Radyal hareket optimizasyonu ile ayarlanmış OİT denetleyicisi için çok değişkenli amaç fonksiyonlarının analizi

Öz

Bu çalışmada, çok değişkenli amaç fonksiyonlarının (ÇDAF) performans analizi için MATLAB/Simulink ortamında ikinci dereceden zaman gecikmeli bir test sistemi oluşturulmuştur. Analiz edilen amaç fonksiyonları, zaman ağırlıklı mutlak hatanın integrali, hatanın karesinin integrali, mutlak hatanın integrali ve zaman ağırlıklı hatanın karesinin integrali gibi klasik hata tabanlı amaç fonksiyonlarının (KHTAF), geçici durum parametreleri yüzde aşma ve yerleşme zamanı ile toplamından elde edilmiştir. Fonksiyonlarda yüzde aşma ve yerleşme zamanı sırasıyla 𝑤1 ve 𝑤2 katsayıları ile ağırlıklandırılmıştır. Sistemin kontrolü oransal integral türev (OİT) denetleyici ile yapılmıştır. OİT denetleyicinin parametreleri radyal hareket optimizasyonu (RHO) kullanılarak ayarlanmıştır. Çalışmada ÇDAF’lerin performansını göstermek için yerleşme süresi, maksimum yüzde aşma, yükselme süresi, tepe süresi ve kalıcı durum hatası bilgileri sayısal ve görsel olarak sunulmuştur. Elde edilen sonuçlar ÇDAF’lerin yerleşme süresi ve aşma değeri bakımından KHTAF’lere göre daha iyi performansa sahip olduğunu açıkça göstermektedir. Aynı zamanda RHO algoritması ilk yedi yinelemede optimal çözüme ulaşarak sağlam yakınsama oranı ve hızına sahip olduğunu kanıtlamıştır.

Anahtar Kelimeler

• OİT denetleyici
• RHO algoritması
• Çok değişkenli amaç fonksiyonları
• Hata tabanlı amaç fonksiyonları

Analysis of multivariable objective functions for the PID controller tuned by a radial movement optimization

Abstract

In this study, a second order plus dead time (SOPDT) test system was designed in MATLAB/Simulink platform to analyze the performance of multivariable objective functions (MOFs). These functions consisted of classical error-based objective functions (CEBOFs): integral of timeweighted absolute error, integral of squared error, integral of absolute error, integral of time-weighted squared error, and transient state parameters: maximum percentage overshoot and settling time which has 𝑤1 and 𝑤2 coefficients, respectively. A proportional integral derivative (PID) controller was employed to control the SOPDT system. In the optimization process, the radial movement optimization (RMO) algorithm was used to tune PID controller parameters. To demonstrate the performance of MOFs, numerical and graphical results were presented in the study, where settling time, maximum percentage overshoot, rise time, peak time and steady state error were given. The obtained results clearly showed that MOFs had a better performance than all CEBOFs in settling time and overshoot value. RMO algorithm also had a robust convergence rate and speed, proving the best optimal solution for all MOFs in the first seven iterations.

Keywords

• PID controller
• RMO algorithm
• Multivariable objective functions
• Error-based objective functions

