Impact of Parametric Variations on Chaotic Behaviour of Indirect Field Controlled Induction Motor Drives
|International Journal of Engineering Trends and Technology (IJETT)||
|© 2017 by IJETT Journal|
|Year of Publication : 2017|
|Authors : Mirza Abdul Waris Begh, Bharat Bhushan Sharma
|DOI : 10.14445/22315381/IJETT-V54P207|
Mirza Abdul Waris Begh, Bharat Bhushan Sharma "Impact of Parametric Variations on Chaotic Behaviour of Indirect Field Controlled Induction Motor Drives", International Journal of Engineering Trends and Technology (IJETT), V54(1),41-47 December 2017. ISSN:2231-5381. www.ijettjournal.org. published by seventh sense research group
Controlling complex chaotic systems and analyzing their behavior have emerged as an attractive field of exploration in different domains of engineering. Over the years, large number of mathematical tools are developed to identify and control the typical behaviour of these systems. The work presented in this manuscript explores chaos in nonlinear dynamics of an indirect field controlled induction motor drive system. For this exploration, impact of variation in rotor inductance is considered while assuming the load torque to be fixed. Chaotic attractors are first verified by investigating Lyapunov Exponents. The range of parametric variation is explored to check for the events where chaos can creep into the system again. Finally, an attempt is made to measure the transition point between stability and instability of the chaotic system. This is verified using the Lyapunov Exponent measure and the phase plots. The detailed simulation results highlight the efficacy of the methodology to identify the chaotic behaviour of the induction motor.
 K. T. Chau and Z. Wang. Chaos in electric Drive Systems Analysis, Control and Application, Wiley-IEEE Press,Singapore (2011).
 Mohamed Zribi, Ahmed Oteafy and Nejib Smaoui, Controlling chaos in the permanent magnet synchronous motor, Chaos, Solitons and Fractals, 41, 1266-1276 (2009).
 R. Femat, R.J. Ortiz, and G.S. Perales, A chaos based communication scheme via robust asymp- totic feedback, IEEE Trans. on Circuits and Systems, Part I, vol. 48, no. 10, pp. 11611169, (2001).
 S. Callegari, R. Rovati and G. Setti , Chaos-based FM signals: applications and implementation issues, IEEE Trans. on Circuits and Systems, Part I, vol. 50, no. 8, pp. 11411147, (2003).
 B.B. Sharma and I.N. Kar, Parametric convergence and control of chaotic system using adaptive feedback linearization, Chaos, Soliton and Fractals, vol. 40, pp. 1475-1483, (2009).
 B.B. Sharma and I.N. Kar, Contraction theory based adaptive synchronization of chaotic systems, Chaos, Soliton and Fractals, vol. 41, no. 5, pp. 2437-2447, (2009).
 M.T. Yassen, Controlling chaos and synchronization for new chaotic system using linear feedback control, Chaos Solitons Fractals vol. 26, pp. 913920, (2005).
Fig. 12: Variation of Lyapunov exponents with time at TL = 8:5 and ratio r > 15.
 Y. Wang, Z.H. Guan and H.O. Wang, Feedback and adaptive control for the synchronization of Chen system via a single variable, Phys. Lett. A, vol. 312, pp. 3440 (2003).
 H. Handa and B.B. Sharma, Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty, Chaos, Soliton and Fractals, vol. 86, pp. 50-63, (2016).
 H. Handa and B.B. Sharma, Simple synchronisation scheme of chaotic Chuas systems with cubic nonlinearity in complex coupled networks, Int. J. Applied Nonlinear Science, Vol. 1, No. 4,pp. 300-311, (2014).
 C. Wu, and Y.C. Lee, Observer-based method for secure communication of chaotic systems, IET Control Theory Applications, vol. 36, no. 22, pp. 18421843, (2000).
 F. Zhu, J. Xu, M. Chen, The combination of high-gain sliding mode observers used as receivers in secure communication, IEEE Trans. on Circuits and Systems, Part I, vol. 59, no. 11, pp. 27022712, (2012).
