Kesir Dereceli Aralık Tip-2 Kayan Kipli Bulanık Kontrol ile Yörünge Takibi

Abstract

Bu çalışma, ters sarkaç sisteminin yörünge takibi için yeni bir kesir dereceli aralık tip-2 kayan kipli bulanık kontrol (FO-IT2SMFC) şeması önermektedir. Temel yenilik, eğimi kesir dereceli kayan kipli kontrol çerçevesi içine gömülü bir aralık tip-2 bulanık mantık sistemi (IT2FLS) aracılığıyla uyarlamalı olarak ayarlanan, zamana göre değişen kesir dereceli kayan yüzeyin tasarımında yatmaktadır. Bu entegrasyon, kontrolörün sistem belirsizliklerini daha etkin biçimde ele almasını sağlarken çatırdamayı azaltmakta ve yakınsama davranışını iyileştirmektedir. Lyapunov tabanlı kararlılık analizi, sınırlı dış bozucu etkiler altında kapalı döngü sisteminin asimptotik kararlılığını garanti etmektedir. Önerilen şemanın performansı benzetimler aracılığıyla doğrulanmış ve iki kayan kipli kontrol yaklaşımıyla kıyaslanmıştır. Sonuçlar, FO-IT2SMFC'nin üstün yörünge takip doğruluğu elde ettiğini ve birden fazla nicel değerlendirme ölçütü üzerinden diğer yöntemleri tutarlı biçimde geride bıraktığını göstermekte; bu durum, belirsiz doğrusal olmayan sistemlere uygulanabilirliğini ve sağlamlığını doğrulamaktadır.

Keywords

• Aralık Tip-2 Bulanık Mantık Sistemleri
• Kesir Dereceli Hesaplama
• Kayan Kipli Kontrol

Fractional-order Interval Type-2 Sliding Mode Fuzzy Control for Trajectory Tracking

Abstract

This study proposes a novel fractional-order interval type-2 sliding mode fuzzy control (FO-IT2SMFC) scheme for trajectory tracking of an inverted pendulum system. The central innovation lies in the design of a time-varying fractional-order sliding surface, whose slope is adaptively adjusted through an interval type-2 fuzzy logic system (IT2FLS) embedded within the fractional-order sliding mode framework. This integration enables the controller to handle system uncertainties more effectively while reducing chattering and improving convergence behavior. Lyapunov-based stability analysis guarantees the asymptotic stability of the closed-loop system under bounded external disturbances. The performance of the proposed scheme is validated through simulations and benchmarked against two conventional control approaches. Results demonstrate that FO-IT2SMFC achieves superior trajectory tracking accuracy and consistently outperforms competing methods across multiple quantitative evaluation indices, confirming its robustness and applicability to uncertain nonlinear systems.

Keywords

• Interval Type-2 Fuzzy Logic Systems
• Fractional-order Calculus
• Sliding Mode Control

References

1. [1] V. I. Utkin and I. Vadim, "Sliding mode control," Variable Structure Systems: From Principles to Implementation, vol. 66, no. 1, 2004.
2. [2] Y. Wang, Y. Feng, X. Zhang, and J. Liang, "A new reaching law for antidisturbance sliding-mode control of PMSM speed regulation system," IEEE Trans. Power Electron., vol. 35, no. 4, pp. 4117–4126, 2019.
3. [3] B. Brahmi, M. H. Laraki, A. Brahmi, M. Saad, and M. H. Rahman, "Improvement of sliding mode controller by using a new adaptive reaching law: Theory and experiment," ISA Trans., vol. 97, pp. 261–268, 2020.
4. [4] L. Morales, J. Aguilar, A. Rosales, and D. Pozo-Espin, "A fuzzy sliding-mode control based on Z-numbers and LAMDA," IEEE Access, vol. 9, pp. 117714–117733, 2021.
5. [5] B. Ma and Y. Wang, "Adaptive type-2 fuzzy sliding mode control of steer-by-wire systems with event-triggered communication," Proc. Inst. Mech. Eng. D, J. Automob. Eng., vol. 235, no. 9, pp. 2442–2455, 2021.
6. [6] S. Wang, Y. Hui, X. Sun, and D. Shi, "Neural network sliding mode control of intelligent vehicle longitudinal dynamics," IEEE Access, vol. 7, pp. 162333–162342, 2019.
7. [7] Z. C. Qiu and S. W. Chen, "Vibration control of a translational coupled double flexible beam system using sliding mode neural network fuzzy control," Trans. Inst. Meas. Control, vol. 44, no. 11, pp. 2264–2288, 2022.
8. [8] N. Patel, K. Nath, I. N. Kar, and S. Mukherjee, "Fixed-time control of nonlinear systems with experimental verification," IEEE Trans. Ind. Electron., 2026, doi: 10.1109/TIE.2026.3663756.

