A New Parameter Identification Algorithm for a Class of Second Order Nonlinear Systems: An On-line Closed-loop Approach

Article

Abstract

This paper presents a novel on-line closed-loop parameter identification algorithm for second order nonlinear systems. Parameter convergence of the proposed methodology is ensured by means of a rigorous Lyapunovbased analysis. The estimated parameters are obtained using the actual and an estimation system. Algebraic techniques are applied for estimating velocity and acceleration signals, which are required in the proposed algorithm. A comparative analysis allows assessing the performance of the new parameter identification algorithm with respect to on-line and off-line least squares algorithms. Numerical simulations indicate that the proposed methodology allows estimating different types of non-linearities, converges faster than other methodologies, is robust against disturbances, outperforms on-line techniques, and provides similar estimates as an off-line technique, but without requiring any type of data pre-processing.

Keywords

Algebraic velocity and acceleration estimation least squares parameter identification persistent excitation second order nonlinear system 

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References

  1. [1]
    H. Garnier, M. Mensler, and A. Richard, “Continuous-time model identification from sampled data: implementation issues and performance evaluation,” Int. J. of Control, vol. 76, no. 13, pp. 1337–1357. 2003. [click]MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    M. Fliess and H. Sira-Ramírez, “Closed-loop parametric identification for continuous-time linear systems via new algebraic techniques,” in H. Garnier and L. Wang (eds): Continuous Time Model Identif. From Sampled Data, Springer, pp. 363–391, 2007. [click]Google Scholar
  3. [3]
    C. Ma, J. Cao, and Y. Qiao, “Polynomial-method-based design of low-order controllers for two-mass systems,” IEEE Trans. Ind. Electron., vol. 60, no. 3, pp. 969–978, 2013. [click]CrossRefGoogle Scholar
  4. [4]
    L. Ljung and T. Söderström, Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA, 1983.MATHGoogle Scholar
  5. [5]
    M. Niedzwiecki, Identification of Time-varying Processes, John Wiley & Sons, Inc., New York, NY, USA, 2000.Google Scholar
  6. [6]
    J. Chen, C. Richard, and J. C. M. Bermudez, “Reweighted nonnegative least-mean-square algorithm,” Signal Processing, vol. 128, pp. 131–141, 2016. [click]CrossRefGoogle Scholar
  7. [7]
    M. Ahsan and M. A. Choudhry, “System identification of an airship using trust region reflective least squares algorithm,” International Journal of Control, Automation and Systems, vol. 15, no. 3, pp. 1384–1393, 2017.CrossRefGoogle Scholar
  8. [8]
    Q. Wu and M. Saif, “Robust fault diagnosis of a satellite system using a learning strategy and second order sliding mode observer,” IEEE Systems Journal, vol. 4, no. 1, 2010.Google Scholar
  9. [9]
    J. A. Moreno and D. Dochain, “Finite time converging input observers for nonlinear second-order systems,” Proc. of 52nd IEEE Conference on Decision and Control, Florence, Italy, December 10-13, 2013.Google Scholar
  10. [10]
    D. Guang-Ren, “Direct parametric control of fully-actuated second-order nonlinear systems-The normal case,” Proc. of the 33rd Chinese Control Conference, Nanjing, China, July 28-30, 2014.Google Scholar
  11. [11]
    X. Cheng, Y. Kawano, and J. M. A. Scherpen, “Reduction of second-order network systems with structure preservation,” IEEE Transactions on Automatic Control, 2017.Google Scholar
  12. [12]
    J. Liu, “Direct parametric control of under-actuated second-order nonlinear systems,” Proc. of 32nd Youth Academic Annual Conference of Chinese Association of Automation (YAC), Hefei, China, May 19-21, 2017.Google Scholar
  13. [13]
    H. Michalska and V. Hayward, “Quantized and sampled control of linear second order systems,” Proc. of the European Control Conference (ECC), Budapest, Hungary, August 23-26, 2009.Google Scholar
  14. [14]
    L. Ljung, System Identification, Prentice Hall, 1987.MATHGoogle Scholar
  15. [15]
    T. Iwasaki, T. Sato, and A. Morita, “Auto-tuning of twodegree-of-freedom motor control for high-accuracy trajectory motion,” Control Eng. Pract., vol. 4, no. 4, pp. 537–544, 1996. [click]CrossRefGoogle Scholar
  16. [16]
    E. J. Adam and E. D. Guestrin, “Identification and robust control for an experimental servo motor,” ISA Trans., vol. 41, no. 2, pp. 225–234, 2002. [click]CrossRefGoogle Scholar
  17. [17]
