کنترل همزمان ساز تطبیقی سیستم‌های غیرخطی آشوب در حضور اشباع ورودی و عیب عملگر

نوع مقاله: مقاله پژوهشی

نویسندگان

1 استادیار – دانشکده مهندسی برق، واحد نجف‌آباد، دانشگاه آزاد اسلامی، نجف‌آباد، ایران

2 کارشناس ارشد - دانشکده مهندسی برق، واحد نجف‌آباد، دانشگاه آزاد اسلامی، نجف‌آباد، ایران

چکیده

در این مقاله، یک کنترل کننده تطبیقی برای کنترل سیستم‌های غیرخطی جرک در معرض پارامترهای نامعین و محدودیت‌های کنترلی عیب عملگر و اشباع ورودی ارائه شده است. عیب عملگر در نظر گرفته شده عیوب کاهش کارایی و قفل شونده را پوشش می‌دهد. مقدار، زمان و الگوی عیوب در نظر گرفته شده کاملاً نامعین است یعنی مشخص نیست در چه زمانی، کدام عملگرها و با چه وضعیتی دچار عیب می‌شوند.کنترل کننده تطبیقی مقاوم پیشنهادی بر اساس روش کنترلی گام به عقب طراحی شده است. در این مقاله، با معرفی توابع لیاپانوف- کراسوسکی جدید، کرانداری سیگنالهای سیستم حلقه بسته و همگرایی خطای تعقیب به یک همسایگی نزدیک مبدأ تضمین شده است. روش تطبیقی پیشنهادی، عیوب عملگر را بدون نیاز به واحد تشخیص عیب جبران می‌کند. نتایج شبیه سازی، کارایی و صحت روش کنترلی ارائه شده را در همزمان سازی سیستم آشوب در حضور عیب عملگر، اشباع ورودی و نامعینی پارامتری نشان می‌دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Adaptive synchronization control of chaotic nonlinear systems in the presence of input saturation and actuator faults

نویسندگان [English]

  • mahnaz hashemi 1
  • Amir Pooyan 2
1 Assistant Professor - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 MSc - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
چکیده [English]

In this paper, the control problem is investigated for Jerk chaotic systems against unknown parameters, actuator faults and input saturation. The considered actuator fault covers both of the stuck faults and loss of effectiveness faults in actuators. The values, times and patterns of the considered faults are completely unknown. That is, during the system operation it is unknown when, by how much and which actuators fail. A robust adaptive controller is presented based on the backstepping design method to achieve complete synchronization of the identical Jerk chaotic systems. By introducing the new Lyapunov functions, it is proved that all the closed loop signals are bounded and the tracking error converges to a small neighborhood of the origin. The proposed adaptive method compensates the actuator faults without any need for explicit fault detection. Simulation results represent that the designed controller can synchronize the identical chaotic systems in the presence of actuator fault, input saturation and unknown parameters.
 

کلیدواژه‌ها [English]

  • Input Saturation
  • Chaotic systems
  • Actuator fault
  • Adaptive control
  • Backstepping control method
[1] B. E. Nieuwenhuys, A. C. Gluhoi, “Chaos, oscillations and the golden future of catalysis”, Catalysis Today,Vol. 100,pp. 49-54,Feb. 2005(doi.org/10.1016/j.cattod.2004.12.022).

[2] X. Wang, J. Zhang, “Chaotic secure communication based on nonlinear autoregressive filter with changeable parameters”, Physics Letters A, Vol. 357, No. 4-5, pp. 323-329, Sep. 2006 (doi:10.1016/j.physleta.2006.04.070).

[3] H. Zhang, X. Ma, B. Xue, W. Liu, “Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models”, ChaosSolutions Fractals, Vol. 23, No. 2, pp. 433-444, Jan. 2005 (doi:/10.1016/j.chaos.2004.04.020).

[4] V. E.Orel, A. V. Romanov, N. N.Dzyatkovskaya, Y. I. Mel’nik,“The device and algorithm forestimation of the mechanoemission chaos in blood of patients with gastric cancer”, Medical Engineering & Physics, Vol, 24,No. 5, pp. 365-371, Jun. 2002(doi.org/10.1016/S1350-4533(02)00022-X).

[5] J. C.Sprott, J. A.Vano, J. C.Wildenberg,M. B.Anderson, J. K Noel,“Coexistence and chaos in complex ecologies”, Phys.Letters A, Vol. 335, No. 2-3, pp. 207-212 Feb. 2005(doi.org/10.1016/j.physleta.2004.12.068).

