طراحی رویتگر حالت تعمیم‌یافته فازی-تطبیقی برای سیستم‌های غیرخطی اَفاین با اغتشاش خارجی

نوع مقاله : گرایش دینامیک، ارتعاشات و کنترل

نویسندگان

1 دانشجوی دکتری، دانشکده مهندسی برق، دانشگاه علم و صنعت ایران، تهران، ایران

2 نویسنده مسئول: استاد، دانشکده مهندسی برق، دانشگاه علم و صنعت ایران، تهران، ایران

چکیده

در این مقاله، هدف طراحی رویتگر تعمیم‌یافته فازی-تطبیقی برای تخمین همزمان حالت‌ها و اغتشاش خارجی در سیستم‌های غیرخطی افاینِ تک‌ورودی-تک‌خروجی است. دراین رابطه، بهره‌های رویتگر به‌صورت متغیر با زمان درنظر گرفته شده و با استفاده از قانون تطبیق، تنظیم شده‌ است. مدل‌سازیِ سیستم نیز توسط سیستم فازیِ تاکاگی-سوگنو انجام شده است که بر خلاف روش ممدانی، تحلیل دقیق‌تر و جامع‌تری را در اختیار قرارمی‌دهد. رویتگر فازی-تطبیقی پیشنهادی که تابعی از خطای تخمین است، به‌منظور کاهش محدودیت‌ها از جمله وابستگی به پهنای باند رویتگر و بهبود عملکرد سیستم نسبت به روش‌های کلاسیک، در حضور اغتشاش خارجی متغیر با زمان طراحی شده است. همچنین، ضمن تضمین پایداری روش پیشنهادی با استفاده از نظریه پایداری لیاپانوف، همگرایی خطای تخمین نیز مورد تجزیه و تحلیل قرار گرفته است. عملکرد روش پیشنهادی در کنترل آونگ وارون شبیه‌سازی شده است. نتایج شبیه‌سازی در مقایسه با رویتگر فازی، نشان از عملکرد بسیار بهتر آن در پاسخ‌های گذرا و حالت ماندگار و همچنین دامنه سیگنال ورودی و مقاوم بودن روش پیشنهادی در حضور اغتشاش خارجی، نویز اندازه‌گیری، و تغییر ناگهانی پارامترهای سیستم دارد.

کلیدواژه‌ها


عنوان مقاله [English]

Designing an Adaptive Fuzzy Extended State Observer for Nonlinear Affine Systems with External Disturbance

نویسندگان [English]

  • Mahtab Delpasand 1
  • Mohammad Farrokhi 2
1 Ph.D. Student, Faculty of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran
2 Corresponding author: Professor, Faculty of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran
چکیده [English]

In this paper, an adaptive fuzzy extended state observer is proposed to estimate the states and external disturbances simultaneously for Single-Input-Single-Output nonlinear affine systems. The observer gains are time-varying and adjusted using an adaptive law. The Takagi-Sugeno fuzzy system is used for modeling that, unlike Mamdani methods, provides a more precise and comprehensive analysis. The proposed adaptive fuzzy observer is designed to relax the limitations of the extended state observers and improve system performance as compared to the classical methods in presence of time-varying disturbances. Moreover, the stability of the proposed method and the convergence of the estimation error are analyzed using the Lyapunov stability Theory. The performance of the proposed method is shown in simulations of control of the inverted pendulum. The simulation results, as compared to the non-adaptive fuzzy observer, show better performance in terms of transient and steady-state responses, control input amplitude, and robustness in presence of measurement noise and external disturbances.