9. [9] H. L. N. N. Thanh, "Finite-time robust composite backstepping control based on a high-order sliding mode observer for quadcopter AAV trajectory tracking," IEEE Access, vol. 13, pp. 198164–198177, 2025.
10. [10] Z. Li, K. Luo, L. Tao, and Y. Zhou, "Adaptive sliding mode control via multiscale super-twisting algorithm," IEEE Access, vol. 14, pp. 21607–21619, 2026, doi: 10.1109/ACCESS.2026.3660973.
11. [11] Z. Sun, Y. Zhou, S. P. Kim, G. Zhou, and F. S. Kang, "Super-twisting sliding mode control for ANPC-driven permanent magnet synchronous motor with midpoint voltage balancing strategy," IEEE J. Emerg. Sel. Topics Power Electron., 2026, doi: 10.1109/JESTPE.2026.3665476.
12. [12] T. S. Das, U. D. Annakkage, I. K. Park, and D. Muthumuni, "Robust higher-order sliding mode control for virtual synchronous generators to enhance stability under varying network conditions," IEEE Access, vol. 13, pp. 197710–197734, 2025.
13. [13] Y. Gong, X. Zhao, and L. Wang, "Improved robust model predictive current control via high-order terminal sliding mode control for permanent magnet synchronous motor," IEEE Trans. Autom. Sci. Eng., vol. 23, pp. 5237–5249, 2026.
14. [14] M. K. Azeem, W. Hassan, M. Negnevitsky, E. Franklin, and P. A. Hosseinabadi, "Chattering-free robust terminal sliding mode control for DC nanogrids," IEEE Trans. Smart Grid, vol. 17, no. 1, pp. 83–96, 2026.
15. [15] Z. Sun, Z. Li, B. Chen, Y. Zhou, J. Zheng, and Z. Man, "A further study on terminal sliding mode control for nonlinear systems," IEEE/CAA J. Autom. Sinica, vol. 13, no. 1, pp. 43–56, 2026.
16. [16] G. Narayanan, S. Lee, and S. Ahn, "Reinforcement learning-based IT-2 fuzzy fractional-order sliding mode control for leader-follower formation tracking of flexible-joint robots," IEEE Trans. Fuzzy Syst., vol. 34, no. 2, pp. 503–516, 2026.
17. [17] A. S. Alsafran et al., "A robust fractional-order nonsingular terminal sliding mode control with deep learning-based Lie derivative estimation for maximum power point tracking in wind turbine," IEEE Access, vol. 13, pp. 127423–127435, 2025.
18. [18] O. Eray and S. Tokat, "The design of a fractional-order sliding mode controller with a time-varying sliding surface," Trans. Inst. Meas. Control, vol. 42, no. 16, pp. 3196–3215, 2020.
19. [19] K. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. New York, NY, USA: Academic Press, 2020.
20. [20] K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. New York, NY, USA: Wiley, 1993.
21. [21] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. San Diego, CA, USA: Academic Press, 1999.
22. [22] S. Das, Functional Fractional Calculus for System Identification and Controls. Berlin, Germany: Springer, 2008.
23. [23] I. Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Berlin, Germany: Springer, 2011.
24. [24] H. P. Ren, S. S. Jiao, X. Wang, and O. Kaynak, "Fractional order integral sliding mode controller based on neural network: Theory and electro-hydraulic benchmark test," IEEE/ASME Trans. Mechatronics, vol. 27, no. 3, pp. 1457–1466, 2022.
25. [25] G. Narayanan, M. S. Ali, Y. H. Joo, R. Perumal, B. Ahmad, and H. Alsulami, "Robust adaptive fractional sliding-mode controller design for Mittag-Leffler synchronization of fractional-order PMSG-based wind turbine system," IEEE Trans. Syst. Man Cybern. Syst., vol. 53, no. 12, pp. 7646–7655, 2023.
26. [26] B. Alizadeh, A. Hajipour, H. Tavakoli, and A. Nasrabadi, "Robust trajectory tracking of delta parallel robot using fractional-order sliding mode control," IEEE Access, vol. 11, pp. 86397–86412, 2023.
27. [27] G. Wang, W. Yuan, and X. Wang, "Minimal-learning-parameter based adaptive neural network with fractional-order sliding mode control for satellite formation flying," IEEE Access, vol. 12, pp. 108389–108398, 2024.
28. [28] L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I," Inf. Sci., vol. 8, no. 3, pp. 199–249, 1975.
29. [29] J. M. Mendel, Uncertain Rule-Based Fuzzy Systems: Introduction and New Directions. Berlin, Germany: Springer, 2001.
