dSPACE Kullanılarak Elastik Kablolu Bir Vinç Sisteminin Fal Fonksiyonuna Dayalı Doğrusal Olmayan PID Kontrolü

Abstract

Kablo tahrikli mekanizmalarda, kablo esnekliği doğrusal kontrolcü düşürerek salınımlara neden olmakta ve konumlandırma doğruluğunu azaltmaktadır. Bu çalışmanın temel yeniliği, esnek kablolu bir vinç sistemindeki bu salınımları etkili bir şekilde bastırmak amacıyla fal fonksiyonuna dayalı doğrusal olmayan bir PID (NPID) kontrolcüsünün gerçek zamanlı deneysel uygulamasıdır. Fal fonksiyonu, hata büyüklüğüne bağlı olarak dinamik kazanç adaptasyonu sağlamaktadır. Deneysel kurulum, tüm çalışma koşullarını tek bir deneyde değerlendirmek için beş döngülü periyodik trapez referans kullanan ve örnekleme zamanı 0.001 s olan bir dSPACE DS1104 kartı ile çalıştırılmıştır. Aynı donanım koşulları altında ayarlanan geleneksel bir PID ile karşılaştırıldığında, önerilen NPID maksimum mutlak hatayı %57, birikimli hatayı %42, ortalama hata genliğini %40 ve toplam kontrol eforunu %26 oranında azaltmıştır. Sonuç olarak NPID, aşina olunan PID yapısından sapmadan, esnek elektromekanik sistemlerde izleme doğruluğunu ve eyleyici verimliliğini önemli ölçüde artırmaktadır.

Keywords

• Elastik kablolu vinç sistemi
• PID
• Doğrusal Olmayan PID
• Gerçek zamanlı kontrol
• dSPACE DS1104

Supporting Institution

TÜBİTAK

Project Number

123C313

Ethical Statement

Bu çalışma, 123C313 numaralı proje kapsamında TÜBİTAK-2218 Ulusal Doktora Sonrası Araştırma Burs Programı tarafından desteklenmiştir.

Nonlinear PID Control Based on the Fal Function of an Elastic Cable Winch System Using dSPACE

Abstract

In cable-driven mechanisms, cable elasticity degrades linear controller performance, causing oscillations and reducing positioning accuracy. The main novelty of this study is the real-time experimental application of a nonlinear PID (NPID) controller based on the fal function to effectively suppress these oscillations in an elastic cable winch system. The fal function enables dynamic gain adaptation based on error magnitude. The experimental setup was driven by a dSPACE DS1104 board with a sampling time of 0.001 s, utilizing a five-cycle periodic trapezoidal reference to evaluate all operating conditions in a single run. Compared to a conventional PID tuned under identical hardware conditions, the proposed NPID reduced the maximum absolute error by 57%, accumulated error by 42%, average error amplitude by 40%, and total control effort by 26%. Ultimately, the NPID significantly improves tracking accuracy and actuator efficiency in flexible electromechanical systems without deviating from the familiar PID structure.

Keywords

• Elastic cable winch system
• PID
• Nonlinear PID
• Real-time control
• dSPACE DS1104

Supporting Institution

TÜBİTAK

Project Number

123C313

Ethical Statement

This study was supported by the TÜBİTAK-2218 National Post-Doctoral Research Fellowship Programme under Project No: 123C313.

References

1. Zhang X, Du J, Shi Y, Du K. Hybrid Force-Pose PD Control of DR-CDPRs Based on the Cable Speed. In: 2025 8th International Conference on Intelligent Robotics and Control Engineering (IRCE); 18-21 August 2025; Kunming, China. pp. 87-87.
2. Zou W, Yu N. Modeling and Control of a Cable-Driven Series Elastic Actuator. arXiv:1701.03913, 2017.
3. Khosravi MA, Taghirad HD. Robust PID control of cable-driven robots with elastic cables. In: 2013 First RSI/ISM International Conference on Robotics and Mechatronics (ICRoM); 13-15 February 2013; Tehran, Iran. pp. 331-336.
4. Khosravi MA, Taghirad HD. Stability Analysis and Robust PID Control of Cable-Driven Robots Considering Elasticity in Cables. Amirkabir International Journal of Science & Research Electrical & Electronics Engineering 2016; 48(2): 113-125.
5. Baklouti S, Caro S, Courteille E. Elasto-dynamic Model-Based Control of Non-redundant Cable-Driven Parallel Robots. In: Arakelian V, Wenger P, editors. ROMANSY 22 – Robot Design, Dynamics and Control. Cham, Switzerland: Springer, 2019; pp. 238-246.
6. Begey J, Cuvillon L, Lesellier M, Gouttefarde M, Gangloff J. Dynamic Control of Parallel Robots Driven by Flexible Cables and Actuated by Position-Controlled Winches. IEEE Trans Robot 2019; 35(1): 286-293.
7. Han J. From PID to Active Disturbance Rejection Control. IEEE Trans Ind Electron 2009; 56(3): 900-906.
8. Zhu M. Nonlinear Digital Control for a 1-KW PWM DC/DC Switching Power Converter. MSc, Cleveland State University, Cleveland, USA, 2002.

