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Parameter estimation for control systems based on impulse responses

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  • Control Theory and Applications
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International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

The impulse signal is an instant change signal in very short time. It is widely used in signal processing, electronic technique, communication and system identification. This paper considers the parameter estimation problems for dynamical systems by means of the impulse response measurement data. Since the cost function is highly nonlinear, the nonlinear optimization methods are adopted to derive the parameter estimation algorithms to enhance the estimation accuracy. By using the iterative scheme, the Newton iterative algorithm and the gradient iterative algorithm are proposed for estimating the parameters of dynamical systems. Also, a damping factor is introduced to improve the algorithm stability. Finally, using simulation examples, this paper analyzes and compares the merit and weakness of the proposed algorithms.

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References

  1. X. K. Wan, Y. Li, C. Xia, M. H. Wu, J. Liang, and N. Wang, “A T-wave alternans assessment method based on least squares curve fitting technique,” Measurement, vol. 86, 93–100, May 2016. [click]

    Article  Google Scholar 

  2. J. Pan, X. H. Yang, H. F. Cai, and B. X. Mu, “Image noise smoothing using a modified Kalman filter,” Neurocomputing, vol. 173, 1625–1629, January 2016. [click]

    Article  Google Scholar 

  3. L. Xu, “A proportional differential control method for a time-delay system using the Taylor expansion approximation,” Applied Mathematics and Computation, vol. 236, pp. 391–399, June 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Feng, M. H. Wu, Q. X. Li, et al, “Array factor forming for image reconstruction of one-dimensional nonuniform aperture synthesis radiometers,” IEEE Geoscience and Remote Sensing Letters, vol. 13, no. 2, pp. 237–241, February 2016. [click]

    Article  Google Scholar 

  5. H. E. Emara-Shabaik, “Nonlinear systems modeling & identification using higher order statistics/polyspectra,” Control and Dynamic Systems, vol. 76, pp. 289–322, 1996. [click]

    Article  MATH  Google Scholar 

  6. G. M. Malwatkar, S. H. Sonawane, and L. M. Waghmare, “Tuning PID controllers for higher-order oscillatory systems with improved performance,” ISA Transanctions, vol. 48, no. 3, pp.347–353, 2009.

    Google Scholar 

  7. Q. Fan, Z. Y. Huang, B. Zhang, and D. Y. Chen, “Highorder dynamic modeling and parameter identification of structural discontinuities in Timoshenko beams by using reflection coefficients,” Journal of Sound and Vibration, vol. 332, no. 4, pp. 752–765, 2013. [click]

    Article  Google Scholar 

  8. S. N. Deepa and G. Sugumaran, “Model order formulation of a multivariable discrete system using a modified particle swarm optimization approach,” Swarm & Evolutionary Computation, vol. 1, no. 4, pp. 204–212, 2011. [click]

    Article  Google Scholar 

  9. X. L. Luan, Q. Chen, and F. Liu, “Equivalent Transfer Function based Multi-loop PI Control for High Dimensional Multivariable Systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 346–352, 2015. [click]

    Article  Google Scholar 

  10. L. Xu and F. Ding, “The parameter estimation algorithms for dynamical response signals based on the multiinnovation theory and the hierarchical principle,” IET Signal Processing, vol. 11, no. 2, pp. 228–237, April 2017.

    Google Scholar 

  11. K. Barbé, O. J. Rodriguez, W. V. Moer, and L. Lauwers, “Fractional models for modeling complex linear systems under poor frequency resolution measurements,” Digital Signal Processing, vol. 23, no. 4, pp. 1084–1093, 2013. [click]

    Article  MathSciNet  Google Scholar 

  12. L. Xu, L. Chen, and W. L. Xiong, “Parameter estimation and controller design for dynamic systems from the step responses based on the Newton iteration,” Nonlinear Dynamics, vol. 79, no. 3, pp. 2155–2163, February 2015. [click]

    Article  MathSciNet  Google Scholar 

  13. F. Ding, F. F. Wang, L. Xu, T. Hayat, and A. Alsaedi, “Parameter estimation for pseudo-linear systems using the auxiliary model and the decomposition technique,” IET Control Theory and Applications, vol. 11, no. 3, pp. 390–400, 2017.

    Article  MathSciNet  Google Scholar 

  14. D. Q. Wang and W. Zhang, “Improved least squares identification algorithm for multivariable Hammerstein systems,” Journal of the Franklin Institute, vol. 352, no. 11, pp. 5292–5307, November 2015. [click]

    Article  MathSciNet  Google Scholar 

  15. F. Ding, X. H. Wang, L. Mao, and L. Xu, “Joint state and multi-innovation parameter estimation for time-delay linear systems and its convergence based on the Kalman filtering,” Digital Signal Processing, vol. 62, pp. 211–223, 2017. [click]

    Article  Google Scholar 

  16. J. Pan, X. Jiang, X. K. Wan, and W. Ding, “A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems,” International Journal of Control, Automation, and Systems, vol. 15, no. 3, pp. 1189–1197, June 2017.

