Starfish Optimization Algorithm-Tuned PID Controller for Automatic Voltage Regulation: A Multi-Criteria Time- and Frequency-Domain Study

Öz

Reliable terminal-voltage regulation is essential for preserving power quality and the secure operation of synchronous generators, yet the dynamic performance of an automatic voltage regulator (AVR) depends strongly on the tuning of its controller parameters. This study proposes a starfish optimization algorithm (SFOA)-tuned proportional-integral-derivative (PID) controller for the standard linearized AVR benchmark. The proportional, integral and derivative gains are optimized simultaneously by minimizing a composite objective function that accounts for overshoot, steady-state error, rise time and settling time. Performance is benchmarked against PID controllers tuned by the reptile search algorithm (RSA), genetic algorithm (GA), and symbiotic organisms search (SOS) under identical plant and operating conditions. SFOA determines the gain set K_P  = 0.6329, K_I=0.5165, and K_D=0.2275. The resulting controller achieves a rise time of 0.2900 s, a settling time of 0.4405 s, an overshoot of 1.1624%, a steady-state error of 4.7740×〖10〗^(-13)%, and the lowest objective-function value of 0.0627 among the compared methods. Frequency-domain analysis further shows that the phase margin increases from 16.1028 degrees to 68.3451 degrees, the gain margin from 4.6176 dB to 26.4043 dB, and the bandwidth from 6.9454 rad/s to 7.7374 rad/s. The controller also follows a multi-level time-varying voltage command without persistent offset or growing oscillations. These results indicate that SFOA provides an effective multi-criteria PID-tuning framework that improves transient response, relative stability, and reference-tracking performance for the investigated AVR system.

Anahtar Kelimeler

• automatic voltage regulator (AVR)
• frequency-domain stability
• PID controller
• starfish optimization algorithm
• transient response.

Etik Beyan

This study is based entirely on mathematical modeling and computer simulations. It does not involve human participants, animals, or personal data; therefore, ethical approval was not required.

Otomatik Gerilim Düzenlemesi için Deniz Yıldızı Optimizasyon Algoritması ile Ayarlanmış PID Kontrol Cihazı: Çok Kriterli Zaman ve Frekans Alanı Çalışması

Öz

Güvenilir terminal gerilim regülasyonu, güç kalitesinin korunması ve senkron jeneratörlerin güvenli çalışması için çok önemlidir; ancak otomatik gerilim regülatörünün (AVR) dinamik performansı, kontrolör parametrelerinin ayarlanmasına büyük ölçüde bağlıdır. Bu çalışma, standart doğrusal AVR kıyaslama modeli için deniz yıldızı optimizasyon algoritması (SFOA) ile ayarlanmış oransal-integral-türev (PID) kontrolörü önermektedir. Oransal, integral ve türev kazançları, aşırı salınım, kararlı durum hatası, yükselme süresi ve yerleşme süresini hesaba katan bileşik bir amaç fonksiyonunu en aza indirgeyerek eş zamanlı olarak optimize edilir. Performans, aynı tesis ve çalışma koşulları altında sürüngen arama algoritması (RSA), genetik algoritma (GA) ve simbiyotik organizma arama (SOS) ile ayarlanmış PID kontrolörlerine karşı kıyaslanmıştır. SFOA, Kp = 0,6329, Ki = 0,5165 ve Kd = 0,2275 kazanç setini belirler. Elde edilen kontrolör, 0,2900 s'lik bir yükselme süresi, 0,4405 s'lik bir yerleşme süresi, %1,1624'lük bir aşırı salınım, %4,7740E-13'lük bir kararlı durum hatası ve karşılaştırılan yöntemler arasında en düşük hedef fonksiyon değeri olan 0,0627'yi elde etmektedir. Frekans alanı analizi ayrıca, faz marjının 4,6176 dereceden 26,4043 dereceye, kazanç marjının 16,1028 dB'den 68,3451 dB'ye ve bant genişliğinin 6,9454 rad/s'den 7,7374 rad/s'ye arttığını göstermektedir. Kontrolör ayrıca, kalıcı sapma veya artan salınımlar olmadan çok seviyeli zamanla değişen voltaj komutunu takip etmektedir. Bu sonuçlar, SFOA'nın incelenen AVR sistemi için geçici tepkiyi, göreceli kararlılığı ve referans izleme performansını iyileştiren etkili bir çok kriterli PID ayarlama çerçevesi sağladığını göstermektedir.

