Super-Twisting Control of the Duffing-Holmes Chaotic System

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DOI: 10.4236/ijmnta.2016.54016    319 Downloads   443 Views  
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In this paper, a super twisting controller (STC) is designed to control the chaotic behavior of the Duffing-Holmes system in stabilization and tracking cases. Due to lack of availability of the performance evaluation of STC in controlling Duffing-Holmes system, this paper aims to test the performance of STC in controlling Duffing-Holmes system. In order to achieve this control design, a modification of the conventional super twisting algorithm is adapted. Numerical simulations showed that the modified STC had high performance and ability to ensure robustness with respect to bounded external disturbances.

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Abu Khadra, F. (2016) Super-Twisting Control of the Duffing-Holmes Chaotic System. International Journal of Modern Nonlinear Theory and Application, 5, 160-170. doi: 10.4236/ijmnta.2016.54016.


[1] Sharma, A., Patidar, V., Purohit, G. and Sud, K.K. (2012) Effects on the Bifurcation and Chaos in Forced Duffing Oscillator Due to Nonlinear Damping. Communications in Nonlinear Science and Numerical Simulation, 17, 2254-2269.
[2] Kyriazis, M. (1991) Applications of Chaos Theory to the Molecular Biology of Aging. Experimental Gerontology, 26, 569-572.
[3] Petrov, V., Gaspar, V., Masere, J. and Showalter, K. (1993) Controlling Chaos in the Belousov-Zhabotinsky Reaction. Nature, 361, 240-243.
[4] Gaspard, P. (1999) Microscopic Chaos and Chemical Reactions. Physica A: Statistical Mechanics and Its Applications, 263, 315-328.
[5] Mondal, S. and Mahanta, C. (2014) Adaptive Second Order Terminal Sliding Mode Controller for Robotic Manipulators. Journal of the Franklin Institute, 351, 2356-2377.
[6] Volos, C.K., Kyprianidis, I.M. and Stouboulos, I.N. (2013) Experimental Investigation on Coverage Performance of a Chaotic Autonomous Mobile Robot. Robotics and Autonomous Systems, 61, 1314-1322.
[7] Yuan, G., Zhang, X. and Wang, Z. (2014) Generation and Synchronization of Feedback-Induced Chaos in Semiconductor Ring Lasers by Injection-Locking. Optik-International Journal for Light and Electron Optics, 125, 1950-1953.
[8] Li, N., Pan, W., Yan, L., Luo, B. and Zou, X. (2014) Enhanced Chaos Synchronization and Communication in Cascade-Coupled Semiconductor Ring Lasers. Communications in Nonlinear Science and Numerical Simulation, 19, 1874-1883.
[9] Huang, X., Zhao, Z., Wang, Z. and Li, Y. (2012) Chaos and Hyperchaos in Fractional-Order Cellular Neural Networks. Neurocomputing, 94, 13-21.
[10] Kaslik, E. and Sivasundaram, S. (2012) Nonlinear Dynamics and Chaos in Fractional-Order Neural Networks. Neural Networks, 32, 245-256.
[11] Lian, S. and Chen, X. (2011) Traceable Content Protection Based on Chaos and Neural Networks. Applied Soft Computing, 11, 4293-4301.
[12] Njah, A.N., Ojo, K.S., Adebayo, G.A. and Obawole, A.O. (2010) Generalized Control and Synchronization of Chaos in RCL-Shunted Josephson Junction Using Back Stepping Design. Physica C: Superconductivity, 470, 558-564.
[13] Tu, J., He, H. and Xiong, P. (2014) Adaptive Backstepping Synchronization between Chaotic Systems with Unknown Lipschitz Constant. Applied Mathematics and Computation, 236, 10-18.
[14] Vaidyanathan, S. (2012) Adaptive Backstepping Controller and Synchronizer Design for Arneodo Chaotic System with Unknown Parameters. International Journal of Computer Science and Information Technology, 4, 145-159.
[15] Zhang, J., Li, C., Zhang, H. and Yu, J. (2004) Chaos Synchronization Using Single Variable Feed-Back Based on Backstepping Method. Chaos, Solitons & Fractals, 21, 1183-1193.
[16] Vaidyanathan, S. (2012) Sliding Mode Control Based Global Chaos Control of Liu-Liu-Liu-Su Chaotic System. International Journal of Control Theory and Applications, 5, 15-20.
[17] Lin, T.-C., Lee, T.-Y. and Balas, V.E. (2011) Adaptive Fuzzy Sliding Mode Control for Synchro-Nization of Uncertain Fractional Order Chaotic Systems. Chaos, Solitons & Fractals, 44, 791-801.
[18] Roopaei, M. and Jahromi, M.Z. (2008) Synchronization of Two Different Chaotic Systems Using Novel Adaptive Fuzzy Sliding Mode Control. Chaos, 18, Article ID: 033133.
[19] Utkin, V.I. (1992) Slides Modes in Control and Optimization. Springer, Berlin.
[20] Sun, H., Li, S. and Sun, C. (2013) Finite Time Integral Sliding Mode Control of Hypersonic Vehicles. Nonlinear Dynamics, 73, 229-244.
[21] Lu, K. and Xia, Y. (2013) Adaptive Attitude Tracking Control for Rigid Spacecraft with Finite-Time Convergence. Automatica, 49, 3591-3599.
[22] Qiao, Z., et al. (2013) New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor. IEEE Transactions on Industrial Electronics, 60, 710-719.
[23] Moradi, H., Saffar-Avval, M. and Bakhtiari-Nejad, F. (2012) Sliding Mode Control of Drum Water Level in an Industrial Boiler Unit with Time Varying Parameters: A Comparison with H∞-Robust Control Approach. Journal of Process Control, 22, 1844-1855.
[24] Levant, A. and Levantovsky, L.V. (1993) Sliding Order and Sliding Accuracy in Sliding Mode Control. International Journal of Control, 58, 1247-1263.
[25] Fridman, L. and Levant, A. (2002) Higher Order Sliding Modes. Sliding Mode Control in Engineering, 11, 53-102.
[26] Moreno, J.A. and Osorio, M. (2012) Strict Lyapunov Functions for the Super-Twisting Algorithm. IEEE Transactions on Automatic Control, 57, 1035-1040.
[27] Chen, G. and Yu, X. (Eds.) (2003) Chaos Control: Theory and Applications. Vol. 292, Springer, Berlin.
[28] Defoort, M. and Djema?, M. (2012) A Lyapunov-Based Design of a Modified Super-Twisting Algorithm for the Heisenberg System. IMA Journal of Mathematical Control and Information, Online.

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