Parameter identification of a non-minimum phase second order system with time delay using relay test and PSO, CS, FA algorithms

Öz

In this study, the parameters of a non-minimum phase second-order system with time delay, which is accepted as gray box, are found out using dual channel relay test and Cuckoo Search, Particle Swarm Optimization, Firefly Algorithms. For this purpose, gray box was implemented as two channel test systems to obtain signals belong to system inputs and outputs. After that, these signals are used to identify system parameter according to a performance criteria, which is integral absolute error between difference of real system and model outputs that was tried to be minimized by Cuckoo search, Particle Swarm Optimization and Firefly Algorithms. General system block diagram and its input and output are given at Figure A. Figure A. Two Channel System Block Diagram Purpose: Cuckoo Search, Particle Swarm Optimization and Firefly Algorithms are heuristic algorithms which are inspired from nature itself. Also these algorithm are capable of to solve benchmark problems. In this study a non-minimum phase second order system with time delay is tried to be identified by using Cuckoo Search, Particle Swarm Optimization and Firefly algorithms according to two channel relay test and performances of these algorithms are compared with each other for this problem. Theory and Methods: Firstly, a real system is implemented into the two channel relay test. This test allows the system to enter a graded oscillation in a limited range. Thus, different dynamics of the system can be stimulated. After that the model parameters are identified by the same test using Cuckoo Search, Particle Swarm Optimization and Firefly Algorithms. These algorithms were tried to minimize or maximize a performance criterion. In this problem, this criterion is integral absolute error between the model output and the system output that is tried to be minimized to identify the system parameters. Results: It is found that the obtained results using Cuckoo Search, Particle Swarm Optimization and Firefly Algorithms gave closer results to the real system than the results obtained with the Genetic Algorithm cited in the literature. Conclusion: In this study, a non-minimum phase second order system with time delay was tried to be identified using cuckoo search, particle swarm optimization and firefly algorithms with two channels relay test. Each algorithms run 10 times and their standard deviations and expected values were calculated. As a result, it is shown that these algorithms gave better performances than the performances cited in the literature. 

Anahtar Kelimeler

• Cuckoo search
• Pso
• Firefly
• Relay feedback
• Modelling

İkinci dereceden ölü zamanlı ve geri tepmeli sistem parametrelerinin, röle testi ve PSO, CS, FA algoritmaları ile belirlenmesi

Öz

Bu çalışmada, gri kutu olarak kabul edilen ikinci dereceden ölü zamanlı ve geri tepmeli bir sistemin parametreleri, çift röleli autotuning testi ve Cuckoo Search, Parçacık Sürü Optimizasyonu, FireFly Algoritmaları kullanılarak belirlenmiştir. Bunun için öncelikle gri kutu, çift röleli auto-tuning testine tabi tutularak, sistem giriş ve çıkışlarına ait sinyaller elde edilmiştir. Ardından bu giriş-çıkış sinyalleri arasındaki hata değeri, belirlenen amaç fonksiyonuna göre Cuckoo Search, Parçacık Sürü Optimizasyonu ve FireFly Algoritmaları kullanılarak minimize edilmekte ve sistem parametreleri belirlenmektedir. Amaç fonksiyonu olarak hatanın mutlak değerinin integrali(Integral Absolute Error) kriteri kullanılmıştır. Elde edilen sonuçlar analiz edilerek, literatürde var olan ve Genetik Algoritma ile yapılan çalışmalar ile kıyaslanmıştır. Cuckoo Search, Parçacık Sürü Optimizasyonu ve FireFly Algoritmaları kullanılarak bu çalışmada elde edilen sonuçların, Genetik Algoritma ile elde edilen sonuçlara göre gerçeğe daha yakın olduğu görülmüştür

Anahtar Kelimeler

• Cuckoo search
• pso
• firefly
• röle geri-besleme
• sistem modelleme

Kaynakça

1. Ziegler J. G.,Nichols N. B., and Rochester N. Y. "Optimum settings for automatic controllers," trans. ASME, vol. 64, 1942.
2. Åström K. J.,Hägglund T., "Automatic Tuning of Simple Regulators With Specifications on Phase and Amplitude Margins," Automatica, vol. 20, pp. 645-651, 1984.
3. Tsypkin Y. Z., "Frequency responses of relay systems," Automat. i Telemekh.,vol. 20, pp. 1603-1610, 1959.
4. Tsypkin Y. Z., "Relay Control Systems," Cambridge University Press, 1984.
5. Luyben W. L., "Derivation of Transfer Functions for Highly Nonlinear Distillation Columns," Ind. Eng. Chem. Res. 1987,26, 2490-2495, 1987.
6. Yu C. C., "Autotuning of PID Controllers A Relay Feedback Approach", 2nd Edition ed.: Springer Science& Business Media, 2006.
7. Shen S. H.,Wu J. S., Yu C. C., "Use of biased‐relay feedback for system identification," AIChE Journal, vol. 42, pp. 1174-1180, 1996.
8. Li W.,Eskinat E., Luyben W. L., "An improved autotune identification method", Industrial&engineering chemistry research, vol. 30, pp. 1530-1541, 1991.

