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International Journal of Sensors, Wireless Communications and Control

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ISSN (Print): 2210-3279
ISSN (Online): 2210-3287

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Research Article

Fractional Dynamic Sliding Mode Control for Uncertain Chaotic Systems Applied to a Chaotic Robot Arm Under Dynamic Load

Author(s): Sara Gholipour P., Sara Minagar, Javad Kazemitabar* and Mobin Alizadeh

Volume 10, Issue 6, 2020

Page: [1023 - 1031] Pages: 9

DOI: 10.2174/2210327910999200818091512

Price: $65

Abstract

Background: A novel type of control strategy is presented for the control of chaotic systems, particularly a chaotic robot in joint and workspace, which is the result of applying fractional calculus to dynamic sliding mode control.

Objectives: To guarantee the sliding mode condition, a control law is introduced based on the Lyapunov stability theory.

Methods: A control scheme is proposed for reducing the chattering problem in finite time tracking and robust in the presence of system matched disturbances.

Results: Qualitative and quantitative characteristics of the chaotic robot are all proven to be viable thru simulations.

Conclusion: In addition, all of the chaotic robot’s qualitative and quantitative characteristics have been investigated. Numerical simulations indicate the viability of our control method.

Keywords: Fractional dynamic sliding mode control, chaotic robot system, lyapunov exponent, bifurcation diagram, poincaré map, numerical simulations.