    Y. Zhou, A. Han, S. Yan, et al., “A fast method for online closed-loop system identification,” The Int. J. Adv. Manuf. Technol., vol. 31, no. 1, pp. 78–84, 2006.CrossRefGoogle Scholar
  18. [18]
    J. S. C. Yuan and W. M. Wonham, “Probing signals for model reference identification,” IEEE Trans. Autom. Control, vol. 22, no. 4, pp. 530–538, 1977. [click]MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    K. J. Aström and T. Bohlin, “Numerical identification of linear dynamic systems from normal operating records,” in Hammond P. H. (eds) Theory Self-Adapt. Control Syst., Springer, Boston, MA, pp. 96–111, 1966.CrossRefGoogle Scholar
  20. [20]
    W. Khalil and E. Dombre, Modeling, Identification and Control of Robots, 3rd Edition, Taylor & Francis, Bristol, 2002.MATHGoogle Scholar
  21. [21]
    V. Adetola and M. Guay, “Parameter convergence in adaptive extremum-seeking control,” Automatica, vol. 43, no. 1, pp. 105–110, 2007.MathSciNetCrossRefGoogle Scholar
  22. [22]
    J. S. Lin and I. Kanellakopoulos, “Nonlinearities enhance parameter convergence in strict feedback systems,” IEEE Trans. Autom. Control, vol. 44, no. 1, pp. 89–94, 1999.MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    X. Wang and F. Ding, “Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle,” Signal Processing, vol. 117, pp. 208–218, 2015.CrossRefGoogle Scholar
  24. [24]
    B. Toplis and S. Pasupathy, “Tracking improvements in fast RLS algorithms using a variable forgetting factor,” IEEE Trans. Acoust., Speech, and Signal Process, vol. 36, no. 2, pp. 206–227, 1988. [click]CrossRefMATHGoogle Scholar
  25. [25]
    R. Miranda-Colorado and J. Moreno-Valenzuela, “An efficient on-line parameter identification algorithm for nonlinear servomechanisms with an algebraic technique for state estimation,” Asian Journal of Control, vol. 19, no. 6, pp. 2127–2142, 2017.MathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    X. Xie, D. Yue, H. Zhang, and Y. Xue, “Control synthesis of discrete-time T-S fuzzy systems via a multi-instant homogeneous polynomial approach,” IEEE Transactions on Cybernetics, vol. 46, no. 3, pp. 630–640, 2016. [click]CrossRefGoogle Scholar
  27. [27]
    X. Xie, D. Yue, H. Zhang, and C. Peng, “Control synthesis of discrete-Time T-S fuzzy systems: reducing the conservatism whilst alleviating the computational burden,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2480–2491, 2017. [click]CrossRefGoogle Scholar
  28. [28]
    A. Besançon-Voda and G. Besançon, “Analysis of a tworelay system configuration with application to Coulomb friction identification,” Automatica, vol. 35, no. 8, pp. 1391–1399, 1999. [click]MathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    K. K. Tan, T. H. Lee, S. N. Huang, and X. Jiang, “Friction modeling and adaptive compensation using a relay feedback approach,” IEEE Transactions on Industrial Electronics, vol. 48, no. 1, pp. 169–176, 2001.CrossRefGoogle Scholar
  30. [30]
    S. L. Chen, K. K. Tan, and S. Huang, “Friction modelling and compensation of servomechanical systems with dualrelay feedback approach,” Trans. Control Syst. Technol., vol. 17, no. 6, pp. 1295–1305, 2009. [click]CrossRefGoogle Scholar
  31. [31]
    M. S. Aslam, “Maximum likelihood least squares identification method for active noise control systems with autoregressive moving average noise,” Automatica, vol. 69, pp. 1–11, 2016.MathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    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, 2014. [click]CrossRefGoogle Scholar
  33. [33]
    R. Garrido and A. Concha, “An algebraic recursive method for parameter identification of a servo model,” IEEE/ASME Trans. Mechatron., vol. 18, no. 5, pp. 1572–1580, 2012. [click]CrossRefGoogle Scholar
  34. [34]
    T. Kara and I. Eker, “Nonlinear closed-loop identification of a DC motor with load for low speed two-directional operation,” Electr. Eng., vol. 86, no. 2, pp. 87–96, 2004.CrossRefGoogle Scholar
  35. [35]
    F. Ding, X. Wang, Q. Chen, and Y. Xiao, “Recursive least squares parameter estimation for a class of output nonlinear systems based on the model decomposition,” Circuits, Syst. Signal Process., vol. 35, no. 9, pp. 3323–3338, 2016. [click]MathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    F. Ding, X. Liu, and M. Liu, “The recursive least squares identification algorithm for a class of Wiener nonlinear systems,” J. Franklin Inst., vol. 353, no. 7, pp. 1518–1526, 2016.MathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    R. Garrido and R. Miranda, “DC servomechanism parameter identification: a closed loop input error approach,” ISA Trans., vol. 51, no. 1, pp. 42–49, 2012.CrossRefGoogle Scholar