Kaynakça

1. [1] Lee CC. “Fuzzy logic in control systems: fuzzy logic controller”. I. IEEE Transactions on Systems, Man, and Cybernetics, 20(2), 404-418, 1990.
2. [2] Li X, Wen H, Hu Y, Jiang L. “A novel beta parameter based fuzzy-logic controller for photovoltaic MPPT application”. Renewable Energy, 130, 416-427, 2019.
3. [3] Roumila, Z, Rekioua, D, Rekioua, T. “Energy management based fuzzy logic controller of hybrid system wind/photovoltaic/diesel with storage battery”. International Journal of Hydrogen Energy, 42(30), 19525-19535, 2017.
4. [4] Wu L, Gao Y, Liu J, Li H. “Event-triggered sliding mode control of stochastic systems via output feedback”. Automatica, 82, 79-92, 2017.
5. [5] Vazquez S, Rodriguez J, Rivera M, Franquelo L.G, Norambuena M. “Model predictive control for power converters and drives: Advances and trends”. IEEE Transactions on Industrial Electronics, 64(2), 935-947, 2016.
6. [6] Camacho EF, Alba CB. Model Predictive Contro”. 2nd ed. Berlin, Germany, Springer Science & Business Media, 2013.
7. [7] Cortés P, Kazmierkowski MP, Kennel RM, Quevedo, DE, Rodríguez J. “Predictive control in power electronics and drives”. IEEE Transactions on Industrial Electronics, 55(12), 4312-4324, 2008.
8. [8] Åström KJ, Hägglund T, Astrom KJ. Advanced PID Control. Research Triangle Park, NC: ISA-The Instrumentation, Systems, and Automation Society. 2006.

