Chaos Control in Gear Transmission System using GPC and SMC ‎Controllers

[1] Slotine, J.-.E., Li, W.P., Applied Non-linear Control, 199(1), Englewood Cliffs, NJ: Prentice hall, 1991.

[2] Faieghi, M.R., Delavari, H., Baleanu, B., A novel adaptive controller for two-degree of freedom polar robot with unknown perturbations, Communications in Nonlinear Science and Numerical Simulation, 17(2), 2012, 1021-1030.

[3] Li, J., Li, W., Li, Q., Sliding mode control for uncertain chaotic systems with input nonlinearity, Communications in Nonlinear Science and Numerical Simulation, 17(1), 2012, 341-348.

[4] Yadav, V.K., Shukla, V.K., Das, S., Difference synchronization among three chaotic systems with exponential term and its chaos control, Chaos, Solitons & Fractals, 124, 2019, 36-51.

[5] Mendoza, S.A., et al, Parrondo’s paradox or chaos control in discrete two-dimensional dynamic systems, Chaos, Solitons & Fractals, 106, 2018, 86-93.

[6] Ge, Z-M., et al, Regular and chaotic dynamics of a rotational machine with a centrifugal governor, International Journal of Engineering Science, 37(7), 1999, 921-943.

[7] Zhou, S., et al, Non-linear dynamic response analysis on gear-rotor-bearing transmission system, Journal of Vibration and Control, 24(9), 2018, 1632-1651.

[8] Pan, H., et al, Finite-time stabilization for vehicle active suspension systems with hard constraints, IEEE Transactions on Intelligent Transportation Systems, 16(5), 2015, 2663-2672.

[9] Byrtus, M., Zeman, V., On modeling and vibration of gear drives influenced by non-linear couplings, Mechanism and Machine theory, 46(3), 2011, 375-397.

[10] de Souza, S.L.T., et al, Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes, Chaos, Solitons & Fractals, 21(3), 2004, 763-772.

[11] Wang, J., Li, R., Peng, X., Survey of non-linear vibration of gear transmission systems, Applied Mechanics Reviews, 56(3), 2003, 309-329.

[12] Farshidianfar, A., Saghafi, A., Global bifurcation and chaos analysis in non-linear vibration of spur gear systems, Nonlinear Dynamics, 75(4), 2014, 783-806.

[13] Theodossiades, S., Natsiavas, S., Periodic and chaotic dynamics of motor-driven gear-pair systems with backlash. Chaos, Solitons & Fractals, 12(13), 2001, 2427-2440.

[14] Spitas, C., Spitas, V., Coupled multi-DOF dynamic contact analysis model for the simulation of intermittent gear tooth contacts, impacts and rattling considering backlash and variable torque, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(7-8), 2016, 1022-1047.

[15] Litak, G., Friswell, M. I., Vibration in gear systems, Chaos, Solitons & Fractals, 16(5), 2003, 795-800.

[16] Sakaridis, E., Spitas, V., Spitas, C., Non-linear modeling of gear drive dynamics incorporating intermittent tooth contact analysis and tooth eigenvibrations, Mechanism and Machine Theory, 136, 2019, 307-333.

[17] Jingyue, W., Lixin, G., Haotion, W., Analysis of bifurcation and non-linear control for chaos in gear transmission system, Research Journal of Applied Sciences, Engineering and Technology, 6(10), 2013, 1818-1824.

[18] Saghafi, A., Farshidianfar, A., An analytical study of controlling chaotic dynamics in a spur gear system, Mechanism and Machine Theory, 96, 2016, 179-191.

[19] Cai-Wan, G.J., Strong nonlinearity analysis for gear-bearing system under non-linear suspension-bifurcation and chaos, Nonlinear Analysis: Real World Applications, 11(3), 2010, 1760-1774.

[20] Sheng, L., et al, Non-linear dynamic analysis and chaos control of multi-freedom semi-direct gear drive system in coal cutters, Mechanical Systems and Signal Processing, 116, 2019, 62-77.

[21] Xie, B., Wang, W., Zuo, Z., Adaptive output feedback control of uncertain gear transmission system with dead zone nonlinearity, 13th IEEE Conference on Industrial Electronics and Applications (ICIEA), 2018, 438-443.

[22] Shen, Y., Yang, S., Liu, X., Non-linear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method, International Journal of Mechanical Sciences, 48(11), 2006, 1256-1263.

[23] Clarke, D.W., Mohtadi, C., Properties of generalized predictive control, Automatica, 25(6), 1989, 859-875.

[24] Clarke, D.W., Application of generalized predictive control to industrial processes, IEEE Control Systems Magazine, 8(2), 1988, 49-55.

[25] Tao, J., et al, A generalized predictive control-based path following method for parafoil systems in wind environments, IEEE Access, 7, 2019, 42586-42595.

[26] Yang, Z.Q., Wang, X., Yu, H., Study on generalized predictive control of cement rotary kiln calcining zone temperature, IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference (IMCEC), 2016, 1653-1658.

[27] Zhang, X., et al, Generalized predictive contour control of the biaxial motion system, IEEE Transactions on Industrial Electronics, 65(11), 2018, 8488-8497.

[28] Valencia, A., et al, Hardware in loop of a generalized predictive controller for a micro grid DC system of renewable energy sources, International Journal of Engineering, 31(8), 2018, 1215-1221.

[29] Wang, G., et al, Design of a model predictive control method for load tracking in nuclear power plants, Progress in Nuclear Energy, 101, 2017, 260-269.

[30] Vajpayee, V., Mukhopadhyay, S., Tiwari, A.P., Data-driven subspace predictive control of a nuclear reactor, IEEE Transactions on Nuclear Science, 65(2), 2017, 666-679.

[31] Azar, A.T., Zhu, Q., Advances and applications in sliding mode control systems, Cham: Springer International Publishing, 2015.

[32] Li, H., et al, Observer-based adaptive sliding mode control for non-linear Markovian jump systems, Automatica, 64, 2016, 133-142.

[33] Wang, Y., et al. "Sliding mode control of fuzzy singularly perturbed systems with application to electric circuit, IEEE Transactions on Systems, Man, and Cybernetics Systems, 48(10), 2017, 1667-1675.

[34] Elmokadem, T., Zribi, M., Youcef-Toumi, K., Trajectory tracking sliding mode control of underactuated AUVs, Nonlinear Dynamics, 84(2), 2016, 1079-1091.