Parameters Estimation Algorithm for an Unmeasured Sinusoidal Signal with Time-Varying Amplitude

In this paper the problem of identification algorithm for unknown frequency of a sinusoidal disturbance for a linear plant was considered. This problem is solved in the class of plants with known parameters and a measured of state variables. Regarding the frequency of the sinusoidal disturbance was assumed that the it upper limit is known. Despite the seeming triviality the considered problem is difficult. Using of numerous methods for parameters identification of the measured sinusoidal signals does not give success if the amplitude of sinusoidal disturbance is time-varying. In this paper we will assume that amplitude is the product of an unknown constant by a known strictly positive function of time. For the time-varying strictly positive function we will suppose that the upper boundary of its derivative is known. We note that such assumption on the amplitude of a time-varying sinusoidal disturbance is not a mathematical abstraction. Similar models arise in fault-detection strategy in DC/ AC conversion. It is well known that alternative energy sources require a high level of integration into the electrical power grids. For this purpose, DC/AC and AC/AC power converter are used to provide the coupling, synchronization and appropriate power flow to the electrical networks. These power converters employ high-frequency switching to manipulate the energy conversion process. As a result of a constant operation and load transients, the power switches in the DC/AC and AC/AC topologies are facing voltage, current and temperature stresses that could lead to a fault. After a fault, the DC/AC and AC/AC power converter will not be able to provide a symmetric voltage and current to the electrical network and, consequently, the faulty converter will induce harmonic noise. By evaluating such harmonic noise / disturbance, emergency situations can be avoided. In this paper the asymptotic convergence of the estimation of the frequency of the perturbing effect to the true value is proven. For clarification of design procedure of estimation algorithm and performance illustration an example was presented. The computer simulation results are demonstrating the achievement of a given purpose.

unknown parameters estimation, external disturbance state observers, time-varying signals

1. Fedele G., Ferrise A., D’Aquila G. A global frequency estimator based on a frequency-locked-loop filter, American Control Conference (ACC), 2016, pp. 7001—7006.

2. Aranovskiy S. V., Bobtsov A. A., Kremlev A. S., Nikolaev N. A., Slita O. V. Identification of Frequency of Biased Harmonic Signal, European Journal of Control, 2010, vol. 50, pp. 129—139.

3. Le Van Tuan, Korotina M. M., Bobtsov A. A., Aranovskiu S. V., Pyrkin A. A. Online estimation of time-varying frequency of a sinusoidal signal, IFAC-PapersOnLine, 2019, vol. 52, pp. 245—250.

4. Vedyakov A. A., Vedyakova A. O., Bobtsov A. A., Pyrkin A. A., Aranovskiy S. V. Frequency estimation of a sinusoidal signal with time-varying amplitude, IFAC-PapersOnLine, 2017, vol. 50, pp. 12880—12885.

5. Vedyakov A. A., Vedyakova A. O., Bobtsov A. A., Pyrkin A. A., Kakanov M. A. Frequency estimation of a sinusoidal signal with time-varying amplitude and phase, IFAC-PapersOnLine, 2018, vol. 51, pp. 663—668.

6. Vedyakov A. A., Bobtsov A. A., Pyrkin A. A. Otsenivanie parametrov sinusoidal’nogo signala s nestatsionarnoy amplitudoy (Parameters estimation of a sinusoidal signal with non-stationary amplitude), Izv. vuzov. Priborostroenie, 2017, vol. 60, no. 9, pp. 812—817 (in Russian).

7. Praly L., Isidori A., Marconi L. A new observer for an unknown harmonic oscillator, 17th International Symposium on Mathematical Theory of Networks and Systems, 2006, pp. 24—28.

8. Singh P., Singhal A. Frequency estimation of a sinusoidal signal, 2016 International Conference on Signal Processing and Communication (ICSC), 2016, pp. 320—322.

9. Pyrkin A. A., Bobtsov A. A., Vedyakov A. A., Kolyubin S. A. Estimation of polyharmonic signal parameters, Automation and Remote Control, 2015, vol. 76, no. 8, pp. 1400—1416.

10. Le Van Tuan, Bobtsov A. A. Parameters estimation of a sinusoidal signal with time-varying amplitude, Nauchno-tekhnicheskiy vestnik informatsionnikh tekhnologiy, mekhaniki i optiki, 2018, vol. 18, no. 6, pp. 976—981 (in Russian).

11. Pyrkin A. A., Bobtsov A. A., Kolyubin S. A., Vedyakov A. A., Borisov O. I., Gromov V. S., Margun A. A., Bazylev D. N. Fast Compensation of Unknown Multiharmonic Disturbance for Nonlinear Plant with Input Delay, IFAC Proceedings Volumes, 2013, vol. 46, pp. 546—551.

12. 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 in state and output of a linear system with delay in control channel, Avtomatika I telemekhanika, 2015, no. 12, pp. 43—64 (in Russian).

13. Bobtsov A. A. New approach to the problem of globally convergent frequency estimator, International Journal of Adaptive Control and Signal Processing, 2008, vol. 22, no. 3, pp. 306—317.

14. Salehifar M., Arashloo R. S., Moreno-Eguilaz M., Sala V., and Romeral L. Observer-based open transistor fault diagnosis and fault-tolerant control of five-phase permanent magnet motor drive for application in electric vehicles, IET Power Electronics, 2015, vol. 8, pp. 76—87.

15. Yang S., Bryant A., Mawby P., Xiang D., Ran L., Tavner P. An industry-based survey of reliability in power electronic converters, IEEE Transactions on Industry Applications, 2011, vol. 47, no. 3, pp. 1441—1451.

16. Salimian H., Iman-Eini H. Fault-tolerant operation of three-phase cascaded H-bridge converters using an auxiliary module, IEEE Transactions on Industrial Electronics, 2017, vol. 64, no. 2, pp. 1018—1027.

17. Jlassi I., Estima J. O., El-Khil K., Bellaaj N. M., Marques A. J. Multiple open-circuit faults diagnosis in back-to-back converters of pmsg drives for wind turbine systems, IEEE Transactions on Power Electronics, 2015, vol. 30, no. 5, pp. 2689—2702.

18. Mirafzal B. Survey of fault-tolerance techniques for threephase voltage source inverters, IEEE Transactions on Industrial Electronics, 2014, vol. 61, no. 10, pp. 5192—5202.

19. Miroshnik I. V., Nikiforov V. O., Fradkov A. L. Nonlinear and adaptive control of complex dynamical systems, Saint-Petersburg, Nauka, 2000, 549 p. (in Russian).

20. Sastry S., Bodson M. Adaptive Control: Stability, Convergence and Robustness. Courier Dover Publications, 2011, 400 p.