9. [9] Shah P, Agashe, S. “Review of fractional PID controller”. Mechatronics, 38, 29-41, 2016.
10. [10] Zhao C, Guo L. “PID controller design for second order nonlinear uncertain systems”. Science China Information Sciences, 2017. https://doi.org/10.1007/s11432-016-0879-3
11. [11] Díaz-Rodríguez ID, Han S, Keel, LH, Bhattacharyya SP. “Advanced tuning for Ziegler-Nichols plants”. IFAC-PapersOnLine, 50(1), 1805-1810, 2017.
12. [12] Åström KJ, Hägglund T. “Revisiting the Ziegler–Nichols step response method for PID control”. Journal of Process Control, 14(6), 635-650, 2004.
13. [13] Yuwana M, Seborg DE. “A new method for on‐line controller tuning”. AIChE Journal, 28(3), 434-440, 1982.
14. [14] Azman AA, Rahiman MHF, Mohammad NN, Marzaki MH, Taib MN, Ali MF. “Modeling and comparative study of PID Ziegler Nichols (ZN) and Cohen-Coon (CC) tuning method for multi-tube aluminum sulphate water filter (MTAS)”. IEEE 2017 2nd International Conference on Automatic Control and Intelligent Systems (I2CACIS), Kinabalu, Malaysia 21 October 2017.
15. [15] Cominos P, Munro N. “PID controllers: recent tuning methods and design to specification”. IEE ProceedingsControl Theory and Applications, 149(1), 46-53, 2020.
16. [16] Ye Y, Yin CB, Gong Y, Zhou, JJ. “Position control of nonlinear hydraulic system using an improved PSO based PID controller”. Mechanical Systems and Signal Processing, 83, 241-259, 2017.
17. [17] Pandey ND, Tiwari P. “Comparison between Speed Control DC Motor Using Genetic Algorithm and PSO-PID Algorithm”. International Journal of Electrical Engineering & Technology, 8(1), 17-25, 2017.
18. [18] Kaya S, Karaçizmeli İH, Aydilek İB, Tenekeci ME, Gümüşçü A. “The effects of initial populations in the solution of flow shop scheduling problems by hybrid firefly and particle swarm optimization algorithms.” Pamukkale University Journal of Engineering Sciences, 26(1), 140-149, 2020.
19. [19] İşcan S, Kaplan O. “Power loss and voltage stability optimization with meta-heuristic algorithms in power system”. Pamukkale University Journal of Engineering Sciences, 27(2), 199-209, 2021.
20. [20] Bingul Z, Karahan O. “A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system”. Journal of the Franklin Institute, 355(13), 5534-5559, 2018.
21. [21] Zamani AA, Tavakoli S, Etedali S. “Fractional order PID control design for semi-active control of smart baseisolated structures: a multi-objective cuckoo search approach”. ISA Transactions, 67, 222-232, 2017.
22. [22] Feng H, Yin CB, Weng WW, Ma W, Zhou JJ, Jia WH, Zhang ZL. “Robotic excavator trajectory control using an improved GA based PID controller”. Mechanical Systems and Signal Processing, 105, 153-168, 2018.
23. [23] Gündoğdu Ö. “Optimal tuning of PID controller gains using genetic algorithms”. Pamukkale University Journal of Engineering Sciences, 11(1), 131-135, 2005.
24. [24] Dhieb Y, Yaich M, Guermazi A, Ghariani M. “PID controller tuning using ant colony optimization for induction motor”. Journal of Electrical Systems, 15(1), 133-141, 2019.
25. [25] Vanithasri M, Balamurugan R, Lakshminarasimman, L. “Radial movement optimization (RMO) technique for solving unit commitment problem in power systems”. Journal of Electrical Systems and Information Technology, 5(3), 697-707, 2018.
26. [26] Rahmani R, Yusof R. “A new simple, fast and efficient algorithm for global optimization over continuous searchspace problems: Radial Movement Optimization”. Applied Mathematics and Computation, 248, 287-300, 2014.
27. [27] Chen XDW, Qian F. “Multi-objective differential evolution with ranking-based mutation operator and its application in chemical process optimization”. Chemometrics and Intelligent Laboratory Systems, 136, 85-96, 2014.
28. [28] Wang LLQ, Zhang B, Ding R, Sun M. “Robust multiobjective optimization for energy production scheduling in microgrids”. Engineering Optimization, 51(2), 332-351, 2019.
29. [29] Awouda, Mamat R. “New PID tuning rule using ITAE criteria”. International Journal of Engineering, 3(6), 597-608, 2010.
30. [30] Jagatheesan K, Anand B, Dey KN, Ashour AS, Satapathy SC. “Performance evaluation of objective functions in automatic generation control of thermal power system using ant colony optimization technique-designed proportional–integral–derivative controller”. Electrical Engineering, 100(2), 895-911, 2018.
31. [31] Fini MH, Yousefi GR, Alhelou HH. “Comparative study on the performance of many-objective and single-objective optimisation algorithms in tuning load frequency controllers of multi-area power systems”. IET Generation, Transmission & Distribution, 10(12), 2915-2923, 2016.
32. [32] Şahin E, Ayas, MS. “Performance Analysis of Error-Based and User-Defined Objective Functions for a Particle Swarm Optimization Tuned PID Controller with Derivative Filter”. Afyon Kocatepe University Journal of Science and Engineering, 19(3), 682-689, 2019.
33. [33] Naidu K, Mokhlis H, Bakar AA. “Multiobjective optimization using weighted sum artificial bee colony algorithm for load frequency control”. International Journal of Electrical Power & Energy Systems, 55, 657-667, 2014.
34. [34] Latha K, Rajinikanth V, Surekha PM. “PSO-based PID controller design for a class of stable and unstable systems”. ISRN Artificial Intelligence, 2013. https://doi.org/10.1155/2013/543607
35. [35] Liu GP, Yang JB. Whidborne JF. Multiobjective Optimization and Control. 1st ed. New Delhi, India, Printice Hall, 2008.
36. [36] Zhao SZ, Iruthayarajan MW, Baskar S, Suganthan PN. “Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization”. Information Sciences, 181(16), 3323-3335, 2011.
37. [37] Reynoso-Meza G, Garcia-Nieto S, Sanchis J, Blasco FX. “Controller tuning by means of multi-objective optimization algorithms: A global tuning framework”. IEEE Transactions on Control Systems Technology, 21(2), 445-458, 2012.
38. [38] Ge M, Chiu MS, Wang QG. “Robust PID controller design via LMI approach”. Journal of Process Control, 12(1), 3-13, 2002.
39. [39] Aström KJ, Hagglund T. “Revisiting the Ziegler-Nichols step response method for PID control”. Journal of Process Control, 14(6), 635-650, 2004.