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UKF 기반한 동역학 시스템 파라미터의 추정

Parameter Estimation of Dynamic System Based on UKF

  • Seung, Ji-Hoon (Electronics and Information Department, Chonbuk National University) ;
  • Chong, Kil-To (Electronics and Information Department, Chonbuk National University)
  • 투고 : 2011.11.16
  • 심사 : 2012.02.10
  • 발행 : 2012.02.29

초록

본 논문은 비선형 시스템의 상태 추정에 널리 사용 되는 Unscented Kalman Filter(UKF)를 활용하여 동역학 시스템의 상태를 추정함과 동시에 파라미터를 추정하였다. 파라미터의 추정은 시스템 제어, 모델링, 성능분석 및 예측 등 다양한 분야에서 매우 중요하다. 공학에서 다루는 대부분의 시스템은 비선형성과 잡음이 존재하므로 파라미터 추정이 매우 어렵다. 이러한 경우에 대하여 본 논문에서는 비선형 필터로서 잡음에 강한 UKF를 이용하여 상태와 파라미터를 추정하였다. 본 논문에서 제안한 파라미터 추정은 기존의 상태방정식에 파라미터 항을 추가하여 확장된 비선형 방정식을 사용하였으며, 진자와 슬라이드로 구성된 2-자유도 동역학 시스템에 적용하였으며, 시스템 운동방정식의 측정 잡음으로 가우시안 잡음을 추가하여 컴퓨터 시뮬레이션을 실시하였다. 시뮬레이션 결과 제안한 방법이 LSM보다 좋은 성능을 보였다. 추정 오차는 3%이내이며, 0.1sec 이내의 수렴하는 것을 확인하였다. 결과적으로 UKF는 상태나 측정 데이터에 잡음이 존재하더라도 시스템의 상태 및 파라미터 추정이 가능하다.

In this paper, the states and the parameters in the dynamic system are simultaneously estimated by applying the UKF(Unscented Kalman Filter), which is widely used for estimating the state of non-linear systems. Estimating the parameter is very important in various fields, such as system control, modeling, analysis of performance, and prediction. Most of the dynamic systems which are dealt with in engineering have non-linearity as well as some noise. Therefore, the parameter estimation is difficult. This paper estimates the states and the parameters applying to the UKF, which is a non-linear filter and has strong noise. The augmented equation is used by including the addition of the parameter factors to the original state equation of the system. Moreover, it is simulated by applying to a 2-DOF(Degree of Freedom) dynamic system composed of the pendulum and the slide. The measurement noise of the dynamic equation is assumed to be a Gaussian distribution. As the simulation results show, the proposed parameter estimation performs better than the LSM(Least Square Method). Furthermore, the estimation errors and convergence time are within three percent and 0.1 second, respectively. Consequentially, the UKF is able to estimate the system states and the parameters for the system, despite having measurement data with noise.