[6] A. Shabunin,V. Astakhov, V. Demidov, A. Provata,F. Baras,G. Nicolis,V. Anishchenko,“Modeling chemical reactions by forced limit-cycle oscillator, synchronization phenomena and transition to chaos”, ChaosSolutions Fractals,Vol.15, No. 2, pp. 395-405, Jan. 2003(doi.org/10.1016/S0960-0779(02)00106-6).

[7] M. Xiao, J. Cao, “Synchronization of a chaotic electronic circuit system with cubic term via adaptive feedback control”, Commun. Nonlinear Sci. Numer. Simulation,Vol. 14, No. 8,pp. 3379–3388,Aug. 2009 (doi.org/10.1016/j.cnsns.2008.12.023).

[8] M. P. Aghababa,A. Heydari, “Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknownparameters and input nonlinearities”, Applied Mathematical Modelling, Vol. 36, No. 4, pp. 1639–1652, Apr. 2012(doi.org/10.1016/j.apm.2011.09.023).

[9] S. Vaidyanathan,A. TaherAzar, “Adaptive Backstepping control and Synchronization of a Novel 3-D Jerk System with an exponential Nonlinearity”, Advances in Chaos Theory and Intelligent Control, Stud. Fuzz.Soft Comput. V. 337, pp. 249-274, Apr.2016(doi.org/10.1007/978-3-319-30340-6_11).

[10] H. Li,X. Liao, C. Li, “Chaos control and synchronization via a novel chatter free sliding mode strategy”, Neurocomputing Vol. 74, No. 17,pp. 3212–3222, Oct. 2011(doi.org/10.1016/j.neucom.2011.05.002).

[11] M. Pourmahmood, S.Khanmohammadi, G. Alizadeh, “Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive slidingmode controller”, Commun. Nonlinear Sci. Numer. Simulation Vol. 16, No. 7, pp. 2853–2868, Jul. 2011(doi.org/10.1016/j.cnsns.2010.09.038).

[12] C. Mou, S. Jiang, J. Bin, Q. X. Wu,“Slidingmode synchronization controller design with neural network for uncertain chaotic systems”, Chaos Solutions Fractals,Vol. 39, No. 4, pp.1856–1863, Feb. 2009 (doi.org/10.1016/j.chaos.2007.06.113).

[13] M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, “Diagnosis and Fault-Tolerarant control”, Springer, Heidelberg,New York, 2006(doi.org/10.1007/978-3-540-35653-0).

[14] L. Wu, G. Yang, D. Ye, “Robust adaptive fault-tolerant control for linear systems with actuator failures and mismatched parameter uncertainties”, IET Control Theory Appl, Vol. 8, no. 6, pp. 441–449, Apr. 2014 (doi.10.1049/iet-cta.2013.0334).

[15] Y. Li, X, Jin,G. Yang, “Robust adaptive fault-tolerant control for uncertain linear systems with actuator failures”, IET Control Theory Appl. Vol. 6, No. 10, pp. 1544–1551, Jul. 2012(10.1049/iet-cta.2011.0599).

[16] M. Hashemi,J. Askari,J. Ghaisari,“Adaptive control of uncertain nonlinear time delay systems in the presence of actuator failures and applications to chemical reactor systems”, Eur. J. Control Vol. 29, pp. 62–73, May.2016(doi.org/10.1016/j.ejcon.2016.03.002).

[17] X. Tang,G. Tao,S. M. Joshi, “Adaptive actuatorfailure compensation of nonlinear MIMO systems with an aircraft control application”, Automatica Vol. 43, No. 11, pp. 1869–1883, Nov. 2007 (doi.org/10.1016/j.automatica.2007.03.019).

[18] M. Hashemi,J. Askari,J.Ghaisari,“Adaptive control for a class of MIMO nonlinear time delay systems against time varying actuator failures”, ISA Trans. Vol. 57, pp. 23–42, Jul. 2015(doi.org/10.1016/j.isatra.2015.02.012).

[19] D. Ye, G. Yang,“Adaptive Fault-Tolerant Tracking Control Against Actuator Faults With Application to Flight Control”, IEEE Trans. Control syst. Tech,Vol. 14, No. 6, pp. 6-15 Nov. 2006(doi.10.1109/TCST.2006.883191 ).