  38. [38]
    R. Miranda-Colorado and G. C. Castro, “Closed-loop identification applied to DC servomechanisms: controller gains analysis,” Math. Prob. Eng., Article ID 519432, 10 pages, 2013. [click]Google Scholar
  39. [39]
    J. Ma, W. Xiong, and F. Ding, “Iterative identification algorithms for input nonlinear output error autoregressive systems,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 140–147, 2016. [click]CrossRefGoogle Scholar
  40. [40]
    P. Huang, Z. Lu, and Z. Liu, “State estimation and parameter identification method for dual-rate system based on improved Kalman prediction,” International Journal of Control, Automation and Systems, vol. 14, no. 4, pp. 998–1004, 2016. [click]CrossRefGoogle Scholar
  41. [41]
    Q. Zhang, Q. Wang, and G. Li, “Switched system identification based on the constrained multi-objective optimization problem with application to the servo turntable,” International Journal of Control, Automation and Systems, vol. 14, no. 5, pp. 1153–1159, 2016.CrossRefGoogle Scholar
  42. [42]
    J. Davila, L. Fridman, and A. Poznyak, “Observation and identification of mechanical systems via second order sliding modes,” Int. J. Control, vol. 79, no. 10, pp. 1251–1262, 2006. [click]MathSciNetCrossRefMATHGoogle Scholar
  43. [43]
    H. Xu and C. G. Soares, “Vector field path following for surface marine vessel and parameter identification based on LS-SVM,” Ocean Engineering, vol. 113, pp. 151–161, 2016. [click]CrossRefGoogle Scholar
  44. [44]
    H. Thabet, M. Ayadi, and F. Rotella, “Experimental comparison of new adaptive PI controllers based on the ultralocal model parameter identification,” International Journal of Control, Automation and Systems, vol. 14, no. 6, pp. 1520–1527, 2016. [click]CrossRefGoogle Scholar
  45. [45]
    G. Mamani, J. Becedas, V. Feliu-Batlle, and H. Sira-Ramírez, “Open-and closed-loop algebraic identification method for adaptive control of DC motors,” International Journal of Adaptive Control Signal Processing, vol. 23, no. 12, pp. 1097–1103, 2009.CrossRefMATHGoogle Scholar
  46. [46]
    J. Becedas, M. Mamani, and V. Feliu, “Algebraic parameters identification of DC motors: methodology and analysis,” Int. J. Syst. Sci., vol. 41, no. 10, pp. 1241–1255, 2010. [click]MathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    P. A. Ioannou and J. Sun, Robust Adaptive Control, Dover Publications, 2012.MATHGoogle Scholar
  48. [48]
    S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence and Robustness, Englewood Cliffs NJ Prentice Hall, 1989.MATHGoogle Scholar
  49. [49]
    H. Flanders, “Differentiation under the integral sign,” The Am. Math. Mon., vol. 80, no. 6, pp. 615–627, 1973.MathSciNetCrossRefMATHGoogle Scholar
  50. [50]
    R. Miranda-Colorado and J. M. Valenzuela, “Experimental parameter identification of flexible joint robot manipulators,” Robotica, vol. 36, pp. 313–332, 2018.CrossRefGoogle Scholar
  51. [51]
    J. M. Valenzuela, R. Miranda-Colorado, and C. A. Avelar, “A matlab-based identification procedure applied to a two-degrees-of-freedom robot manipulator for engineering students,” International Journal of Electrical Engineering Education, vol. 54, no. 4, pp. 1–22, 2017.Google Scholar
  52. [52]
    I. P. Mariño and J. Míguez, “On a recursive method for the estimation of unknown parameters of partially observed chaotic systems,” Physica D., vol. 220, pp. 175–182, 2006. [click]MathSciNetCrossRefMATHGoogle Scholar
  53. [53]
    M. Gautier, A. Janot, and P. O. Vandanjon, “A new closed-loop output error method for parameter identification of robot dynamics,” IEEE Trans. Control Syst. Technol., vol. 21, no. 2, pp. 428–444, 2013. [click]CrossRefGoogle Scholar
  54. [54]
    H. Sira-Ramírez, C. G. Rodríguez, J. C. Romero, and A. L. Juárez, Algebraic Identification and Estimation Methods in Feedback Control Systems, Wiley series in Dynamics and Control of Electromechanical Systems, 2014.CrossRefMATHGoogle Scholar
  55. [55]
    B. Borsotto, E. Godoy, D. Beauvois, and E. Devaud, “An identification method for static and Coulomb friction coefficients,” International Journal of Control, Automation, and Systems, vol. 7, no. 2, pp. 305–310, 2009.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CONACyT-Instituto Politécnico Nacional-CITEDIAv. Instituto Politécnico Nacional no. 1310, Nueva TijuanaTijuana, BajaMéxico

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