 N. Jabli, H. Khammari, M. F. Mimouni, R. Dhifaoui, Bifurcation and chaos phenomena appearing in induction motor under variation of PI controller parameters, WSEAS Transactions on Systems, vol. 9, no. 7, pp. 784-793, (2010).
 R. Sangrody and S.M. Shariatmadar, A Lyapunov Function for Vector Control Drives in Induction Machines, Engineering, Technology Applied Science Research, vol. 6, no. 5, pp. 1167-117, (2016).
 M. Zribi, A. Oteafy and N. Smaoui, Controlling chaos in the permanent magnet synchronous motor, Chaos, Solitons and Fractals, vol. 41, pp. 12661276 (2009).
 Y. Huang, Controlling Chaos in Permanent Magnet Synchronous Motor, Chemical Engineering Transactions, vol. 46, pp. 1183-1188 (2015).
 J.K. Seok, J.K. Lee and D.C. Lee, Sensorless speed control of nonsalient permanent-magnet synchronous motors using rotor-position-tracking PI controller, IEEE Trans. Ind. Appl., no. 53, pp. 399-405 (2006).
 H. Trabelsi and M. Benrejeb, Control of chaos in permanent magnet synchronous motor with parameter uncertainties: a Lyapunov approach, International Journal of Innovation and Scientific Research, Vol. 13 No. 1, pp. 279-285 (2015).
 M. Rafikov and J. M. Balthazar, Control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Communications in Nonlinear Science and Numerical Simulation, vol.13, no.7, 1246-1255 (2008).
 A. A. Golovin, Y. Kanevsky and A. A. Nepomnyashchy, Feedback control of subcritical Turing instability with zero mode, Physical Reiview E, vol.79, no.4, 046218 (2009).
 Diyi Chen, Peng Shi and Xiaoyi Ma, Control and synchronization of chaos in an induction mo- tor system, International Journal of Innovative Computing, Information and Control, Volume 8, Number 10(B), 7237-7248 (2012).
 K. Geist, U. Parlitz, W. Lauterborn, Comparison of different methods for computing Lyapunov exponents, Prog Theor Phys:83(5), 87593 (1990).
 A. Wolf, J. B. Swift, H. L.Swinney, J. A. Vastano, Determining Lyapunov exponents from a time series, Physica D:16, 285317 (1985).
 W. Kinsner, Characterizing chaos through Lyapunov metrics, IEEE Trans Syst Man Cybernet , 36(2), 141151, (2003).
 C. Li, G. Chen, Estimating the Lyapunov exponents of discrete systems. Chaos: An Interdisci- plinary J Nonlinear Science, 14(2),343-346 (2004).
 A.Stefanski , T. Kapitaniak. Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization, Chaos, Solitons and Fractals, 15(2),233-244 (2003).
 S.L.T De Souz, I.L. Caldas, Calculation of Lyapunov exponents in systems with impacts, Chaos, Solitons and Fractals, 23(3), 569579 (2004).
 O. Alvarez-Llamoza, M.G. Cosenza, G.A. Ponce, Critical behavior of the Lyapunov exponent in type-III intermittency, Chaos, Solitons and Fractals, 36, 150156 (2008).
 A. Jayaraman , J. Scheel , H. Greenside , P. Fischer, Characterization of the domain of chaos convection state by the largest Lyapunov exponent, Phys Rev E,74(016209) (2006).
 G. Benettin, L. Galgani, A. Giorgilli and J.-M. Strelcyn, Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; A Method for Computing All of Them, Meccanica 15 (1980).
 I. Shimada and T. Nagashima, A Numerical Approach to Ergodic Problem of Dissipative Dy- namical Systems, Prog. Theor. Phys. 61, 1605,(1979).
 M. Cencini, Chaos From Simple models to complex systems,World Scientific, ed.(2010).
 D. Y. Chen, R. F. Zhang, X. Y. Ma et al., Chaotic synchronization and anti-synchronization for a novel class of multiple chaotic systems via a sliding mode control scheme, Nonlinear Dynamics, vol.69, no.1-2, 35-55 (2012).
Chaotic behaviour, Field Controlled Induction Motor, Hopf Bifurcation, Chaos Control.