[20] S. Tong, T. Wang, Y. Li, "Fuzzy adaptive actuator failure compensation control of uncertain stochastic nonlinear systems with unmodeled dynamics", IEEE Trans. Fuzzy Syst,Vol. 22, No. 3,pp. 563–574, May. 2014 (doi.10.1109/TFUZZ.2013.2264939).

[21] P. Li, G. Yang,"Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults", J. Control Theory Appl,Vol. 7, No. 3, pp. 248–256, Aug. 2009(doi.org/10.1007/s11768-009-8074-6).

[22] M. Hashemi,J. Askari,J. Ghaisari, M. Kamali, “Adaptive compensation for actuator failure in a class of nonlinear time-delay systems”, IET Control Theory Appl,Vol. 9, No. 5,  pp.710–722, Mar. 2015(10.1049/iet-cta.2014.0504).

[23] M. Hashemi,J. Askari,J. Ghaisari,“Adaptive actuator failure compensation for a class of MIMOnonlinear time delay systems”, Nonlinear Dyn, Vol.  79, No. 2, pp. 865–883,Sep. 2015(doi.org/10.1007/s11071-014-1708-3).

[24] M. Hashemi, J. Askari, J. Ghaisari, “Adaptive decentralised dynamic surface control for nonlinear large-scale systems against actuator failures”, IET Control Theory Appl,Vol. 10, No. 1, pp. 1–14,Jan. 2015(doi.10.1049/iet-cta.2015.0418).

[25] M. Hashemi, “Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time varying actuator failures”, Int. J. Adapt. Control Signal Process, Vol. 31, No. 2, pp. 275–296 Sep. 2017 (doi.org/10.1002/acs.2715).

[26] S. P. Karason,A. M, Annaswamy, “Adaptive control in the presence of input constraints”, IEEE Trans. Automatic Control, Vol. 39, pp. 2325–2330, Jun. 1994(doi.10.23919/ACC.1993.4793095).

[27] G. Nicolao,R. Scattolini, G. Sala, “An adaptive predictive regulator with input saturations”, Automatica,Vol. 32, No. 4, pp. 597–601, Apr. 1996(doi.org/10.1016/0005-1098(95)00166-2).

[28] F. Z. Chaoui,F. Giri,M. M’Saad, J. M.Dion, “Adaptive control of input-constrained type-1 plants stabilization and tracking”, Automatica,Vol. 37, No. 2, pp. 197–203, Feb. 2001(doi.org/10.1016/S0005-1098(00)00154-0).

[29] F. Z. Chaoui,F. Giri,M. M’Saad, J. M. Dion, “Adaptive tracking with saturating input and controller integration action”, IEEE Trans. Automatic Control, Vol. 43,No. 11, pp. 1638–1643,Nov. 1998(doi.10.1109/9.728887).

[30] Y. Zhang, C. Wen, Y. Soh, “Adaptive backstepping control design for systems with unknown high-frequency gain”, IEEE Trans. Automatic Control.Vol. 45, No. 12, pp. 2350–2354, Dec. 2000(doi.10.1109/9.895572).

[31] T. Li,R. Li,J. Li, “Decentralized adaptive neural control of nonlinear interconnected large scale systems with unknown time delays and input saturation”, Neurocomputing,Vol. 74, No. 14-15, pp. 2277–2283,Jul. 2011(doi.org/10.1016/j.neucom.2011.03.005).

[32] Y. Li, S. Tong, T. Li, “Direct adaptive fuzzy backstepping control of uncertain nonlinear systems in the presence of input saturation”, Neural Comput. Appl, Vol. 23, No. 5, pp. 1207–1216, Jun. 2012 (doi.org/10.1007/s00521-012-0993-3).

[33] H. Wang,B. Chen, X. Liu, K. Liu, C. Lin, “Adaptive neural tracking control for stochastic nonlinear strict-feedback systems with unknown input saturation”, Inf. Sci,Vol. 269, pp. 300–315,Jun. 2014 (doi.org/10.1016/j.ins.2013.09.043).

[34] S. Li, Z. Xiang, “Adaptive Prescribed performance control for switched nonlinear systems with input saturation”, Int. J. Syst. Science, Vol. 49, No. 1,pp. 111-123, Oct. 2018 (doi.org/10.1080/00207721.2017.1390706).

[35] A. Peydayesh, M. Arefi, H. Modares, “Distributed neuro-adaptive control protocols for non-strict feedback nonlinear MASs with input saturation”, IET Control Theory Appl,Vol. 12, No. 11,pp. 1611-1620,Jul. 2018(doi.10.1049/iet-cta.2017.0875).