طراحی کنترل‌کننده با تحمل عیب حسگری مبتنی بر رویتگر برای سیستم‌های مرتبه کسری غیرخطی

نوع مقاله : علمی-پژوهشی

نویسندگان

گروه مهندسی برق و کامپیوتر- دانشکده فنی و مهندسی - دانشگاه خوارزمی

چکیده

در این مقاله، مساله طراحی کنترل‌کننده با تحمل عیب برای سیستم‌های غیرخطی مرتبه کسری در حضور عیب حسگری بررسی شده است. با استفاده از تئوری سیستم‌های توصیفی، تخمین صحیحی از بردار حالت سیستم به‌دست آمده و براساس آن، یک کنترل‌کننده پایدارساز فیدبک حالت طراحی می‌شود. با استفاده از تکنیک‌های مناسب، طراحی پارامترهای رویتگر و کنترل‌کننده بر حسب نامساوی‌های ماتریسی خطی بیان می‌شود که ابزارهای قدرتمندی جهت حل آن‌ها وجود دارد. رویتگر پیشنهادی قادر است تخمین صحیحی از بردار عیب حسگری نیز ارائه دهد بنابراین، می‌توان از آن به‌عنوان واحد آشکارساز، جداساز و شناسایی‌کننده عیب استفاده نمود. همچنین ساختار روش پیشنهادی به‌گونه‌ای است که طراحی رویتگر و کنترل‌کننده به‌طور مستقل قابل‌انجام هستند که منجربه سادگی روند طراحی می‌شود. کارآیی روش پیشنهادی توسط نتایج شبیه‌سازی عددی نشان داده شده است.

کلیدواژه‌ها

عنوان مقاله [English]

Observer-based Sensor Fault-tolerant Controller Design for Nonlinear Fractional-Order Systems

نویسندگان [English]

  • S. Ghobadian
  • A. A. Ahmadi
Department of Electrical and Computer Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran
چکیده [English]

In this paper, fault-tolerant controller design problem for Lipschitz nonlinear fractional-order systems in presence of sensor fault is considered. By using the descriptor system theory, a correct estimation of the state vector is achieved and then by using it, a stabilizing state feedback controller is designed. By employing some appropriate techniques, parameters design of the observer and controller are stated in terms of linear matrix inequalities, which there exist powerful toolbox for solving them. The proposed observer can estimate the correct value of the sensor fault vector, thus, it can be utilized for the fault detection, isolation, and identification unit.  Besides, the structure of the proposed method is such that the observer and controller design can be performed independently, which facilitate the design process. The effectiveness of the proposed method is shown with numerical simulation results.

کلیدواژه‌ها [English]

  • Fractional-order systems
  • lipschitz nonlinear system
  • descriptor system
  • fault-tolerant control
  • sensor fault
  • linear matrix inequality

