Journals / Turkish Journal of Science and Technology / 2026 / Volume: 21 Issue: 2

Underwater-Mission-Oriented Objective Function Design for Metaheuristic Tuning of PID and Fractional-Order PID Controllers

Sualtı Görevlerine Yönelik Amaç Fonksiyonu Tasarımı ile PID ve Kesir Dereceli PID Denetleyicilerin Meta-Sezgisel Ayarlanması

Hakan Ersoy(YILDIZ TECHNICAL UNIVERSITY)0000-0001-5556-547X
Aslıhan Kartcı(YILDIZ TEKNİK ÜNİVERSİTESİ)0000-0001-5690-7574
Pages
—
Publication Date
2026-09-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The study is simulation-based and one-dimensional; no hardware validation is claimed.

📌 3 Key Takeaways

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Objective & Hypothesis:Metaheuristic tuning of depth controllers for remotely operated vehicles is usually performed against a generic error integral, which does not encode mission priorities such as battery use, actuator stress from chattering, direction-dependent overshoot risk and post-event recovery.
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Key Findings & Data:A mission-oriented cost augments a time-weighted error integral with baseline-normalized effort, smoothness, asymmetric-overshoot and recovery terms on a one-degree-of-freedom BlueROV2 heave model with saturation, actuator lag and sensor noise.
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Conclusion & Impact:The study is simulation-based and one-dimensional; no hardware validation is claimed.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:bluerov2 · fractional-order PID · mission-oriented tuning

Abstract

Metaheuristic tuning of depth controllers for remotely operated vehicles is usually performed against a generic error integral, which does not encode mission priorities such as battery use, actuator stress from chattering, direction-dependent overshoot risk and post-event recovery. This paper treats the objective function itself as the design object. A mission-oriented cost augments a time-weighted error integral with baseline-normalized effort, smoothness, asymmetric-overshoot and recovery terms on a one-degree-of-freedom BlueROV2 heave model with saturation, actuator lag and sensor noise. Adding the terms cumulatively raises the advantage of the fractional controller over PID from 7.0 to 22.7 percent over ten runs per level, and encoding survey, near-bottom inspection and long-endurance missions as weight profiles gives it the lower cost in every run, largest at 35.4 percent on inspection. The conclusion is then tested against the designer's choices: 160 random weight vectors, four normalization schemes, Monte-Carlo sweeps over noise and plant parameters, and eleven held-out scenarios. A linear analysis exposes one negative result: the cost carries no frequency-domain specification, so the tuned loops have small phase margins that saturation hides, and an explicit margin requirement is needed to restore them. The study is simulation-based and one-dimensional; no hardware validation is claimed.

Özet

Uzaktan kumandalı su altı araçlarının derinlik denetleyicileri meta-sezgisel yöntemlerle çoğunlukla genel bir hata integraline göre ayarlanır; bu ölçüt batarya kullanımı, denetim salınımlarının oluşturduğu aktüatör yükü, yön bağımlı aşım riski ve akıntı olayı sonrası toparlanma gibi göreve özgü öncelikleri temsil etmez. Bu çalışmada amaç fonksiyonunun kendisi tasarım nesnesi olarak ele alınmıştır. Zaman ağırlıklı hata integrali; denetim çabası, denetim düzgünlüğü, asimetrik aşım ve olay sonrası toparlanma terimleriyle genişletilmiş, tüm terimler referans bir PID tasarımına göre normalize edilmiş ve doygunluk, aktüatör gecikmesi ve gürültü içeren tek serbestlik dereceli bir BlueROV2 düşey hareket modelinde sınanmıştır. Terimler kademeli olarak eklendiğinde kesir dereceli denetleyicinin PID'ye üstünlüğü, seviye başına on koşuda yüzde 7,0'den yüzde 22,7'e yükselmiştir. Tarama, deniz tabanına yakın inceleme ve uzun süreli görevler ağırlık profilleri olarak kodlandığında kesir dereceli denetleyici tüm koşularda daha düşük maliyet üretmiş, en büyük fark yüzde 35,4 ile inceleme görevinde elde edilmiştir. Sonuç, tasarımcı tercihlerine karşı sınanmıştır: 160 rastgele ağırlık vektörü, dört normalizasyon şeması, ölçüm gürültüsü ve model belirsizliği üzerinde Monte-Carlo taramaları ve on bir tutulan senaryo. Doğrusal analiz olumsuz bir sonuç vermiştir: amaç fonksiyonunda frekans bölgesi kısıtı bulunmadığından ayarlanan çevrimlerin faz payları düşüktür ve bu durum itici doygunluğunca gizlenmektedir. Çalışma benzetim tabanlıdır; donanım doğrulaması iddia edilmemektedir.