    Article  Google Scholar 

  17. L. Xu and F. Ding, “Recursive least squares and multiinnovation stochastic gradient parameter estimation methods for signal modeling,” Circuits, Systems and Signal Processing, vol. 36, no. 4, pp. 1735–1753, April 2017.

    Article  MATH  Google Scholar 

  18. F. Ding, L. Xu, and Q. M. Zhu, “Performance analysis of the generalised projection identification for time-varying systems,” IET Control Theory and Applications, vol. 10, no. 18, pp. 2506–2514, 2016. [click]

    Article  MathSciNet  Google Scholar 

  19. X. H. Wang and F. Ding, “Convergence of the recursive identification algorithms for multivariate pseudo-linear regressive systems,” International Journal of Adaptive Control and Signal Processing, vol. 30, no. 6, pp. 824–842, 2016. [click]

    Article  MathSciNet  Google Scholar 

  20. A. G. Wu, Y. Y. Qian, and W. J. Wu, “Bias compensationbased recursive least-squares estimation with forgetting factors for output error moving average systems,” IET Signal Processing, vol. 8, no. 5, pp. 483–494, 2014. [click]

    Google Scholar 

  21. Y. W. Mao and F. Ding, “A novel parameter separation based identification algorithm for Hammerstein systems,” Applied Mathematics Letters, vol. 60, pp. 21–27, 2016. [click]

    Article  MathSciNet  MATH  Google Scholar 

  22. D. Q. Wang and F. Ding, “Parameter estimation algorithms for multivariable Hammerstein CARMA systems,” Information Sciences, vol. 355, pp. 237–249, 2016.

    Article  MathSciNet  Google Scholar 

  23. T. Liu, Q. G. Wang, and H. P. Huang, “A tutorial review on process identification from step or relay feedback test,” Journal of Process Control, vol. 23, no. 10, pp. 1597–1623, 2013.

    Article  Google Scholar 

  24. S. Ahmed, B. Huang, and S. L. Shah, “Novel identification method from step response,” Control Engineering Practice, vol. 15, no. 5, pp. 545–556, 2007. [click]

    Article  Google Scholar 

  25. S. Ahemd, B. Huang, and S. L. Shah, “Identification from step responses with transient initial conditions,” Journal of Process Control, vol. 2008, no. 2, pp. 121–130, 2008. [click]

    Article  Google Scholar 

  26. E. Hidayat and A. Medvedev, “Laguerre domain identification of continuous linear time-delay systems from impulse response data,” Automatica, vol. 48, no. 11, pp. 2902–2907, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  27. Q. G. Wang, X. Guo, and Y. Zhang, “Direct identification of continuous time delay systems from step responses,” Journal of Process Control, vol. 11. no. 5, pp. 531–542, 2001. [click]

    Article  Google Scholar 

  28. G. Fedele, “A new method to estimate a first-order plus time delay model from step response,” Journal of Franklin Institute, vol. 346, no. 1, pp. 1–9, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  29. Y. Y. Du, J. S. H. Tsai, H. Patil, L. S. Shieh, and Y. Chen, “Indirect identification of continuous-time delay systems from step responses,” Applied Mathematical Modelling, vol. 35, no. 2, pp. 594–611, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  30. S. Y. Li, W. J. Cai, H. Mei, and Q. Xiong, “Robust decentralized parameter identification for two-input two-output process from closed-loop step responses,” Control Engineering Practice, vol. 13, no. 4, pp. 519–531, 2005.

    Article  Google Scholar 

  31. K. H. Ryu, S. N. Lee, C. M. Nam, J. Lee, and S. W. Sung, “Discrete-time frequency response identification method for processes with final cyclic-steady-state,” ournal of Process Control, vol. 24, no. 6, pp. 1002–1014, 2014.

    Article  Google Scholar 

  32. R. C. Panda, V. Vijayan, V. Sujatha, P. Deepa, D. Manamali, and A. B. Mandal, “Parameter estimation of integrating and time delay processes using single relay feedback test,” ISA Transanctions, vol. 50, no. 4, pp. 529–537, 2011.

    Google Scholar 

  33. M. Jafari, M. Salimifard, and M. Dehghani, “Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm,” SA Transanctions, vol. 53, no. 4, pp. 1243–1252, 2014.