키워드

참고문헌

  1. K. V. Fernando and H. Nicholson, "Identification of linear systems with input and output noise: The Koopmans-Levin method," Proc. Inst. Elect. Eng. D, vol.132, pp. 30-36, 1985.
  2. Pintelon, R., Schoukens, J., "Identification of stochastic linear systems in the presence of Nonlinear Distortion", Instrumentation and Measurement Technology Conference, 2000. IMTC 2000. Proceedings of the 17th IEEE, Vol.2, 879-884, 2000.
  3. Sohns, B., Allison, J., Fathy, H. K., Stein, J. L., "Efficient Parameterization of LargeScale Dynamic Models Through the Use of Activity Analysis", Proceedings of the ASME IMECE 2006, IMECE2006, Nov 5-10, 2006.
  4. Hurtig, J., Yurkovich, S., "Parameter set estimation for nonlinear systems", System Theory, 2001. Proceedings of the 33rd Southeastern Symposium on, 275-280, Mar 2001.
  5. Nagatsuka, H., "A Study of Estimation for the Three-Parameter Weibull Distribution Based On Doubly Type-II Censored Data Using a Least Squares Method", Secure System Integration and Reliability Improvement, 2008. SSIRI '08. Second International Conference on, 158-165, 2008.
  6. Aksoy, S., Muhurcu, A., Kizmaz, H., "State and Parameter Estimation in Induction Motor Using the Extended Kalman Filtering Algorithm", Modern Electric Power Systems (MEPS), 2010 Proceedings of the International Symposium, 2010.
  7. Sahar Pirooz Azad, Joseph Euzebe Tate, "Parameter Estimation of Doubly Fed Induction Generator Driven by Wind Turbine", Power Systems Conference and Exposition (PSCE), 2011 IEEE/PE, March 2011.
  8. Panuska, V. "A new form of the extended Kalman filter for parameter estimation in linear systems with correlated noise", Automatic Control, IEEE Transactions on, Vol.25, 229-235, Apr 1980. https://doi.org/10.1109/TAC.1980.1102269
  9. Emmanuel Blanchard, Adrian Sandu, Corina Sandu, "Parameter Estimation Method using an Extended Kalman Filter", Proceedings of the Joint North America, Asia-Pacific ISTVS Conference and Annual Meeting of Japanese Society for Terramechanics 2007.
  10. Jeng-Ming Chen, Bor-Sen Chen, "System Parameter Estimation with Input/Output Noisy Data and Missing Measurements", IEEE Transactions on Signal Processing, Vol. 48, No. 6, June 2000.
  11. Wang Wan-ping, Liao Sheng, Xing Ting-wen, "Particle Filter for State and Parameter Estimation in Passive Ranging", Intelligent Computing and Intelligent Systems, 2009. ICIS 2009. IEEE International Conference on, Vol.3, 257-261, Nov. 2009.
  12. Jin-Woo Park, Cheol-Kwan Yang, Duk-Sun Shim, "Particle Filter Performance for Ultra-tightly GPS/INS integration", Journal of Institute of Control, Robotics and Systems, Vol. 14, No. 8, August 2008. https://doi.org/10.5302/J.ICROS.2008.14.8.785
  13. S. Julier, J. Uhlmann, "A new extension of the Kalman filter to nonlinear systems", in: Proceedings of the 1997 SPIE AeroSense Symposium, SPIE, 21-24, April 1997.
  14. Julier. S. J, "The Scaled Unscented Transformation", Proceednig of the American Control Conference, Anchorage, AK, Vol.6 4555 - 4559, May 2002.
  15. Joongsup Yun, Chang-Kyung Ryoo, Taek-Lyul Song, "Guidance Filter Design Based on Strapdown Seeker and MEMS Sensors", Journal of the Korean Society for Aeronautical & Space Sciences, vol .37, no. 10, 1002-1009, 2009. https://doi.org/10.5139/JKSAS.2009.37.10.1002
  16. Young-Seok Cho, Duk-Sun Shim, Chel-Kwan Yang, Jin-Woo Park, "Performance Investigation of the Unscented Kalman Filter for Ultra-tightly GPS/INS Integration", Journal of Institute of Control, Robotics and Systems, vol. 13, no. 8, 817-823, 2007. https://doi.org/10.5302/J.ICROS.2007.13.8.817
  17. Oh Shin Kwon, "Parameter Estimation of Recurrent Neural Networks Using A Unscented Kalman Filter Training Algorithm and Its Applications to Nonlinear Channel Equalization", Journal of Korean Institute of Intelligent Systems, vol. 15, no. 5, 552-559, 2005. https://doi.org/10.5391/JKIIS.2005.15.5.552
  18. K. T. Chong, J. H. Park, A. G. Parlos, "Control-Relevant Discretization of Nonlinear Systems With Time-Delay Using Taylor-Lie Series," Journal of Dynamic Systems, Measurement, and Control, Vol.127, 153-159, 2005. https://doi.org/10.1115/1.1870046
  19. Andrew K. Stimac, "Standup and Stabilization of the Inverted Pendulum," MIT, master thesis, 1999.

피인용 문헌

  1. Nonlinear System State Estimating Using Unscented Particle Filters vol.17, pp.6, 2013, https://doi.org/10.6109/jkiice.2013.17.6.1273