A Simple Method for Identifying Mechanical Parameters Based on Integral Calculation

  • Han, Sang-Heon ;
  • Yoo, Anno ;
  • Yoon, Sang Won ;
  • Yoon, Young-Doo
  • Received : 2015.07.22
  • Accepted : 2016.04.04
  • Published : 2016.07.20


A method for the identification of mechanical parameters based on integral calculation is presented. Both the moment of inertia and the friction constant are identified by the method developed here, which is based on well-known mechanical differential equations. The mechanical system under test is excited according to a pre-determined low-frequency sinusoidal motion, minimizing the distortion, and increasing the accuracy of the results. The parameters are identified using integral calculation, increasing the robustness of the results against measurement noise. Experimental data are supported by simulation, confirming the effectiveness of the proposed technique. The performance improvements shown here are of use in the design of speed and position controllers and observers. Owing to its simplicity, this method can be readily applied to commercial inverter products.


Integral calculation;Mechanical parameter identification;Moment of inertia;off-line identification;Viscous friction coefficient


  1. S. K. Kuo and C. H. Menq, “Modeling and control of a six-axis precision motion control stage,” IEEE/ASME Trans. Mechatronics, Vol. 10, No. 1, pp. 50–59, Feb. 2005.
  2. J. H. Kim, J. W. Choi, and S. K. Sul, “ High precision position control of linear permanent magnet synchronous motor for surface mount device placement system,” Conf. Rec. of PCC, pp. 37-42, 2002.
  3. D. Li-Jun, S. Da-nan, D. Kan, Z. Lei-Ting, and L. Zhi-Gang, “Optimized design of discrete traction induction motor model at low-switching frequency,” IEEE Trans. Power Electron., Vol. 28, No. 10, pp. 4803-4810, Oct. 2013.
  4. S. Ziaeinejad, Y. Sangsefidi, H. P. Nabi, and A. Shoulaie, “Direct torque control of two-phase induction and synchronous motors,” IEEE Trans. Power Electron., Vol. 28, No. 8, pp. 4041-4050, Aug. 2013.
  5. S. K. Sahoo, S. Dasgupta, S. K. Panda, and J. X. Xu, “A lyapunov function-based robust direct torque controller for a switched reluctance motor drive system,” IEEE Trans. Power Electron., Vol. 27, No. 2, pp. 555-564, Feb. 2012.
  6. M. Pacas and J. Weber, “Predictive direct torque control for the PM synchronous machine,” IEEE Trans. Ind. Electron., Vol. 52, No. 5, pp. 1350-1356, Oct. 2005.
  7. H. Jiabing and Z. Q. Zhu, “Improved voltage-vector sequences on deadbeat predictive direct power control of reversible three-phase grid-connected voltage-source converters,” IEEE Trans. Power Electron., Vol. 28, No. 1, pp. 254-267, Jan. 2013.
  8. J. C. Moreno, J. M. E. Huerta, R. G. Gil, and S. A. Gonzalez, “A robust predictive current control for three-phase grid-connected inverters,” IEEE Trans. Ind. Electron., Vol. 56, No. 6, pp. 1993-2004, Jun. 2009.
  9. H. B. Shin and J. G. Park, “Anti-windup PID controller with integral state predictor for variable-speed motor drives,” IEEE Trans. Ind. Electron., Vol. 59, No. 3, pp. 1509-1516, Mar. 2012.
  10. W. S. Huang, C. W. Liu, P. L. Hsu, and S. S. Yeh, “Precision control and compensation of servomotors and machine tools via the disturbance observer,” IEEE Trans. Ind. Electron., Vol. 57, No. 1, pp. 420-429, Jan. 2010.
  11. T. J. Kweon and D. S. Hyun, “High-performance speed control of electric machine using low-precision shaft encoder,” IEEE Trans. Power Electron., Vol. 14, No. 5, pp. 838-849, Sep. 1999.
  12. H. Kobayashi, S. Katsura, and K. Ohnishi, “An analysis of parameter variations of disturbance observer for motion control,” IEEE Trans. Ind. Electron., Vol. 54, No. 6, pp. 3413-3421, Dec. 2007.
  13. J. Yao, Z. Jiao, and D. Ma, “Adaptive robust control of DC motors with extended state observer,” IEEE Trans. Ind. Electron., Vol. 61, No. 7, pp. 3630-3637, Jul. 2014.
  14. J. W. Choi, S. C. Lee, and H. G. Kim, “Inertia identification algorithm for high-performance speed control of electric motors,” IEE Proc.— Electr. Power Appl., Vol. 153, No. 3, pp. 379-386, 2006.
  15. K. B. Lee, J. Y. Yoo, J. H. Song, and I. Choy, “Improvement of low speed operation of electric machine with an inertia identification using ROELO,” IEE Proc.— Electr. Power Appl., Vol. 151, No. 1, pp. 116-120, Jan. 2004.
  16. A. K. Sanyal, M. Chellappa, J. L. Valk, J. Ahmed, J. Shen, and D. S. Bernstein, "Globally convergent adaptive tracking of spacecraft angular velocity with inertia identification and adaptive linearization," in Proc. 42nd IEEE Int. Conf. Decision Control, Vol. 3, pp. 2704-2709, 2003.
  17. Y. Guo, L. Huang, and M. Muramatsu, "Research on inertia identification and auto-tuning of speed controller for AC servo system," in Proc. Power Conversion Conf., Vol. 2, pp. 896-901, 2002.
  18. N. Li, X. Dianguo, Y. Ming, G. Xianguo, and L. Zijian, “On-line inertia identification algorithm for PI parameters optimization in speed loop,” IEEE Trans. Power Electron., Vol. 30, No. 2, pp. 849-859, Feb. 2015.
  19. T. S. Kwon, S. K. Sul, H. Nakamura, and K. Tsuruta, “Identification of the mechanical paramteres for servo drive,” Conf. Rec. of IAS Annual Meeting, pp. 905-910, 2006.
  20. F. Andoh, “Moment of inertia identification using the time average of the product of torque reference input and motor position,” IEEE Trans. Power Electron., Vol. 22, No. 6, pp. 2534-2542, Nov. 2007.
  21. F. Andoh, "Inertia identification method based on the product of the integral of torque reference input and motor speed," in Proc. IEEE Int. Conf. Control Appl., pp. 1151-1158, 2008.
  22. R. Garrido and A. Concha, “Inertia and friction estimation of a velocity-controlled servo using position measurements,” IEEE Trans. Ind. Electron., Vol. 61, No. 9, pp. 4759-4770, Sep. 2014.
  23. T. Ohmae, T. Matsuda, K. Kamiyama and M. Tachikawa, “A microprocessor-controlled high-accuracy wide-range speed regulator for motor drives,” IEEE Trans. Ind. Electron., Vol. 29, No. 3, pp. 207-211, Aug. 1982.
  24. H. W. Kim and S. K. Sul, “A new motor speed estimator using Kalman filter in low-speed range,” IEEE Trans. Ind. Electron., Vol. 43, No. 4, pp. 498-504, Aug. 1996.