Uyarlamalı genişletilmiş bulanık fonksiyon durum gözetleyici temelli bilinmeyen yönlü kontrol

Öz

Bu çalışmada, uyarlamalı genişletilmiş bulanık fonksyion durum gözetleyici temelli denetleyici, doğrusal olmayan bilinmeyen ve belirsiz sistemlerin kontrolü için önerilmiştir. Nussbaum-Kazanç tekniği kullanarak bilinmeyen kontrol işareti yönündeki tekil durum engellenerek denetleyicinin serbestlik derecesi artırılmıştır. Uyarlamalı genişletilmiş bulanık fonksiyon ile bilinmeyen sistem dinamikleri yaklaşıklanmakta ve ölçülemeyen durumlar gözetlenmektedir. Kapalı çevrim kontrol sistemindeki sinyallerin sınırlılığı Lyapunov kararlılık kriteri ve Nussbaum fonksiyon özellikleri ile gösterilmiştir. Önerilen ve literatürde bilinen bulanık sistem temelli denetleyiciler ters sarkaç sistemine benzetim ortamında, esnek bağlantılı robot koluna ise gerçek zamanlı olarak uygulanmıştır. İzleme hatası için mutlak hata toplamı (IAE), karesel hatanın toplamı (IAE) ve gerekli kontrol işaretinin toplamı (IAU) performansları kullanarak tasarlanan denetleyiciler karşılaştırılmıştır. Çalışmanın amacı sadece izleme performansını artırmak değil, uyarlamalı genişletilmiş bulanık fonksiyon gözetleyici temelli denetleyiciyi gerçek zamanlı sisteme uygulamak ve bilinmeyen kontrol işareti yönünde denetlemeyi sağlamaktır.

Anahtar Kelimeler

• Genişletilmiş bulanık fonksiyon,Uyarlamalı gözetleyici temelli kontrol,Nussbaum-kazanç tekniği,Ters sarkaç,Esnek bağlantılı robot kolu

An adaptive extended fuzzy function state-observer based control with unknown control direction

Abstract

In this paper, a novel adaptive extended fuzzy function state observer-based controller is proposed to control a class of unknown or uncertain nonlinear systems. The controller uses Nussbaum-gain technique from literature to prevent controller singularity with unknown control direction and the controller degree of freedom is increased. A state observer which employs the adaptive extended fuzzy function system to approximate a nonlinear system dynamics and estimates the unmeasurable state. The stability of closed-loop control system are shown using Lyapunov stability criterion and Nussbaum function property. The proposed and conventional fuzzy system based controllers are designed to control an inverted pendulum in simulation and a flexible-joint manipulator in real-time experiment. The integral of absoulte error (IAE) of tracking, integral of squared error (ISE) of tracking and integral of required absolute control signal (IAU) performances are compared in applications. The aim of the paper is not only to improve the tracking performances, but also to implement the adaptive extended fuzzy function based controller to a real-time system and conduct the tracking with unknown control direction.

Keywords

• Extended fuzzy functions,Adaptive observer-based control,Nussbaum gain technique,Inverted pendulum,Flexible-joint manipulator

References

1. Landau ID, Rey D, Karimi A, Voda A, Franco A. “A flexible transmission system as a benchmark for robust digital control”. European Journal of Control, 1(2), 77-96, 1995.
2. Moberg S, Öhr J, Gunnarsson S. “A benchmark problem for robust control of a multivariable nonlinear exible manipulator”. 17th IFAC World Congress, Seoul, South Korea, 6-11 July 2008.
3. Quanser Inc. Rotary Flexible Joint User Manual, 2012.
4. Jayawardene TSS, Nakamura M, Goto S. “Accurate control position of belt drives under acceleration and velocity constraints”. International Journal of Control, Automation, and Systems, 1(3), 474-483, 2003.
5. Kune-Shiang T, Jian-Shiang C. “Toward the iterative learning control for belt-driven system using wavelet transformation”. Journal of Sound and Vibration, 286(4-5), 781-798, 2005.
6. ConsoliniL, Gerelli O, Guarino Lo Bianco C, Piazzi A. “Flexible joints control: A minimum-time feed-forward technique”. Mechatronics, 19(3), 348-356, 2009.
7. Talole SE, Kolhe JP, Phadke SB. “Extended-state-observer-based control of exible-joint system with experimental validation”. IEEE Transactions on Industrial Electronics, 57(4), 1411-1419, 2010.
8. Wang LX, Mendel JM. “Fuzzy basis functions, universal approximation, and orthogonal least-squares learning”. IEEE Transactions on Neural Networks, 3(5), 807-814, 1992.