Anahtar Kelimeler

• Otomatik voltaj regülatörü (AVR)
• frekans alanı kararlılığı
• PID kontrolcüsü
• deniz yıldızı optimizasyon algoritması
• geçici tepki.

Etik Beyan

Bu çalışma tamamen matematiksel modelleme ve bilgisayar simülasyonlarına dayanmaktadır. İnsan katılımcı, hayvan veya kişisel veri içermediğinden etik kurul onayı gerektirmemektedir.

Kaynakça

1. Gozde, H., & Taplamacioglu, M. C. (2011). Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system. Journal of the Franklin Institute, 348(8), 1927-1946.
2. Köse, E. (2020). Optimal control of AVR system with tree seed algorithm-based PID controller. IEEE access, 8, 89457-89467.
3. Ekinci, S., & Hekimoğlu, B. (2019). Improved kidney-inspired algorithm approach for tuning of PID controller in AVR system. IEEE Access, 7, 39935-39947.
4. Bingul, Z., & Karahan, O. (2018). 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.
5. Ekinci, S., Izci, D., Almomani, M. H., Saleem, K., Zitar, R. A., Smerat, A., ... & Abualigah, L. (2025). Advanced control parameter optimization in DC motors and liquid level systems. Scientific Reports, 15(1), 1394.
6. Liu, N., Chai, T., Zhang, Y., & Gao, W. (2025). Data-driven optimal tuning of PID controller parameters. Science China Information Sciences, 68(7), 172201.
7. Gupta, M., Tiwari, P. M., Viral, R. K., Shrivastava, A., Zneid, B. A., & Hunko, I. (2025). Grid-connected PV inverter system control optimization using Grey Wolf optimized PID controller. Scientific reports, 15(1), 28869.
8. El‐Rifaie, A. M., Abid, S., Ginidi, A. R., & Shaheen, A. M. (2025). Fractional order PID controller based‐neural network algorithm for LFC in multi‐area power systems. Engineering Reports, 7(2), e70028.

