Keywords
structure
parameter
nonlinear
feedback
How to Cite
Abstract
The problems of structure and parameter identification of nonlinear dynamic systems operating with positive feedback in the frequency domain are considered. It is assumed that the input to the investigation system is a harmonic signal. The identification problems are considered on a set of block-oriented models, the elements of which are Hammerstein and Wiener models with unitary feedback. Taking into account the peculiarities of such systems functioning in manufacturing, the equations describing the models are reduced to ordinary nonlinear differential equations, known as the Riccati equation. The developed method for identifying the model structure is based on observations of the system's input and output variables in a steady state. The solution of the parameter identification problem is carried out by the method of least squares. The developed identification method is investigated in terms of accuracy.
References
Nagiev M.F. Theoretical foundation of recirculation processes. Academy of Sciences of the USSR, Moscow, 1962. (in Russian).
Arefiev B.A. Inertial processes optimization. Mashinostroenie, Leningrad, 1969. (in Russian).
Eykhoff, P. System identification. parameter and state estimation. John Wiley and Sons Ltd, London. 1974.
Shanshiashvili B.G. On the selection of the model structure under the nonlinear dynamic system identification with a closed cycle. 8th IFAC/IFORS Symposium on Identification and System Parameter Estimation. Preprints. Oxford, Pergamon Press, vol. 2, 1988, pp. 933-938.
Haber R., Unbehauen H. Structure identification of nonlinear dynamic systems – a survey on input/output approaches. Automatica. 26(4), 1990, pp. 651-667.
Shanshiashvili B.G. Frequency method for identification of a model structure of nonlinear continuous-time systems. Preprints of the 9 th IFAC/IFORS Symposium on Identification and System Parameter Estimation, vol. 1, Budapest, 1991, pp. 640 – 643.
Haber, R, and Unbehauen, H. Structure identification of nonlinear dynamic systems – a survey on input/output approaches. Automatica, vol. 26, no. 4, 1990, pp. 651-677.
Giri, F., Bai, E-W. (eds). Block-oriented nonlinear system identification. Springer, Berlin, 2010.
Shanshiashvili B., Prangishvili A. and Tsveraidze Z. Structure identification of continuous-time block-oriented nonlinear systems in the frequency domain. IFAC-PapersOnLine, vol. 52, Issue 13, 2019, pp. 463-468.
Shanshiashvili B., Rigishvili T. parameter identification of block-oriented nonlinear systems in the frequency domain. IFAC PapersOnLine, vol. 53, issue 2, 2020, pp. 10695–10700.
Liu X.., Wang C., Dai W. Probability-Based identification of Hammerstein systems with asymmetric noise characteristics. IEEE Transactions on Instrumentation and Measurement, vol. 73, 2024, pp.1-11.
Jing Sh., Pan T., Zhu Q. Identification of Wiener systems based on the variable forgetting factor multi-error stochastic gradient and the key term separation. International Journal of Adaptive Control and Signal Processing, vol. 35, issue 12, 2021, pp. 2537-2549.
Brouri A. Wiener–Hammerstein nonlinear system identification using spectral analysis. International Journal of Robust and Nonlinear Control, 2022, 32 (10): 6184-6204.
Brouri A., El Mansouri F.Z., F.Z. Chaoui F.Z., Abdelaali C., Giri F. Identification of Hammerstein-Wiener model with discontinuous input nonlinearity. Science China Information Sciences, vol. 66, 2023, pp.1-15.
Salukvadze M., Shanshiashvili B. Identification of nonlinear continuous dynamic systems with closed cycle. International Journal of Information Technology & Decision Making, vol. 12, no. 2, 2013, pp. 179-199.
Prangishvili A., Shanshiashvili B., Tsveraidze Z. Identification of nonlinear dynamic systems with feedback of manufacturing processes. ScienceDirect. IFAC-PapersOnLine, vol. 49, issue 12, 2016, pp. 580-585.
Burghi T., Schoukens M., Sepulchre R. Feedback for nonlinear system identification. 18th European Control Conference (ECC), 2019, pp. 1344-1349.
Shakib M.F., Toth R., Pogromsky A.Y., Pavlov A., van de Wouw N. state-space kernelized closed-loop identification of nonlinear systems. Preprints of the 21st IFAC World Congress (Virtual) Berlin, 2020, pp. 1148-1153.
Hamming R. W. Numerical methods for scientists and engineers. Dover Publications Inc., New York, 1987.