9. Park JH, Park GT. “Robust adaptive fuzzy controller for non-a_ne nonlinear systems with dynamic rule activation”. International Journal of Robust and Nonlinear Control, 13(2), 117-139, 2003.
10. Shaocheng T, Shuai S, Yongming L. “Adaptive fuzzy decentralized control for stochastic large-scale nonlinear systems with unknown dead-zone and unmodeled dynamics”. Neurocomputing, 135, 367-377, 2014.
11. Boulkroune A, Bounar N, M'Saad M, Farza M. “Indirect adaptive fuzzy control scheme based on observer for nonlinear systems: A novel SPR-filter approach”. Neurocomputing, 135, 378-387, 2014.
12. Young HK., FL. Lewis, and CT. Abdallah, “A dynamic recurrent neural-network-based adaptive observer for a class of nonlinear systems”. Automatica, 33(8), 1539-1543, 1997.
13. Park JH, Yoon PS, Park GT. “Robust adaptive observer using fuzzy systems for uncertain nonlinear systems”. 10th IEEE International Conference on Fuzzy Systems, 2-5 December 2001.
14. Ionnou PA, Sun J. Robust Adaptive Control. Englewood Clifs, New Jersey, USA, Prentice-Hall, 1996.
15. Yih-Guang L, Tsu-Tian L, Wei-Yen W. “Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems”. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 29(5), 583-591, 1999.
16. Shaocheng T, Han-Xiong L, Wei W. “Observer-based adaptive fuzzy control for SISO nonlinear systems”. Fuzzy Sets and Systems, 148(3), 355-376, 2004.
17. Park JH, Seo SJ, Park GT. “Robust adaptive fuzzy controller for nonlinear system using estimation of bounds for approximation errors”. Fuzzy Sets and Systems, 133(1), 19-36, 2003.
18. Jang-Hyun P, Gwi-Tae P, Seong-Hwan K, Chae-Joo M. “Output-feedback control of uncertain nonlinear systems using a self-structuring adaptive fuzzy observer”. Fuzzy Sets and Systems, 151(1), 21-42, 2005.
19. Chung-Chun K, Ti-Hung C. “Observer-based indirect adaptive fuzzy sliding mode control with state variable Filters for unknown nonlinear dynamical systems”. Fuzzy Sets and Systems, 155(2), 292-308, 2005.
20. Boulkroune A, M. Tadjine, M. M'Saad, and M. Farza. “How to design a fuzzy adaptive controller based on observers for uncertain a_ne nonlinear systems”. Fuzzy Sets and Systems, 159(8), 926-948, 2008.
21. Qi R.., Mietek AB. “Stable indirect adaptive control based on discrete-time TS fuzzy model”. Fuzzy Sets and Systems, 159(8), 900-925, 2008.
22. Nussbaum RD. “Some remarks on the conjecture on the parameter adaptive control”. Systems and Control Letters, 3, 243-246, 1983.
23. Ge SS, Hong F, Lee TH. “Adaptive neural control of nonlinear time-delay systems with unknown virtual control coefficients”. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 34(1), 499-516, 2004.
24. Zhaoxu Y, Shugang L, Hongbin D. “Razumikhin-nussbaum-lemma-based adaptive neural control for uncertain stochastic pure-feedback nonlinear systems with time-varying delays”. International Journal of Robust and Nonlinear Control, 23(11), 1214-1239, 2013.
25. Wang T., S. Tong, and Y. Li. “Robust adaptive fuzzy output feedback control for stochastic nonlinear systems with unknown control direction”. Neurocomputing, 106, 31-41, 2013.
26. Türkşen IB. “Fuzzy functions with LSE”. Applied Soft Computing, 8(3), 1178-1188, 2008.
27. Beyhan S, Alcı M. “Fuzzy functions based ARX model and new fuzzy basis function models for nonlinear system identi_cation”. Applied Soft Computing, 10(2), 439-444, 2010.
28. Beyhan S, Alcı M. “Extended fuzzy function model with stable learning methods for online system identification”. International Journal of Adaptive Control and Signal Processing, 25(2), 168-182, 2011.
29. Fazel Z. M. H., Zarinbal M, N. Ghanbari, I.B. Turksen. “A new fuzzy functions model tuned by hybridizing imperialist competitive algorithm and simulated annealing. Application: Stock price prediction”. Information Sciences, 222, 213-228, 2013.
30. Alcı M., S. Beyhan, “Fuzzy Functions with function expansion model for nonlinear system identification”. International Journal of Intelligent Automation & Soft Computing, 23(1), 87-94, 2017.
31. Çelikyılmaz A., IB. Türkşen, R. Aktaş, M. M. Doğanay, N. B. Ceylan, “A new classifier design with fuzzy functions”. In Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, volume 4482 of Lecture Notes in Computer Science, pages 136-143. Springer Berlin/Heidelberg, 2007.
32. Çelikyılmaz A, Türkşen IB, Aktaş R, Doganay MM, Ceylan NB. “Increasing accuracy of two-class pattern recognition with enhanced fuzzy functions”. Expert Systems with Applications, 36(2), 1337-1354, 2009.
33. Türkşen IB., Çelikyılmaz A. “Comparison of fuzzy functions with fuzzy rule base approaches”. International Journal of Fuzzy Systems, 8(3), 137-149, 2006.
34. Türkşen IB. “Review of fuzzy system models with an emphasis on fuzzy functions”. Transactions of the Institute of Measurement and Control, 31(1), 7-31, 2009.
35. Zarandi MHF., M. Zarinbal, A. Zarinbal, IB. Turksen., M. Izadi, “Using type-2 fuzzy function for diagnosing brain tumors based on image processing approach”. International Conference on In Fuzzy Systems, Barcelona, Spain, 18-23 July 2010.
36. Yong-Tae K., Z. Z. Bien, “Robust adaptive fuzzy control in the presence of external disturbance and approximation error”. Fuzzy Sets and Systems, 148(3), 377-393, 2004.