30. [30] O. Castillo and P. Melin, Type-2 Fuzzy Logic: Theory and Applications. Berlin, Germany: Springer, 2008.
31. [31] O. Castillo, P. Melin, J. Kacprzyk, and W. Pedrycz, "Type-2 fuzzy logic: Theory and applications," in Proc. IEEE Int. Conf. Granular Comput., Fremont, CA, USA, 2007.
32. [32] O. Castillo and P. Melin, "A review on interval type-2 fuzzy logic applications in intelligent control," Inf. Sci., vol. 279, pp. 615–631, 2014.
33. [33] K. Tai, A. R. El-Sayed, M. Biglarbegian, C. I. Gonzalez, O. Castillo, and S. Mahmud, "Review of recent type-2 fuzzy controller applications," Algorithms, vol. 9, no. 2, p. 39, 2016.
34. [34] N. N. Karnik, J. M. Mendel, and Q. Liang, "Type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 6, pp. 643–658, 1999.
35. [35] D. Wu, "A brief tutorial on interval type-2 fuzzy sets and systems," Fuzzy Sets Syst., 2010.
36. [36] D. Wu and J. M. Mendel, "Enhanced Karnik-Mendel algorithms," IEEE Trans. Fuzzy Syst., vol. 17, no. 4, pp. 923–934, 2008.
37. [37] D. Wu, "Approaches for reducing the computational cost of interval type-2 fuzzy logic systems: Overview and comparisons," IEEE Trans. Fuzzy Syst., vol. 21, no. 1, pp. 80–99, 2012.
38. [38] C. E. Celemin and M. A. Melgarejo, "A faster iterative computation of the centroid of an interval type-2 fuzzy set," in Proc. IEEE Annu. Meet. North Amer. Fuzzy Inf. Process. Soc. (NAFIPS), Berkeley, CA, USA, Aug. 2012, pp. 1–6.
39. [39] M. Biglarbegian, W. W. Melek, and J. M. Mendel, "Design of novel interval type-2 fuzzy controllers for modular and reconfigurable robots: Theory and experiments," IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1371–1384, 2010.
40. [40] S. Zeghlache, T. Benslimane, N. Amardjia, and A. Bouguerra, "Interval type-2 fuzzy sliding mode controller based on nonlinear observer for a 3-DOF helicopter with uncertainties," Int. J. Fuzzy Syst., vol. 19, no. 5, pp. 1444–1463, 2017.
41. [41] J. Huang, M. Ri, D. Wu, and S. Ri, "Interval type-2 fuzzy logic modeling and control of a mobile two-wheeled inverted pendulum," IEEE Trans. Fuzzy Syst., vol. 26, no. 4, pp. 2030–2038, 2018.
42. [42] S. Xu, G. Sun, Z. Ma, and X. Li, "Fractional-order fuzzy sliding mode control for the deployment of tethered satellite system under input saturation," IEEE Trans. Aerosp. Electron. Syst., vol. 55, no. 2, pp. 747–756, 2019.
43. [43] S. A. Moezi, E. Zakeri, and M. Eghtesad, "Optimal adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control method for some classes of nonlinear systems," ISA Trans., vol. 93, pp. 23–39, 2019.
44. [44] N. Ferhat, T. Aounallah, N. Essounbouli, F. Bouchafaa, and A. Hamzaoui, "Adaptive interval type 2 fuzzy fractional order sliding mode control for permanent magnet synchronous generators," in Proc. 9th Int. Conf. Syst. Control (ICSC), Caen, France, Nov. 2021, pp. 139–144.
45. [45] C. Edwards and S. K. Spurgeon, Sliding Mode Control: Theory and Applications. London, U.K.: Taylor & Francis, 1998.
46. [46] S. Tokat, I. Eksin, and M. Guzelkaya, "New approaches for on-line tuning of the linear sliding surface slope in sliding mode controllers," Turk. J. Electr. Eng. Comput. Sci., vol. 11, no. 1, pp. 45–60, 2003.
47. [47] J. M. Mendel, R. I. John, and F. Liu, "Interval type-2 fuzzy logic systems made simple," IEEE Trans. Fuzzy Syst., vol. 14, no. 6, pp. 808–821, 2006.
48. [48] J. Liu and X. Wang, Advanced Sliding Mode Control for Mechanical Systems: Design, Analysis and MATLAB Simulation. Berlin, Germany: Springer, 2012.
49. [49] A. Tepljakov, "FOMCON: Fractional-order modeling and control toolbox," in Fractional-Order Modeling and Control of Dynamic Systems. Cham, Switzerland: Springer, 2017, pp. 107–129.
50. [50] F. Alyoussef and I. Kaya, "A new dynamic sliding mode controller with disturbance observer for controlling integrating processes with time delay," Int. J. Control, vol. 97, no. 5, pp. 1136–1156, 2024.
51. [51] F. Alyoussef and I. Kaya, "Improved adaptive dynamic non-singular terminal sliding mode controller with fractional disturbance observer," Information Sciences, vol. 641, 119110, 2023.