“Online Identification of a Two-Mass System in Frequency Domain using a Kalman Filter”

Authors: Niko Nevaranta, Stijn Derammelaere, Jukka Parkkinen, Bram Vervisch, Tuomo Lindh, Markku Niemelä and Olli Pyrhönen,
Affiliation: Lappeenranta University of Technology and Ghent University
Reference: 2016, Vol 37, No 2, pp. 133-147.

Keywords: Kalman filter, Non-parametric estimation, Online identification, Short-time DFT, Two-mass system

Abstract: Some of the most widely recognized online parameter estimation techniques used in different servomechanism are the extended Kalman filter (EKF) and recursive least squares (RLS) methods. Without loss of generality, these methods are based on a prior knowledge of the model structure of the system to be identified, and thus, they can be regarded as parametric identification methods. This paper proposes an on-line non-parametric frequency response identification routine that is based on a fixed-coefficient Kalman filter, which is configured to perform like a Fourier transform. The approach exploits the knowledge of the excitation signal by updating the Kalman filter gains with the known time-varying frequency of chirp signal. The experimental results demonstrate the effectiveness of the proposed online identification method to estimate a non-parametric model of the closed loop controlled servomechanism in a selected band of frequencies.

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DOI forward links to this article:
[1] Niko Nevaranta, Jan-Henri Montonen, Tuomo Lindh, Markku Niemela and Olli Pyrhoonen (2017), doi:10.1109/DEMPED.2017.8062344
[2] Jan-Henri Montonen, Niko Juhani Nevaranta, Tuomo Lindh, Jani Alho, Paula Immonen and Olli Pekka Pyrhonen (2017), doi:10.1109/TIE.2017.2782202
[3] Foeke Vanbecelaere, Stijn Derammelaere, Niko Nevaranta, Jasper De Viaene, Florian Verbelen, Kurt Stockman and Michael Monte (2020), doi:10.1016/j.mechatronics.2020.102361
[4] A. Putkonen, N. Nevaranta, O. Liukkonen, M. Niemela and O. Pyrhonen (2020), doi:10.23919/EPE20ECCEEurope43536.2020.9215908
[5] Andriy Lozynskyy, Andriy Chaban, Tomasz Perzy ski, Andrzej Szafraniec and Lidiia Kasha (2021), doi:10.3390/en14071854
[6] Jing-Xiang Zhang and Syh-Shiuh Yeh (2023), doi:10.1109/ICIT58465.2023.10143159
[7] David Ceulemans, Foeke Vanbecelaere, Nick Van Oosterwyck, Jasper De Viaene, Jan Steckel and Stijn Derammelaere (2024), doi:10.1007/s44245-024-00036-9
[8] Kai Xu, Xing Wu, Xiaoqin Liu and Dongxiao Wang (2021), doi:10.3390/machines9090204
References:
[1] deArruda, G. and Barros, P. (2003). deArruda, G, and Barros, P. Relay-based closed loop trasfer function frequency points estimation. Automatica. 39(2):309--315. doi:10.1016/S0005-1098(02)00205-4
[2] Balchen, J. and Lie, B. (1987). Balchen, J, and Lie, B. An adaptive controller based upon continous estimation of the closed loop frequency response. Modeling, Identification and Control. 8(4):223--240. doi:10.4173/mic.1987.4.3
[3] Barkley, A. and Santi, E. (2009). Barkley, A, and Santi, E. Improved online identification of a dc-dc converter and its control loop gain using cross-correlation methods. IEEE Trans. on Power. Elect.. 24(8):2021--2031. doi:10.1109/TPEL.2009.2020588
[4] Beineke, S., Wertz, H., Schutte, F., Grotstollen, H., and Frohleke, N. (1998). Beineke, S, , Wertz, H., Schutte, F., Grotstollen, H., and Frohleke, N. Identification of nonlinear two-mass systems for self-commissioning speed control of electrical drives. in Proc. IEEE IECON. pages 2251--2256. doi:10.1109/IECON.1998.724071
[5] Bhardwaj, M., Choudhury, S., Poley, R., and Akin, B. (2016). Bhardwaj, M, , Choudhury, S., Poley, R., and Akin, B. Online frequency response analysis: A poweful plug-in tool for compensation design and health assessment of digitally controlled power controllers. IEEE Trans. Ind. Appl.. 00(99):1--10. doi:0.1109/TIA.2016.2522951