کلیدواژه‌ها [English]

  • Adaptive fuzzy observer
  • Observer estimation error
  • Lyapanov stability
  • Inverted pendulum

Smiley face

[1] Ahmad S, Ali A. Active disturbance rejection control of DC–DC boost converter: A review with modifications for improved performance. IET Power Electronics. 2019;12(8):2095-107.##
[2] Wei Y, Jia S, Liu K. A survey on anti-disturbance control of switched systems with input saturation. Systems Science & Control Engineering. 2020;8(1):241-8.##
[3] Chen W-H, Yang J, Guo L, Li S. Disturbance-observer-based control and related methods—An overview. IEEE Transactions on industrial electronics. 2015;63(2):1083-95.##
[4] Yuan Y, Cheng L, Wang Z, Sun C. Position tracking and attitude control for quadrotors via active disturbance rejection control method. Science China Information Sciences. 2019;62(1):1-10.##
[5] Han T, Li J, Guan Z-H, Cai C-X, Zhang D-X, He D-X. Containment control of multi-agent systems via a disturbance observer-based approach. Journal of the Franklin Institute. 2019;356(5):2919-33.##
[6] Sui S, Tong S, Chen CP. Finite-time filter decentralized control for nonstrict-feedback nonlinear large-scale systems. IEEE Transactions on Fuzzy systems. 2018;26(6):3289-300.##
[7] Ren C-E. Adaptive Fuzzy Disturbance Observer-Based Control for Nonlinear Uncertain Systems with General Exogenous Disturbances. International Journal of Fuzzy Systems. 2021;23(5):1453-61.##
[8] Khamar M, Edrisi M. Designing a nonlinear disturbance observer and LQR based fractional order backstepping controller for a wearable rehabilitation robot. Modares Mechanical Engineering. 2018;18(9):229-41.##
[9] Hua C-C, Wang K, Chen J-N, You X. Tracking differentiator and extended state observer-based nonsingular fast terminal sliding mode attitude control for a quadrotor. Nonlinear Dynamics. 2018;94(1):343-54.##
[10] Feng H, Guo B-Z. Active disturbance rejection control: Old and new results. Annual Reviews in Control. 2017;44:238-48.##
[11] Hall CE, Shtessel YB. Sliding mode disturbance observer-based control for a reusable launch vehicle. Journal of guidance, control, and dynamics. 2006;29(6):1315-28.##
[12] Tatsumi J, Gao Z, editors. On the enhanced ADRC design with a low observer bandwidth. Proceedings of the 32nd Chinese control conference; 2013: IEEE.##
[13] Han J. A class of extended state observers for uncertain systems. Control and decision. 1995;10(1):85-8.##
[14] Xue W, Madonski R, Lakomy K, Gao Z, Huang Y. Add-on module of active disturbance rejection for set-point tracking of motion control systems. IEEE Transactions on Industry Applications. 2017;53(4):4028-40.##
[15] Zhang Y, Zhang J, Wang L, Su J. Composite disturbance rejection control based on generalized extended state observer. Isa Transactions. 2016;63:377-86.##
[16] Castillo A, García P, Sanz R, Albertos P. Enhanced extended state observer-based control for systems with mismatched uncertainties and disturbances. ISA transactions. 2018;73:1-10.##
[17] Yoo D, Yau S-T, Gao Z. Optimal fast tracking observer bandwidth of the linear extended state observer. International Journal of Control. 2007;80(1):102-11.##
[18] Chen S, Bai W, Huang Y, editors. ADRC for systems with unobservable and unmatched uncertainty. 2016 35th Chinese Control Conference (CCC); 2016: IEEE.##
[19] Fu C, Tan W. Tuning of linear ADRC with known plant information. ISA transactions. 2016;65:384-93.##
[20] Zhang C, Zhu J, Gao Y. Order and parameter selections for active disturbance rejection controller. Control Theory & Applications. 2014;31(11):1480-5.##
[21] Naghdi M, Sadrnia MA. A novel fuzzy extended state observer. ISA transactions. 2020;102:1-11.##
[22] Herbst G. Transfer function analysis and implementation of active disturbance rejection control. Control Theory and Technology. 2021;19(1):19-34.##
