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In order to eliminate lateral oscillation of spinning disk with uncertain parameter and dispel their adverse effect on the system performance or the working conditions of the system, supposing that the point force acting on the spinning disk is uncertain and bounded, the chaotic complex dynamic characteristics of the four-dimensional nonlinear equations in lateral oscillations of spinning disk under bounded disturbance were analyzed in view of the ubiquity of disturbance, including the space trajectory, the Lyapunov exponent and the Poincaré map. These characteristics enable us to know them deeply, and indicate that the four-dimensional dynamical system contains chaotic attractor. To ensure the robustness of the system control, the author stabilized the chaotic orbits to arbitrary chosen fixed points and periodic orbits by means of sliding mode method, and MATLAB simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can make the system track target orbit strictly and smoothly with short transition time, and its insensitivity to noise disturbance is shown. It provides reference for relevant chaos control in mechanical system.
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Keywords:
- disk /
- chaos /
- sliding mode control /
- bounded disturbance
[1] Raman A, Mote Jr C D 2002 International Journal of Nonlinear Mechanics 37 35
[2] Hassan Salarieh, Hoda Sadeghian, Kaveh Merat 2009 Nonlinear Analysis: Real World Applications 10 2864
[3] Aline Souza de Paula, Marcelo Amorim Savi 2009 Chaos, Solitons & Fractals 40 1376
[4] Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729(in Chinese)[王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729]
[5] Wei D Q, Zhang B 2009 Chin. Phys. B 18 1399
[6] Lin, Li J F, Liu Y P, Ma J 2008 Acta Phys. Sin. 57 1404(in Chinese)[李 农、李建芬、刘宇平、马 健 2008 物理学报 57 1404]
[7] Li W L, Song Y Z 2008 Acta Phys. Sin. 57 51(in Chinese)[李文林、宋运忠 2008 物理学报 57 51]
[8] Günyaz Ablay 2009 Nonlinear Analysis: Hybrid Systems 3 531
[9] Zhang X H, Li D 2009 Chin. Phys. B 18 1774
[10] Wang C C, Pai N S, Yau H T 2010 Communications in Nonlinear Science and Numerical Simulation 15 741
[11] Lu J, Lü J, XIE J, Chen G 2003 Computers & Mathematics with Applications 46 1427
[12] Zhou J, Chen Z 2008 Phys. Lett. A 372 5394
[13] Cheng C K, Kuo H H, Hou Y Y, Hwang C C, Liao T L 2008 Physica A 387 3093
[14] Jalali M A, Angoshtari A 2006 International Journal of Nonlinear Mechanics 41 726
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[1] Raman A, Mote Jr C D 2002 International Journal of Nonlinear Mechanics 37 35
[2] Hassan Salarieh, Hoda Sadeghian, Kaveh Merat 2009 Nonlinear Analysis: Real World Applications 10 2864
[3] Aline Souza de Paula, Marcelo Amorim Savi 2009 Chaos, Solitons & Fractals 40 1376
[4] Wang X F, Xue H J, Si S K, Yao Y T 2009 Acta Phys. Sin. 58 3729(in Chinese)[王校锋、薛红军、司守奎、姚跃亭 2009 物理学报 58 3729]
[5] Wei D Q, Zhang B 2009 Chin. Phys. B 18 1399
[6] Lin, Li J F, Liu Y P, Ma J 2008 Acta Phys. Sin. 57 1404(in Chinese)[李 农、李建芬、刘宇平、马 健 2008 物理学报 57 1404]
[7] Li W L, Song Y Z 2008 Acta Phys. Sin. 57 51(in Chinese)[李文林、宋运忠 2008 物理学报 57 51]
[8] Günyaz Ablay 2009 Nonlinear Analysis: Hybrid Systems 3 531
[9] Zhang X H, Li D 2009 Chin. Phys. B 18 1774
[10] Wang C C, Pai N S, Yau H T 2010 Communications in Nonlinear Science and Numerical Simulation 15 741
[11] Lu J, Lü J, XIE J, Chen G 2003 Computers & Mathematics with Applications 46 1427
[12] Zhou J, Chen Z 2008 Phys. Lett. A 372 5394
[13] Cheng C K, Kuo H H, Hou Y Y, Hwang C C, Liao T L 2008 Physica A 387 3093
[14] Jalali M A, Angoshtari A 2006 International Journal of Nonlinear Mechanics 41 726
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