[6] Bitmead, R., Tsoi, A.C., and Parker, P.J. (1986). Bitmead, R, , Tsoi, A.C., and Parker, P.J. A kalman filtering approach to short-time fourier analysis. IEEE Trans. Acoust., Speech, Signal Process. 34(6):1493--1501. doi:10.1109/TASSP.1986.1164989
[7] Bittanti, S. and Savaresi, S.M. (2000). Bittanti, S, and Savaresi, S.M. On the parameterization and design of an extended kalman filter frequency tracker. EEE Trans. Aut. Cont.). 45(9):1718--1724. doi:10.1109/9.880631
[8] Duda, K. (2010). Duda, K, Accurate, guaranteed stable, sliding discrete fourier transform. IEEE Signal Processing Magazine,. 27(6):124--127. doi:10.1109/MSP.2010.938088
[9] Ferretti, G., Magnani, G., and Rocco, P. (2003). Ferretti, G, , Magnani, G., and Rocco, P. Load behavior concerned pid control for two-mass servo systems. In Proc. of IEEE/ASEM Int. Conf. on Adv. Intelligent Mechatronics. pages 821--826. doi:10.1109/AIM.2003.1225448
[10] Goubej, M. (2015). Goubej, M, Kalman filter based observer design for real-time frequency identification in motion control systems. in Proc. 20th Conf. on Process Control. pages 296--301. doi:10.1109/PC.2015.7169979
[11] Goubej, M., Krej c i, A., and Schlegel, M. (2013). Goubej, M, , Krej c i, A., and Schlegel, M. Robust frequency identification of oscillatory electromechanical systems. in Proc. 18th Conf. on Process Control. pages 79--84. doi:10.1109/PC.2013.6581387
[12] Heath, W. (2001). Heath, W, Bias of indirect non-parametric transfer function estimates for plants in closed loop. Automatica. 37(10):1529--1540. doi:10.1016/S0005-1098(01)00105-48
[13] Holzel, M. and Morelli, E. (2011). Holzel, M, and Morelli, E. Real-time frequency response estimation from flight data. in Proc. AIAA Atmospheric Flight Mechanics Conference. pages 1--26. doi:10.2514/6.2011-6358
[14] Jenssen, A. and Zarrop, M. (1994). Jenssen, A, and Zarrop, M. Frequency domain change detection in closed loop. in Proc. Int. Conf. in Control. pages 676--680. doi:10.1049/cp:19940213
[15] Kamwa, I., Samantaray, S.R., and Joos, G. (2014). Kamwa, I, , Samantaray, S.R., and Joos, G. Wide frequency range adaptive phasor and frequency pmu algorithms. IEEE Trans. Smart Grid.. 5(2):569--579. doi:10.1109/TSG.2013.2264536
[16] Kshirsagar, P., Juang, D., and Zhang, Z. (2016). Kshirsagar, P, , Juang, D., and Zhang, Z. Implementation and evaluation of online system identification of electromechanical systems using adaptive filters. IEEE Trans. Ind. Appl.. 00(99):1--9. doi:10.1109/TIA.2016.2515994
[17] Kurita, Y., Hashimoto, T., and Ishida, Y. (1999). Kurita, Y, , Hashimoto, T., and Ishida, Y. An application of time delay estimation by anns to frequency domain i-pd controller. in Proc. Int. Joint Conf. on Neural Networks. pages 2164--2167. doi:10.1109/IJCNN.1999.832723
[18] LaMaire, R., Valavani, L., Athans, M., and Gunter, S. (1987). LaMaire, R, , Valavani, L., Athans, M., and Gunter, S. A frequency-domain estimator for use in adaptive control systems. in Proc. American Control Conf.. pages 238--244. .
[19] Ljung, L. (2010). Ljung, L, Perspectives on system identification. Annual Reviews in Control. 34(1):1--12. doi:10.1016/j.arcontrol.2009.12.001
[20] Nevaranta, N., Derammelaere, S., Parkkinen, J., Vervisch, B., Lindh, T., Stockman, K., Pyrhonen, O., and Pyrhonen, J. (2016). Nevaranta, N, , Derammelaere, S., Parkkinen, J., Vervisch, B., Lindh, T., Stockman, K., Pyrhonen, O., and Pyrhonen, J. Online identification of a mechanical system in frequency domain using sliding dft. IEEE Trans. Ind. Electron.. 63(9):5712--5723. doi:10.1109/TIE.2016.2574303
[21] Nevaranta, N., Parkkinen, J., Niemelae, M., Lindh, T., Pyrhonen, O., and Pyrhonen, J. (2014). Nevaranta, N, , Parkkinen, J., Niemelae, M., Lindh, T., Pyrhonen, O., and Pyrhonen, J. Recursive identification of linear tooth belt-drive system. in Proc. EPE. pages 1--8. doi:10.1109/EPE.2014.6910904
[22] Nevaranta, N., Parkkinen, J., Niemelae, M., Lindh, T., Pyrhonen, O., and Pyrhonen, J. (2015). Nevaranta, N, , Parkkinen, J., Niemelae, M., Lindh, T., Pyrhonen, O., and Pyrhonen, J. Online estimation of linear tooth-belt drive system parameters. IEEE Trans. Ind. Electron, 2015. 62(11):7214--7223. doi:10.1109/TIE.2015.2432103