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[1]
Utkin V, Guldner J, Shi J. Sliding mode control in electromechanical systems. Boca Raton, Florida: CRC Press 1999.
[2]
Elmali H, Olgac N. Robust output tracking control of nonlinear MIMO systems via sliding mode technique. J Automatica 1992; 28(1): 145-51.
[http://dx.doi.org/10.1016/0005-1098(92)90014-7]
[3]
Slotin JJE, Sastry SS. Tracking control of nonlinear systems using sliding surfaces with application to robot manipulator. Int J Control 1983; 38(1): 931-8.
[4]
Hajatipour M, Farrokhi M. Chattering free with noise reduction in sliding-mode observers using frequency domain analysis. J Process Contr 2010; 20(8): 912-21.
[http://dx.doi.org/10.1016/j.jprocont.2010.06.015]
[5]
Ho HF, Wong YK, Rad AB. Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems. J Simul Model Pract Theory 2009; 17(7): 1199-210.
[http://dx.doi.org/10.1016/j.simpat.2009.04.004]
[6]
Lee H, Utkin V. Chattering suppression methods in sliding mode control system. Annu Rev Contr 2007; 31(2): 179-88.
[http://dx.doi.org/10.1016/j.arcontrol.2007.08.001]
[7]
Ramírez HS. On the dynamical sliding mode control of nonlinear systems. Int J Control 1993; 57(5): 1039-61.
[http://dx.doi.org/10.1080/00207179308934429]
[8]
Wang Z, Bao W, Li H. Second-order dynamic sliding-mode control for nonminimum phase underactuated hypersonic vehicles. IEEE Trans Ind Electron 2017; 64(4): 3105-12.
[http://dx.doi.org/10.1109/TIE.2016.2633530]
[9]
Sinekli ES, Coban R. Dynamic integral sliding mode control of an electromechanical system. International Conference on Mechanical, System and Control Engineering (ICMSC) 2017 St Petersburg. 160-4.
[10]
Rabah K, Ladaci S. A novel fractional order adaptive sliding mode controller design for chaotic arneodo systems synchronization. 6th International Conference on Systems and Control (ICSC) 2017. 465-9.
[11]
Chen MS, Chen CH, Yang FY. An LTR-observer-based dynamic sliding mode control for chattering reduction. J Automatica 2007; 43(1): 1111-6.
[http://dx.doi.org/10.1016/j.automatica.2006.12.001]
[12]
Davila J, Poznyak A. Dynamic sliding mode control design using attracting ellipsoid method. J Automatica 2011; 47(1): 1467-72.
[http://dx.doi.org/10.1016/j.automatica.2011.02.023]
[13]
Liu J, Sun F. A novel dynamic terminal sliding mode control of uncertain nonlinear systems. J Control Theory Appl 2007; 47(1): 189-93.
[14]
Ansarifar GR, Davilu H, Talebi HA. Gain scheduled dynamic sliding mode control for nuclear steam generators. Prog Nucl Energy 2011; 53(1): 651-63.
[http://dx.doi.org/10.1016/j.pnucene.2011.04.029]
[15]
Podlubny I. Fractional differential equations. San Diego, CA: Academic Press 1999.
[16]
Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam, Netherlands: Elsevier 2006.
[17]
Oldham KB, Spanier J. The fractional calculus. New York: Academic Press 1974.
[18]
Li C, Qian D, Chen Y. On Riemann-Liouville and caputo derivatives. Disc Dyn Nature Soc 2011.
[19]
Li C, Deng W. Remarks on fractional derivatives. Appl Math Comput 2007; 187(2): 777-84.
[http://dx.doi.org/10.1016/j.amc.2006.08.163]
[20]
Vinagre B, Petras I, Podlubny I, Chen Y. Using fractional-order adjustment rules and fractional-order reference models in model-reference adaptive control. Nonlinear Dyn 2002; 29(1): 269-79.
[http://dx.doi.org/10.1023/A:1016504620249]
[21]
Valrio D, Costa J. Tuning of fractional PID controllers with Ziegler–Nichols-type rules. Signal Proc 2006; 86(1): 2771-84.
[http://dx.doi.org/10.1016/j.sigpro.2006.02.020]
[22]
Efe MO. Fractional fuzzy adaptive sliding-mode control of a 2-DOF direct-drive robot arm. IEEE Trans Syst Man Cybern B Cybern 2008; 38(6): 1561-70.
[http://dx.doi.org/10.1109/TSMCB.2008.928227] [PMID: 19022726]
[23]
Vinagre BM, Calder AJ. On fractional sliding mode control. Proceedings of 7th Portuguese Conference for Automatic Control 2006. Lisbon, Portugal.
[24]
Ladaci S, Charef A. On fractional adaptive control. Nonlinear Dyn 2006; 43(1): 365-78.
[http://dx.doi.org/10.1007/s11071-006-0159-x]
[25]
Delavari H, Ghaderi R, Ranjbar A, Momani S. Reply to “Comments on ”Fuzzy fractional order sliding mode controller for nonlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010): 963– 978. Commun Nonlinear Sci Numer Simul 2012; 17(10): 4010-4.
[http://dx.doi.org/10.1016/j.cnsns.2012.02.028]
[26]
Alfi A, Delavari HS. Chaos synchronization of fractional-order chaotic Lorenz-Stenflo system via fractional sliding mode control.International Symposium of Advances in Science and Technology 5th SASTech 2011; Mashhad,Iran.
[27]
Gholipour S, Shandiz HT, Khosravi MN. Control of fractional stochastic chaos with fractional sliding mode. Proceedings of FDA’12 the 5th IFAC workshop on Fractional Differentiation and its Application 2012. Nanjing, China.
[28]
Raynaud H, Inoh A. State-space representation for fractional-order controllers. Automatica 2000; 36(1): 1017-21.
[http://dx.doi.org/10.1016/S0005-1098(00)00011-X]
[29]
Chen Y, Ahna H, Podlubny I. Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Proc 2006; 86(1): 2611-8.
[http://dx.doi.org/10.1016/j.sigpro.2006.02.011]
[30]
Sprott JC. Chaos and time-series analysis. Oxford: Oxford University Press 2003.
[31]
Saif F. Classical and quantum chaos in atom optics. Phys Rep 2005; 419(6): 207-58.
[32]
Ott E. Chaos in Dynamical Systems. Cambridge: Cambridge University Press 2002.
[http://dx.doi.org/10.1017/CBO9780511803260]
[33]
Argyris JH. An exploration of chaos: an introduction for natural scientists and engineers. North-Holland 1994.
[34]
Verhulst F. Nonlinear differential equations and dynamical systems Verlag. Germany: Springer 1990; p. 313.
[http://dx.doi.org/10.1007/978-3-642-97149-5]
[35]
Moon FC. Chaotic and fractal dynamics: Introduction for applied scientists and engineers. New York: John Wiley & Sons 2008.
[http://dx.doi.org/10.1002/9783527617500]
[36]
Kaygisiz BH, Erkmen AM, Erkmen I. Detection of transition to chaos during stability roughness smoothing of a robot arm. IEEE/RSJ International Conference on Intelligent Robots and Systems 2002; 2: pp 1910-191.
[37]
Nazari M, Rafiee G, Jafari AH, Golpayegani SM. Supervisory chaos control of a two-link rigid robot arm using OGY method. IEEE Conference on Cybernetics and Intelligent Systems 2008; pp 41-46.
[38]
Li Y, Asakura T. Occurrence of trajectory chaos and it’s stablizing control due to dead time of a pnumatic manipulator. JSME Int J Series C 2005; 48(1): 640-8.
[http://dx.doi.org/10.1299/jsmec.48.640 ]

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