9. Hong L, Jianing S, Yao C, Qian S, Ruixiang H, Xiaojie Y. The Applications of Nonlinear PI Controller Based on the fal Function in the DC-DC Converter. Trans China Electrotech Soc 2014; 29(1): 326-331.
10. Lei Z, Zhou Y. A kind of nonlinear PID controller for Refrigeration Systems based on Vapour Compression. In: 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control; 9-11 May 2018; Ghent, Belgium. pp. 716-721.
11. Sancak VK, Bayraktaroglu ZY. Nonlinear Computed Torque Control of 6-DoF Parallel Manipulators. Int J Control Autom Syst 2022; 20(7): 2297-2311.
12. Jin K, Wang R, Zhang Y, Li X. Vibration control of Stewart platform based on an improved nonlinear proportional-derivative control method. Int J Adv Robot Syst 2024; 21(6): 1-14.
13. Wu D, Chen K. Frequency-Domain Analysis of Nonlinear Active Disturbance Rejection Control via the Describing Function Method. IEEE Trans Ind Electron 2013; 60(9): 3906-3914.
14. Yue L, Wang Y, Xiao B, Wang Y, Lin J. Improved active disturbance rejection speed control for autonomous driving of highspeed train based on feedforward compensation. Sci Prog 2023; 106(4): 1-26.
15. Ding M, Liu B, Wang L. Position control for ball and beam system based on active disturbance rejection control. Syst Sci Control Eng 2019; 7(1): 97-108.
16. Zhang K, Liu Y, Huo B, Wu Z, Yang L, Yu H. ESO-Based Antisaturation Motion Control for Cable-Driven Continuum Robots. IEEE/ASME Trans Mechatron 2025; 30(1): 517-529.
17. Zhang K, Liu Y, Huo B, Wu Z, Yang L, Yu H. Enhanced extended state observer-based model-free force control for a Series Elastic Actuator. Mech Syst Signal Process 2023; 183: 109584.
18. Zhou B, Yu S, Li S, Zi B, Zhu W. Active Disturbance Rejection Control for Vibration Suppression of a Dual-Arm Cooperative Rigid-Flexible Coupling Hoisting Robot. IEEE Trans Ind Electron 2026; 73(7): 10187-10197.
19. Chang X, Jin C, Cheng Y. Dynamics and advanced active disturbance rejection control of tethered UAV. Appl Math Model 2024; 135: 640-665.
20. Liu J. Enhancing the Control of Tethered Turbofan Rescue Drones Based on Improved Active Disturbance Rejection Control. International Journal for Housing Science and Its Applications 2025; 47(1): 769-782.
21. Ding J, Wei H, Zhang Y, Zhi P, Zhu W. Analysis of Fuzzy Control Strategy Combined with Active Disturbance Rejection for Shore Power Winches. In: 2025 44th Chinese Control Conference (CCC); 28-30 July 2025; Chongqing, China. pp. 2578-2583.
22. Sen DK, Arisoy A, Gokdag H. Real-Time Tracking and Position Control of an Elastic Cable-Driven Winch System. Appl Sci 2025; 15(10): 5462.
23. Gürgöze M. Analitik Mekaniğe Giriş - 2. Baskı (Introduction to Analytical Mechanics- 2nd Edition). İstanbul, Türkiye: İTÜ Vakfı Yayınları, 2019.
24. Ogata K. Modern Control Engineering. New Jersey, USA: Prentice Hall, 2010.