9. Kaya I.,Atherton D., "Parameter estimation from relay autotuning with asymmetric limit cycle data", Journal of Process Control, vol. 11, pp. 429-439, 2001.
10. Friman M.,Waller K. V., "A two-channel relay for autotuning", Industrial&engineering chemistry research, vol. 36, pp. 2662-2671, 1997.
11. Soltesz K.,Hägglund T., Åström K. J., "Transfer function parameter identification by modified relay feedback," in American Control Conference (ACC), 2010, 2010, pp. 2164-2169.
12. Berner J.,Åström K. J., Hägglund T., "Towards a new generation of relay autotuners", IFAC Proceedings Volumes, vol. 47, pp. 11288-11293, 2014.
13. Kaya I., Nalbantoğlu M., "Röle geri-beslemeli sistemlerde genetik algoritma ile modelleme", Dicle Üniversitesi Mühendislik Fakültesi, vol. 3, pp. 31-39, 2012.
14. Yang X.-S., "Nature-inspired optimization algorithms", 1st ed., 2014.
15. Eberhart R., Kennedy J., "A new optimizer using particle swarm theory", in Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on, 1995, pp. 39-43.
16. Kennedy J., Eberhart R., "Particle swarm optimization", in Neural Networks, 1995. Proceedings., IEEE International Conference on, 1995, pp. 1942-1948.
17. Özsağlam M. Y.,Çunkaş M., "Optimizasyon problemlerinin çözümü için parçaçık sürü optimizasyonu algoritması", Politeknik Dergisi vol. 11, pp. 299-305, 2008.
18. Tozan A.,Sevilgen F. E., and İnce O., "Sensör Yerleştirme Probleminin Parçacık Sürü Optimizasyonu ile Çözümü", Elektrik-Elektronik-Bilgisayar Mühendisliği 12. Ulusal Kongresi ve Fuarı, İzmir, 2007.
19. Öztürk A., Alkan S., "Parçacık Sürü Optimizasyonu ile Fotovoltaik Sistemlerde Kullanılan DC-Dc Dönüştürücünün Kontrolü", İleri Teknoloji Bilimleri Dergisi, vol. 2, pp. 110-120, 2013.
20. Gao Z.,Zeng X., Wang J., and J. Liu, "FPGA implementation of adaptive IIR filters with particle swarm optimization algorithm", in Communication Systems, 2008. ICCS 2008. 11th IEEE Singapore International Conference on, 2008, pp. 1364-1367.
21. Tavakoli S.,Banookh A., "Robust PI control design using particle swarm optimization", Journal of Computer Science and Engineering, vol. 1, 2010.
22. Satpati B.,Koley C., andDatta S., "Robust PID controller design using particle swarm optimization-enabled automated quantitative feedback theory approach for a first-order lag system with minimal dead time", SystemsScience& Control Engineering, vol. 2, pp. 502-511, 2014.
23. Kanthaswamy G.,Jerome J., "Control of dead-time systems using derivative free particle swarm optimisation," International Journal of Bio-Inspired Computation, vol. 3, p. 85, 2011.
24. Ahuja A.,Narayan S., Kumar J., "2-DOF Observer Based Controller for First Order with Dead Time Systems", International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:8, No:1, 2014, 2014.
25. Gandomi A. H.,Yang X.-S., Alavi A. H., "Cuckoo Search algorithm: a metaheusristic approch to solve structural optimization problems", Springer-Verlag, vol. 29, p. 18, 2013-01.
26. Elazim S. M. A., Ali E. S., "Optimal Power System Stabilizers design via Cuckoo Search algorithm", International Journal of Electrical Power&Energy Systems, vol. 75, pp. 99-107, 2016.
27. Nema S.,Padhy P. K., "Identification and cuckoo PI-PD controller design for stable and unstable processes", Transactions of the Institute of Measurement and Control, vol. 37, pp. 708-720, 2015.
28. Jin Q.,Qi L., Jiang, B., Wang Q., "Novel improved cuckoo search for PID controller design", Transactions of the Institute of Measurementand Control, vol. 37, pp. 721-731, 2015.
29. Roeva O., Slavov T., "Firefly algorithm tuning of PID controller forglucosecon centration control during E. coli fed-batch cultivation process", Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 455–462, 2014.
30. Sung S. W., Park J. H., Lee I.-B., "Modified Relay Feedback Method", 1995.
31. Soderstrom T.,Stoica P., "System Identification", 1989.
32. Nise N. S., "Control Systems Engineering", 6th ed.: John Wiley&Sons, 2011.
33. Yang X.-S.,Deb S., "Cuckoo Search via L´evy Flights", Nature &Biologically Inspired Computing, pp. 210 - 214, 9-11 Dec. 2009.
34. Karagül K., "Guguk Kuşu Algoritması: Bir Plastik Atık Toplama Uygulaması", 15th International Symposium on Econometrics, Operations Research and Statistic, Isparta, Turkey, vol. 15, pp. 775-784, 22-25 May 2014.
35. Civicioglu P.,Besdok E., "A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms", Artificial Intelligence Review, vol. 39, pp. 315-346, 2011.
36. Yang X.-S., "Firefly Algorithms for Multimodal Optimization", 7 Mar 2010.
37. Belen M. A., Alıcı M., Çor A., Güneş F., "Ateşböceği Algoritması ile Mikrodalga Transistör Performansının Karakterizasyonu", ELECO-2014 Elektrik-Elektronik-Bilgisayar ve Biyomedikal Mühendisliği Sempozyumu, pp. 491-494, 2014.