Wiener Sistemlerinin Gradyan Tabanlı Tanımlaması

Öz

Tek bir bloktan oluşan sistemlerde geribesleme ile kontrol ve giriş-çıkış ilişkisinin kurulması klasik kontrolde yaygın olarak görülmektedir.  Fakat doğal sistemler göz önüne alındığında çok bloklu yapılar ve bu bloklar içerisinde de lineer olmayan fonksiyonlar görülür. Bu çalışmanın konusu, giriş işaretinin lineer bloka uygulandığı ve çıkışın lineer olmayan fonksiyondan alındığı sistem yapısı olan Wiener tipi sistemlerin tanımlamasıdır. Durum geribeslemenin mümkün olmadığı bu sistem tipinde tanımlama ile farklı kontrol algoritmalarının kullanımı mümkündür. Sistem tanımlamada harici girişli otoregresif ağ (ARX)-polinom kaskad bağlantısı tercihi ile en küçük kareler yöntemi ve eğim bilgileri sayesinde sistemin giriş-çıkışı arasındaki matematiksel ilişki elde edilmiştir. Üç farklı örnek sistem üzerinde çalışmalar yapılmış, MATLAB/Simulink ortamında veri kümeleri elde edilmiş ve yapılan sistem tanımlamalarının başarımı grafikler ile sunulmuştur.

Anahtar Kelimeler

• Wiener sistemleri,Sistem tanımlama,Doğrusal olmayan sistemler

Gradient Based Identification of Wiener Systems

Öz

In systems consisting of a single block, the establishment of feedback control and input-output relationship is common in classical control. However, considering natural systems, there are many block structures and non-linear functions within these blocks. The subject of this study is the identification of Wiener type systems, which is the system structure in which the input signal is applied to the linear block and its output is taken from the nonlinear function. It is possible to use different control algorithms with identification in this type of system where state feedback control is not possible. In system identification, the mathematical relationship between the input and output of the system has been obtained by the choice of auto regressive with exogenous inputs (ARX)-polynomial cascade connection with using the least squares method and gradient information. Three different benchmark systems have been studied in MATLAB/Simulink and the performances of the identifications made with the dataset are presented graphically.

Anahtar Kelimeler

• Wiener systems,System identification,Nonlinear systems.

Kaynakça

1. Jafari M, Salimifard M, Dehghani M. “Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares Algorithm”. ISA Transactions, 53 (4), 1243-1252, 2014.
2. Salhi H, Kamoun S. “A recursive parametric estimation algorithm of multivariable nonlinear systems described by Hammerstein mathematical models”. Applied Mathematical Modelling, 39(16), 4951-4962, 2015.
3. Chang F, Luus R. “A nonlinear method for identification using Hammerstein model”. IEEE Transactions on Automatic Control, 16(5), 464-468, 1971.
4. Figueroa L, Cousseau JE, Werner S, Laakso T. “Adaptive control of a Wiener type system: application of a pH neutralization reactor”. Internaional Journal of Control, 80(2), 231-240, 2007.
5. Chi Q, Fei Z, Liu K, Liang J. “Latent-variable nonlinear model predictive control strategy for a pH neutralization process”. Asian Journal of Control, 17(6), 2427-2434, 2015.
6. Guo J, Yin LY, Zhao Y, Zhang JF. “Identification of Wiener systems with quantized inputs and binary-valued output observations”. Automatica, 78, 280-286, 2017.
7. Kibangou AY, Favier G. “Wiener-Hammerstein systems modeling using diagonal Volterra kernels coefficients”. IEEE Signal Processing Letter, 13(6), 381-384, 2006.
8. Lawrynjczuk M. “Nonlinear predictive control for Hammerstein-Wiener systems”. ISA Transactions, 55, 49-62, 2015.

9. Kazemi M, Arefi MM. “A fast iterative recursive least squares algorithm for Wiener model identification of highly nonlinear systems”. ISA Transactions, 67, 382-388, 2017.
10. Kalafatis A, Arifin N, Wang L, Cluett W. “A new approach to the identification of pH processes based on the Wiener model”. Chemical Engineering Science, 50(23), 3693-3701, 1995.
11. Zhang O, Ma Z, Li G, Qian Z, Guo X., “Temperature-dependent demagnetization nonlinear Wiener model with neural network for PM synchronous machines in electric vehicle”. 19th International Conference on Electrical Machines and Systems, Chiba, Japan, 13-16 November 2016.
12. Norquay SJ, Palazoglu A, Romagnoli JA. “Model predictive control based on Wiener models”. Chemical Engineering Science, 53(1), 75-84, 1998.
13. Kazemi M, Arefi MM. “Nonlinear generalized minimum variance control and control performance assessment of nonlinear systems based on a Wiener model”. Transactions of the Institute of Measurement and Control, https://doi.org/10.1177/0142331216685395.
14. Li S, Li Y. “Model predictive control of an intensified continuous reactor using a neural network Wiener model”. Neurocomputing, 185, 93-104, 2016.
15. Yu W, Pineda FJ. “Chemical process modelling with multiple neural networks”. European Control Conference, Porto, Portugal, 4-7 September 2001.
16. Zeydan M. “Bir petrol rafinerisi (TÜPRAŞ) akışkan yataklı katalitik parçalama ünitersinin (FCCU) bulanık modelleme uygulamaı”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 10(1), 101-110, 2002.
17. Ding F, Liu X, Liu M. “The recursive least squares identification algorithm for a class of Wiener nonlinear systems”. Journal of The Franklin Institute, 353(7), 1518-1526, 2016.
18. Liu M, Xiao Y, Ding R. “Iterative identification algorithm for Wiener nonlinear systems using the Newton method”. Applied Mathematical Modelling, 37(9), 6584-6591, 2013.
19. Lawryjnczuk M. “Modelling and predictive control of a neutralisation reactor using sparse support vector machine Wiener models”. Neurocomputing, 205(12), 311-328, 2016.
20. Tang Y, Han Z, Liu F, Guan X. “Identification and control of nonlinear system based on Laguerra-ELM Wiener model”. Communications in Nonlinear Science and Numerical Simulation, 38, 192-205, 2016.
21. Mahmoodi S, Poshtan J, Jahed-Motlagh MR, Montazeri A. “Nonlinear model predictive control of a pH neutralization process based on Wiener-Laguerre model”. Chemical Engineering Journal, 146(3), 328-337, 2009.
22. Chan LLT, Chen T, Chen J. “PID based nonlinear processes control model uncertainty improvement by using Gaussian process model”. Journal of Process Control, 42, 77-89, 2016.
23. Gomez JC, Jutan A, Baeyens E. “Wiener model identification and predictive control of a pH neutralisation process”. IEE Proceedings-Control Theory and Applications, 151(3), 329-338, 2004.
24. Ljung L. System Identification, New Jersey, USA, Prentice Hall, 1999.
25. Gerksic S, Juricic D, Strmcnik S, Matko D. “Wiener model based nonlinear predictive control”. International Journal of Systems Science, 31, 189-202, 2010.
26. Zhou L, Li X, Pan F. “Gradient based iterative parameter identification for Wiener nonlinear systems”. Applied Mathematical Modelling, 37, 8203-8209, 2013.
27. Vatankhah B, Farrokhi M. “Nonlinear model-predictive control with disturbance rejection property using adaptive neural networks”. Journal of the Franklin Institute, 354, 5201-5220, 2017.
28. Xie S, Xie Y, Gui W, Yang C. “Weighted-coupling CSTR modeling and model predictive control with parameter adaptive correction for the goethite process”. Journal of Process Control, 68, 254-267, 2018.