9. Imran, M. H., Billah, M. T., Hanip, A., Aizat, M., & Rahiman, W. (2026). Hybrid Fuzzy-PID Controller for Enhanced Trajectory Accuracy in Differential Drive Mobile Robots. International Journal of Robotics & Control Systems, 6(1), 556.
10. Ekinci, S., Izci, D., Abu Zitar, R., Alsoud, A. R., & Abualigah, L. (2022). Development of Lévy flight-based reptile search algorithm with local search ability for power systems engineering design problems. Neural Computing and Applications, 34(22), 20263-20283.
11. Elsisi, M. (2021). Optimal design of non‐fragile PID controller. Asian Journal of Control, 23(2), 729-738.
12. Çelik, E., & Durgut, R. (2018). Performance enhancement of automatic voltage regulator by modified cost function and symbiotic organisms search algorithm. Engineering science and technology, an international journal, 21(5), 1104-1111.
13. Mok, R., & Ahmad, M. A. (2022). Fast and optimal tuning of fractional order PID controller for AVR system based on memorizable-smoothed functional algorithm. Engineering Science and Technology, an International Journal, 35, 101264.
14. Bouguenna, E., Ladaci, S., Lekouaghet, B., Merrouche, W., & Benghanem, M. (2025). Fractional order PID controller design for an AVR system using the artificial hummingbird optimizer algorithm. International Journal of Robust and Nonlinear Control, 35(9), 3919-3943.
15. Zhang, J., Zhang, T., Zhang, G., & Kong, M. (2023). Parameter optimization of PID controller based on an enhanced whale optimization algorithm for AVR system. Operational Research, 23(3), 44.
16. Hekimoğlu, B. (2023). Determination of AVR System PID Controller Parameters Using Improved Variants of Reptile Search Algorithm and a Novel Objective Function. Energy Engineering, 120(7).
17. Sahin, A. K., Cavdar, B., & Ayas, M. S. (2024). An adaptive fractional controller design for automatic voltage regulator system: sigmoid-based fractional-order PID controller. Neural Computing and Applications, 36(23), 14409-14431.
18. Gopi, P., Reddy, S. V., Bajaj, M., Zaitsev, I., & Prokop, L. (2024). Performance and robustness analysis of V-Tiger PID controller for automatic voltage regulator. Scientific Reports, 14(1), 7867.
19. Mosaad, A. M., Attia, M. A., Elbehairy, N. M., Alruwaili, M., Yousef, A., & Hamed, N. M. (2025). Enhancing AVR System Stability Using Non-Monopolize Optimization for PID and PIDA Controllers. Processes, 13(10), 3072.
20. Shouran, M., Alenezi, M., Muftah, M. N., Almarimi, A., Abdallah, A., & Massoud, J. (2025). A novel AVR system utilizing fuzzy PIDF enriched by FOPD controller optimized via PSO and Sand Cat Swarm Optimization algorithms. Energies, 18(6), 1337.
21. Sekyere, Y. O. M., Ajiboye, P. O., Effah, F. B., & Opoku, B. T. (2025). Optimizing PID control for automatic voltage regulators using ADIWACO PSO. Scientific African, 27, e02562.
22. Andiç, C. (2026). A Novel Superb Fairy-Wren Optimization Algorithm Based PID Controller for an Automatic Voltage Regulator System. Applied Sciences, 16(2), 856.
23. Ala eddine, R., Ramzi, K., Mouassa, S., & Toma, L. (2026). Enhanced AVR System Performance via Optimal PID Controller Design Using the Red-Tailed Hawk Algorithm. Processes, 14(10), 1550.
24. Ayman, M., Attia, M. A., & Asim, A. M. (2026). Cascaded adaptive model predictive and PID control for integrated LFC–AVR enhancement. Scientific Reports, 16(1), 12734.
25. Jegatheesh, A., Thiyagarajan, V., Selvan, N. M., & Raj, M. D. (2024). Voltage regulation and stability enhancement in AVR system based on SOA-FOPID controller. Journal of Electrical Engineering & Technology, 19(1), 31-44.
26. Wen, P., Liang, X., Dai, F., & Wang, S. (2026). Optimal FOPID controller design for an AVR system using a Chaotic-Enhanced Phototropic Growth Algorithm (C-PGA). Scientific Reports.
27. Shouran, M., & Alenezi, M. (2025). A novel fuzzy PIDF enhancing PIDF controller tuned in two stages by TLBO and PSO algorithms for reliable AVR performance. IEEE Access, 13, 93505-93522.
28. Mansour, S., Attia, M. A., Badr, A. O., Shaaban, M. F., & Hamed, N. M. (2025). Improvement of Combined LFC-AVR System Performance with Fuzzy PID Controller in Single and Multi-Area Power Networks. Results in Engineering, 107592.
29. Zhong, C., Li, G., Meng, Z., Li, H., Yildiz, A. R., & Mirjalili, S. (2025). Starfish optimization algorithm (SFOA): a bio-inspired metaheuristic algorithm for global optimization compared with 100 optimizers. Neural Computing and Applications, 37(5), 3641-3683.
30. Ekinci, S., Izci, D., Gider, V., Abualigah, L., Bajaj, M., & Zaitsev, I. (2025). Efficient control strategy for electric furnace temperature regulation using quadratic interpolation optimization. Scientific Reports, 15(1), 154