[23] Nie ZY, Zhang B, Wang QG, Liu RJ, Luo JL. Adaptive active disturbance rejection control guaranteeing uniformly ultimate boundedness and simplicity. International Journal of Robust and Nonlinear Control. 2020;30(17):7278-94.##
[24] Xue W, Bai W, Yang S, Song K, Huang Y, Xie H. ADRC with adaptive extended state observer and its application to air–fuel ratio control in gasoline engines. IEEE Transactions on Industrial Electronics. 2015;62(9):5847-57.##
[25] Han L, Tang G, Cheng M, Huang H, Xie D. Adaptive nonsingular fast terminal sliding mode tracking control for an underwater vehicle-manipulator system with extended state observer. Journal of Marine Science and Engineering. 2021;9(5):501.##
[26] Kazemi A, Abjadi N. Fuzzy Adaptive Control Based on MRAS for SISO Nonlinear Systems with Uncertainty. Tabriz Journal of Electrical Engineering. 2018;47(4):1613-25.##
[27] Pu Z, Yuan R, Yi J, Tan X. A class of adaptive extended state observers for nonlinear disturbed systems. IEEE Transactions on Industrial Electronics. 2015;62(9):5858-69.##
[28] Li Y, Chen Y. The Research of Gain Adaptive Linear Extended State Observer (ALESO) Based Active Disturbance Rejection Speed Control For Permanent Magnet Synchronous Motor. Electrica. 2021;21(1):20-31.##
[29] Zhao ZL, Ma P, Chen S. A new nonlinear extended state observer design for output tracking of uncertain nonlinear systems. Advanced Control for Applications: Engineering and Industrial Systems. 2021;3(2):e46.##
[30] Yang Y, Tan J, Yue D. Prescribed performance tracking control of a class of uncertain pure-feedback nonlinear systems with input saturation. IEEE Transactions on Systems, Man, and Cybernetics: Systems. 2018;50(5):1733-45.##
[31] Izadinasab A, Ghanbari M. Control of sensorless PMSM using state dependent model reference adaptive system and adaptive augmented observer. Journal of Modeling in Engineering. 2021;18(63):85-95.##
[32] Yao W, Hai Tao Y, Rong G, Dong Yang L, Ningjun F, Zheng X. Fuzzy adaptive sliding mode control of PMSM based on extended state observer. International Journal of Applied Electromagnetics and Mechanics. 2020;63(3):391-407.##
[33] Fallah Ghavidel H, Akbarzadeh Kalat A. Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems. Neural Computing and Applications. 2018;30(4):1187-202.##
[34] Fallah Ghavidel H, Akbarzadeh Kalat A, Ghorbani V. Observer-Based robust adaptive fuzzy approach for current control of robot manipulators by estimation of uncertainties. Modares Mechanical Engineering. 2017;17(6):286-94.##
[35] Zhao D, Lam HK, Li Y, Ding SX, Liu S. A novel approach to state and unknown input estimation for Takagi–Sugeno fuzzy models with applications to fault detection. IEEE Transactions on Circuits and Systems I: Regular Papers. 2020;67(6):2053-63.##
[36] Hyun C-H, Park C-W, Kim S. Takagi–Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design. Information Sciences. 2010;180(11):2314-27.##
[37] Lendek Z, Guerra TM, Babuska R, De Schutter B. Stability analysis and nonlinear observer design using Takagi-Sugeno fuzzy models: Springer; 2011.##
[38] Li S, Yang J, Chen W-H, Chen X. Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Transactions on Industrial Electronics. 2011;59(12):4792-802.##
[39] Cui M, Liu H, Liu W. Extended state observer-based adaptive control for a class of nonlinear system with uncertainties. Control and Intelligent Systems. 2017;45(3):132-41.##
[40] Bahrami V, Mansouri M, Teshnehlab M. Designing Model Reference Fuzzy Controller Based on State Feedback Integral Control for Nonlinear Systems. Journal of Control. 2015;9(3):1-18.##
 
دوره 18، شماره 2 - شماره پیاپی 68
شماره پیاپی 68، فصلنامه تابستان
مرداد 1401
صفحه 109-124
  • تاریخ دریافت: 07 دی 1400
  • تاریخ بازنگری: 06 بهمن 1400
  • تاریخ پذیرش: 01 اسفند 1400
  • تاریخ انتشار: 01 مرداد 1401