    Google Scholar 

  34. M. H. Murillo, A. C. Limache, P. S. F. Rojas, and L. L. Giovanini, “Generalized nonlinear optimal predictive control using iterative state-space trajectories: applications to autonomous flight of UAVs,” International Journal of Control, Automation, and Systems, vol. 13, no. 2, pp. 361–370, 2015. [click]

    Article  Google Scholar 

  35. F. Ding, F. F. Wang, L. Xu, and M. H. Wu, “Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering,” Journal of the Franklin Institute, vol. 354, no. 3, pp. 1321–1339, 2017. [click]

    Article  MathSciNet  MATH  Google Scholar 

  36. J. X. Ma, W. L. 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, January 2016. [click]

    Article  Google Scholar 

  37. L. Xu, “Application of the Newton iteration algorithm to the parameter estimation for dynamical systems,” Journal of Computational and Applied Mathematics, vol. 288, pp. 33–43, November 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  38. L. Xu, “The damping iterative parameter identification method for dynamical systems based on the sine signal measurement,” Signal Processing, vol. 120, pp. 660–667, March 2016. [click]

    Article  Google Scholar 

  39. A. Cordero, J. L. Hueso, E. Martínez, and J. R. Torregrosa, “A new technique to obtain derivative-free optimal iterative methods for solving nonlinear equations,” Journal of Computational and Applied Mathematics, vol. 252, no. 11, pp. 95–102, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  40. J. H. Li, W. X. Zheng, J. P. Gu, and L. Hua, “Parameter estimation algorithms for Hammerstein output error systems using Levenberg-Marquardt optimization method with varying interval measurements,” Journal of the Franklin Institute, vol. 354, no. 1, pp. 316–331, January 2017.

    Article  MathSciNet  MATH  Google Scholar 

  41. M. H. Li, X. M. Liu, and F. Ding, “Least-squares-based iterative and gradient-based iterative estimation algorithms for bilinear systems,” Nonlinear Dynamics, vol. 89, no. 1, pp. 197–211, July 2017.

    Article  MathSciNet  MATH  Google Scholar 

  42. M. H. Li, X. M. Liu, and F. Ding, “The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise,” Journal of the Franklin Institute, vol. 354, no. 12, pp. 4861–4881, August 2017.

    Article  MathSciNet  MATH  Google Scholar 

  43. X. F. Li, Y. D. Chu, and Y. T. Andrew, “Synchronization of uncertain chaotic systems via complete-adaptive-impulsive controls,” Chaos Solitons & Fractals, vol. 100, pp. 24–30, July 2017.

    Article  MathSciNet  MATH  Google Scholar 

  44. L. Xu, F. Ding, Y. Gu, A. Alsaedi, and T. Hayat, “A multiinnovation state and parameter estimation algorithm for a state space system with d-step state-delay,” Signal Processing, vol. 140, pp. 97–103, November 2017.

    Article  Google Scholar 

  45. N. Zhao, M. H. Wu, and J. J. Chen, “Android-based mobile educational platform for speech signal processing,” International Journal of Electrical Engineering Education, vol. 54, no. 1, 3–16., February 2017.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi, 214153, P. R. China

    Ling Xu

  2. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, P. R. China

    Ling Xu

  3. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, P. R. China

    Feng Ding

Authors
  1. Ling Xu
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  2. Feng Ding
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Corresponding author

Correspondence to Feng Ding.

Additional information

Recommended by Associate Editor Tae-Hyoung Kim under the direction of Editor PooGyeon Park. This work was supported by the Science Research of Colleges Universities in Jiangsu Province (No. 16KJB120007, China), Postdoctoral Research Funding Plan in Jiangsu Province (No. 1701020A), and sponsored by Qing Lan Project and the National Natural Science Foundation of China (No. 61293194).

Ling Xu was born in Tianjin, China. She received the Master and Ph.D. degrees from the Jiangnan University (Wuxi, China), in 2005 and 2015. She has been an Associate Professor since 2015. She is a Colleges and Universities “Blue Project” Young Teacher (Jiangsu, China). Her research interests include process control, parameter estimation and signal modeling.

Feng Ding received his B.Sc. degree from the Hubei University of Technology (Wuhan, China) in 1984, and his M.Sc. and Ph.D. degrees both from the Tsinghua University, in 1991 and 1994, respectively. He has been a professor in the School of Internet of Things Engineering at the Jiangnan University (Wuxi, China) since 2004. His current research interests include model identification and adaptive control. He authored four books on System Identification.

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Xu, L., Ding, F. Parameter estimation for control systems based on impulse responses. Int. J. Control Autom. Syst. 15, 2471–2479 (2017). https://doi.org/10.1007/s12555-016-0224-2

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  • DOI: https://doi.org/10.1007/s12555-016-0224-2

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