[23] Nevaranta, N., Parkkinen, J., Niemelae, M., Lindh, T., Pyrhonen, O., and Pyrhonen, J. (2015). Nevaranta, N, , Parkkinen, J., Niemelae, M., Lindh, T., Pyrhonen, O., and Pyrhonen, J. Online Identification of a Mechanical System in the Frequency Domain with Short-Time DFT. Modeling, Identification and Control, 2015. 36(3):157--165. doi:10.4173/mic.2015.3.3
[24] Olivier, P.D. (1994). Olivier, P, D. Online system identification using laguerre series. in Proc. IEE Control Theory and Application. 141(4):249--254. doi:10.1049/ip-cta:19941239
[25] Ostring, M., Gunnarsson, S., and Norrlof, M. (2001). Ostring, M, , Gunnarsson, S., and Norrlof, M. Closed loop identification of the physical parameters of an industrial robot. In Proc. of 32th Int. Symp. on Robotics. pages 1--20. .
[26] Ostring, M., Gunnarsson, S., and Norrlof, M. (2003). Ostring, M, , Gunnarsson, S., and Norrlof, M. Closed-loop identification of an industrial robot containing flexibilities. Control Engineering Practice. 11(3):291--300. doi:10.1016/S0967-0661(02)00114-4
[27] Parker, P. and Bitmead, R. (1987). Parker, P, and Bitmead, R. Adaptive frequency response identification. in Proc. 28th Conf. on Decision and Control. pages 348--353. doi:10.1109/CDC.1987.272820
[28] Perdomo, M., Pacas, M., Eutebach, T., and Immel, J. (2013). Perdomo, M, , Pacas, M., Eutebach, T., and Immel, J. Identification of variable mechanical parameters using extended kalman filters. in 9th IEEE Int. Symp. on Diagnostics for Electric Machines, Power Electronics and Drives (SPEMPED). pages 377--383. doi:10.1109/DEMPED.2013.6645743
[29] Saarakkala, S. and Hinkkanen, M. (2015). Saarakkala, S, and Hinkkanen, M. Identification of two-mass mechanical systems using torque excitation: Design and experimental evaluation. IEEE Trans. Ind. Appl.. 51(5):4180--4189. doi:10.1109/TIA.2015.2416128
[30] Saupe, F. and Knoblach, A. (2015). Saupe, F, and Knoblach, A. Experimental determination of frequency response function estimates for flexible joint industrial manipulators with serial kinematics. Mechanical Systems and Signal Processing. 52(4):60--72. doi:10.1016/j.ymssp.2014.08.011
[31] Schoukens, J., Pintelon, R., and Rolain, Y. (2000). Schoukens, J, , Pintelon, R., and Rolain, Y. Broadband versus stepped sine frf measurements. IEEE Trans. Instr. Meas.. 49(1):275--278. doi:10.1109/19.843063
[32] Schoukens, J., Vandersteen, G., Rolain, Y., and Pintelon, R. (2012). Schoukens, J, , Vandersteen, G., Rolain, Y., and Pintelon, R. Frequency response function measurements using concatenated subrecords with arbitrary length. IEEE Trans. Instr. Meas.. 61(10):2682--2688. doi:10.1109/TIM.2012.2196400
[33] Schutte, F., Beineke, S., Rolfsmeir, A., and Grotstollen, H. (1997). Schutte, F, , Beineke, S., Rolfsmeir, A., and Grotstollen, H. Online identification of mechanical parameters using extended kalman filters. in Conf. Rec. IEEE-IAS Annual Meeting. pages 501--508. doi:10.1109/IAS.1997.643069
[34] Villwock, S. and Pacas, M. (2008). Villwock, S, and Pacas, M. Application of the welch-method for the identification of two- and three-mass-systems. IEEE Trans. Ind. Electron. 55(1):457--466. doi:10.1109/TIE.2007.909753
[35] Yen, G.G. (1997). Yen, G, G. Frequency-domain vibration control using adaptive neural network. in Proc. Int. Joint Conf. on Neural Networks. pages 806--810. doi:10.1109/ICNN.1997.616126


BibTeX:
@article{MIC-2016-2-5,
  title={{Online Identification of a Two-Mass System in Frequency Domain using a Kalman Filter}},
  author={Nevaranta, Niko and Derammelaere, Stijn and Parkkinen, Jukka and Vervisch, Bram and Lindh, Tuomo and Niemelä, Markku and Pyrhönen, Olli},
  journal={Modeling, Identification and Control},
  volume={37},
  number={2},
  pages={133--147},
  year={2016},
  doi={10.4173/mic.2016.2.5},
  publisher={Norwegian Society of Automatic Control}
};