مراجع

[1]      J. Sabatier, O. P. Agrawal and J. A. T. Machado, Advances in fractional calculus, Springer Publishing, 2007.
[2]      A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006.
[3]      I. Podlubny, Fractional differential equations, Academic Press, New York, 1999.
[4]       B. M. Vinagre and Y. Q. Chen, “Lecture notes on fractional calculus applications in automatic control and robotics,” The 41st IEEE CDC2002 Tutorial Workshop #2, pages 1-310, Nevada, USA, 2002.
[5]      D. Baleanu, J. A. T. Machado and A. C. J. Luo, Fractional dynamics and control, Springer, New York, 2011.
[6]      N. Engheta, “On fractional calculus and fractional multipoles in electromagnetism” IEEE Transactions on Antennas and Propagation, vol. 44, no. 4, pp. 554-566, 1996.
[7]      X. Yin, D. Yue and S. Hu, “Consensus of fractional Order heterogeneous multi-agent systems”, IET Control Theory and Applications, vol.7, no. 2, pp. 314-322, 2013.
[8]      A. Boulkroune, A. Bouzerbia and T. Bouden, “Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control,” Neural Computing and Applications, vol. 27, no. 5, pp. 1349-1360, 2016.
[9]      N. Laskin, “Fractional market dynamics,” Physica A: Statistical Mechanics and its Applications, vol. 287, no. 3-4, pp. 482-492, 2000.
[10]      N. Ibrahima, M. Darouach, H. Voos and Z. Michel, “Design of unknown input fractional-order observers for fractional-order systems,” International Journal of Applied Mathematics and Computer Science, vol. 23, no. 3, pp. 491-500, 2013.
[11]      Y. H. Lan, L. L. Wang, L. Ding and Y. Zhou, “Full-order and reduced-order observer design for a class of fractional-order nonlinear systems,” Asian Journal of Control, vol. 18, no. 4, pp. 1467-1477, 2016.
[12]      S. Dadras, S. Dadras and H. R. Momeni, “Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems,” Journal of Dynamics, Measurement, and Control, vol. 139, no. 11, pp. 111003–111003-7, 2017.
[13]      الهه اسدی و سعید بلوچیان، «کنترل مقاوم-تطبیقی مدل مرتبه کسری موتور سری جریان مستقیم»، مجله مهندسی برق دانشگاه تبریز، جلد 47، شماره 3، صفحات 827-817، 1396.
[14]      Y. Q. Chen, I. Petras and D. Xue, “Fractional order control – A tutorial,” American Control Conference, St. Louis, MO, USA, 2009, pp. 1397-1411.
[15]      C. A. Monje, Y. Q. Chen, B. Vinagre, D. Xue and V. Fileu, Fractional order controls – Fundamentals and applications, Springer, London, 2009.
[16]      بهروز صفری‌نژادیان و مجتبی اسد، «ارائه دو فیلتر کالمن مرتبه کسری جدید برای سیستم‌های مرتبه کسری خطی در حضور نویز اندازه‌گیری خطی»، مجله مهندسی برق دانشگاه تبریز، جلد 47، شماره 2، صفحات 607-595، تابستان 1396.
[17]      I. Hwang, S. Kim, Y. Kim and C. E. Seah, “A survey of fault detection, isolation, and reconfiguration methods,” IEEE Transactions on Control Systems Technology, vol. 18, no. 3, pp. 636-653, 2010.
[18]      Y. Zhang and J. Jiang, “Bibliographical review on reconfigurable fault-tolerant control systems”, Annual Reviews in Control, vol. 32, no. 2, pp. 229-252, 2008.
[19]      S. X. Ding, Model-based fault diagnosis techniques: design schemes, algorithms and tools, Second Edition, Springer, 2013.
[20]      R. Isermann, Fault diagnosis systems, Springer, 2006.
[21]      M. Blanke, M. Kinnaert, J. Lunze and M. Staroswiecki, Diagnosis and fault-tolerant control, Springer 2006.
[22]      H. Noura, D. Theilliol, C. J. Ponsart and A. Chamseddine, Fault tolerant control systems, Design and Practical Applications, Springer, 2009.
[23]      H. Wang, T. Chai, J. Ding and B. Martin, “Data driven fault diagnosis and fault tolerant control: Some advances and possible new directions,” Acta Automatica Sinica, vol. 35, no. 6, pp. 739-747, 2009.
[24]      Z. Gao, C. Cecati and S. X. Ding, “A survey of fault diagnosis and fault-tolerant techniques-Part I: fault diagnosis with model-based and signal-based approaches,” IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3757-3767, 2015.
[25]      C. Cecati, A survey of fault diagnosis and fault-tolerant techniques-Part II: fault diagnosis with knowledge-based and hybrid/active approaches, IEEE Transactions on Industrial Electronics, vol. 62, no. 6, pp. 3768-3774, 2015.
[26]      I. N’Doye and T. M. L. Kirati, “Fractional order adaptive fault estimation for a class of nonlinear fractional order system,” American Control Conference, Chicago, IL, USA, 2015, pp. 3804-3809.
[27]      H. Shen, X. Song and Z. Wang, “Robust fault-tolerant control of uncertain fractional-order systems against actuator faults,” IET Control Theory and Applications, vol. 7, no. 9, pp. 1233-1241, 2013.
[28]      X. Song and H. Shen, “Fault tolerant control for interval fractional-order systems with sensor failures,” Advances in Mathematical Physics, DOI: 10.1155/2013/836743.
[29]      E. A. Boroujeni and H. R. Momeni, “Non-fragile nonlinear fractional order observer design for a class of nonlinear fractional order systems,” Signal Processing, vol. 92, no. 10, pp. 2365-2370, 2012.
[30]      E A. Boroujeni and H. R. Momeni, “An iterative method to design optimal non-fragile  observer for lipschitz nonlinear fractional order systems,” Nonlinear Dynamics, vol. 80, no. 4, pp. 1801-1810, 2015.
[31]      A. Jmal, O. Naifar, A. B. Makhlouf, N. Derbel and M. A. Hammami, “Robust sensor fault estimation for fractional-order systems with monotone nonlinearities,” Nonlinear Dynamics, vol. 90, no. 4, pp. 2673-2685, 2017.
[32]      Y. Farid, V. J. Majd and A. Ehsani-seresht, “Fractional-order active fault-tolerant force-position controller design for the legged robots using saturated actuator with unknown bias and gain degradation,” Mechanical Systems and Signal Processing, vol. 104, no. 5, pp. 465-486, 2018.
[33]      A. Jmal, O. Naifar, A. B. Makhlouf, N. Derbel and M. A. Hammami, “Sensor fault estimation for fractional-order descriptor one-sided Lipschitz systems,” Nonlinear Dynamics, vol. 91, no. 3, pp. 1713-1722, 2018.
[34]      A. Jmal, O. Naifar, A. B. Makhlouf and N. Derbel, “Fault tolerant control for linear fractional order systems with sensor faults,” 15th International Multi-Conference on Systems, Signals & Devices, Hammamet, Tunisia, 2018, pp. 105-110.
[35]      H. K. Khalil, Nonlinear Systems, Third Edition, Prentice Hall, 2002.
[36]      Y. Li, Y. Q. Chen and I. Podlubny, “Mittag–Leffler stability of fractional order nonlinear dynamic systems,” Automatica, vol. 45, no. 8, pp. 1965-1969, 2009.
[37]      A. D. M. Manuel, A. C. Norelys and A. G. Javier, “Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems,” Communications in Nonlinear Science and Numerical Simulations, vol. 22, no. 1-3, pp. 650-659, 2015.
[38]      S. Boyd, L. Ghaoui and E. Feron, Linear matrix inequalities in system and control theory, SIAM, 1994.
[39]      A. A. Ahmadi and V. J. Majd, “GCS of a class of chaotic systems with controller gain variations,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1238-1245, 2009.
[40]      Z. Gao, T. Breikin and H. Wang, “Reliable observer-based control against sensor failures for systems with time delays in both state and input,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 38, no. 5, pp. 1018-1029, 2008.
[41]      M. Abbaszadeh and H. J. Marquez, “Design of Nonlinear State Observers for One-Sided Lipschitz Systems,” arXiv preprint arXiv: 1302.5867, 2013.
[42]      J. Lofberg, “YALMIP: a toolbox for modeling and optimization in MATLAB,” in Proceeding of the International Symposium on Computer Aided Control Systems Design, pp. 284-289, Taipei, Taiwan, 2004. 

فایل ها

هم رسانی

ارجاع به این مقاله

آمار