. 277–286. https://doi.org/10.1080/002071797223604
Umari A.M.J., Gorelick S.M. Evaluation of the matrix exponential for use in ground-water-flow and solute-transport simulations: theoretical framework. Water-Resources Investigations Report 86-4096. U.S. Geological Survey, 1986, pp. 12. https://doi.org/10.3133/wri864096
Ljung L. System Identification: Theory for the User.NJ, Prentice-Hall, 1987.

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