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Cite This Article

Ersoy, H., Kartcı, A. (2026). Underwater-Mission-Oriented Objective Function Design for Metaheuristic Tuning of PID and Fractional-Order PID Controllers. Turkish Journal of Science and Technology, Volume: 21 Issue: 2. https://doi.org/10.55525/tjst.1989945

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References (29)

  1. Fossen TI. Handbook of Marine Craft Hydrodynamics and Motion Control. Chichester, UK: Wiley, 2011.
  2. von Benzon M, Sørensen FF, Uth E, Jouffroy J, Liniger J, Pedersen S. An open-source benchmark simulator: Control of a BlueROV2 underwater robot. J Mar Sci Eng 2022; 10(12): 1898.
  3. Podlubny I. Fractional-order systems and PI^λ D^μ-controllers. IEEE Trans Autom Control 1999; 44(1): 208-214.
  4. Shah P, Agashe S. Review of fractional PID controller. Mechatronics 2016; 38: 29-41.
  5. Oustaloup A, Levron F, Mathieu B, Nanot FM. Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans Circuits Syst I Fundam Theory Appl 2000; 47(1): 25-39.
  6. Akgul B, Güler E, Ersoy H, Kartci A, Ayten UE. Resource-efficient design of high-speed FIR filter: Fractional-order integrator/differentiator on FPGAs. Circuits Syst Signal Process 2026; 1-24.
  7. Ersoy H, Akgül B, Akpinar E, Kartci A, Ayten UE. A robust speed controller design for PMSM using PI^λ D^μ controllers. In: 2024 47th International Conference on Telecommunications and Signal Processing (TSP). New York, NY, USA: IEEE, 2024. pp. 289-293.
  8. Ersoy H, Akgül B, Akpınar E, Kartci A, Ayten UE. Design and implementation of PI^λ D^μ controller for ROVs: Thruster modeling, controller parameter optimization, and FPGA realization. Eng Sci Technol Int J 2026; 73: 102261.
  9. Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks. New York, NY, USA: IEEE, 1995. pp. 1942-1948.
  10. Mirjalili S, Mirjalili SM, Lewis A. Grey wolf optimizer. Adv Eng Softw 2014; 69: 46-61.
  11. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2002; 6(2): 182-197.
  12. Joseph SB, Dada EG, Abidemi A, Oyewola DO, Khammas BM. Metaheuristic algorithms for PID controller parameters tuning: review, approaches and open problems. Heliyon 2022; 8(5): e09399.
  13. Tian T, Huang Q, Lv J, Zhou M, Tang J. Application of multiobjective optimization based on modified SPEA2 method for tuning FOPID plus second-order derivative controller in hydraulic turbine governing system. J Electr Comput Eng 2024; 2024: 4217192.
  14. Marler RT, Arora JS. Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 2004; 26(6): 369-395.
  15. Das I, Dennis JE. A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Struct Optim 1997; 14(1): 63-69.
  16. Yao F, Yang C, Zhang M, Wang Y. Optimization of the energy consumption of depth tracking control based on model predictive control for autonomous underwater vehicles. Sensors 2019; 19(1): 162.
  17. Pinto JB, Carneiro JF, de Almeida FG, Cruz NA. Variable structure depth controller for energy savings in an underwater device: proof of stability. Actuators 2025; 14(7): 340.
  18. Türetken AE, Ersoy H, Kartci A. Energy-efficient and actuator-friendly control under wave disturbances: Model reference vs. PID for thruster surge. In: 2025 16th International Conference on Electrical and Electronics Engineering (ELECO). New York, NY, USA: IEEE, 2025. pp. 1-5.
  19. Ng P, Krieg M. Modifications to ArduSub that improve BlueROV SITL accuracy and design of hybrid autopilot. Appl Sci 2024; 14(17): 7453.
  20. Öztürk Ö, Çavdar B. Otomatik gerilim regülatörü sistemi denetleyici tasarımı için meta-sezgisel algoritmaların performansı. Karadeniz Fen Bilimleri Dergisi 2024; 14(4): 2258-2289.
  21. Li J, Liu Y, Shan C, Dai C. Implementation of simplified fractional-order PID controller based on modified Oustaloup’s recursive filter. J Shanghai Jiaotong Univ Sci 2020; 25(1): 44-50.
  22. Bohn C, Atherton DP. A SIMULINK package for comparative studies of PID anti-windup strategies. In: Proceedings of the IEEE/IFAC Joint Symposium on Computer-Aided Control System Design. New York, NY, USA: IEEE, 1994. pp. 447-452.
  23. Mann HB, Whitney DR. On a test of whether one of two random variables is stochastically larger than the other. Ann Math Stat 1947; 18(1): 50-60.
  24. Cureton EE. Rank-biserial correlation. Psychometrika 1956; 21(3): 287-290.
  25. Derrac J, Garcia S, Molina D, Herrera F. A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol Comput 2011; 1(1): 3-18.
  26. Vargha A, Delaney HD. A critique and improvement of the CL common language effect size statistics of McGraw and Wong. J Educ Behav Stat 2000; 25(2): 101-132.
  27. Storn R, Price K. Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 1997; 11(4): 341-359.
  28. Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 2010; 181(2): 259-270.
  29. He L, Zhang Y, Xie M, Yuan Z, Bai C. Three-dimensional trajectory tracking control of underactuated AUV based on fractional-order PID and super-twisting extended state observer. Fractal Fract 2025; 9(9): 580.