Effect of a fractional-order PID controller on the dynamical response of a linear single degree-of-freedom oscillator

被引：0
|
作者：
Niu J. [1 ]
Shen Y. [1 ]
Yang S. [1 ]
Li S. [1 ]
机构：
[1] School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang
来源：
Shen, Yongjun (shenyongjun@126.com) | 1600年 / Chinese Vibration Engineering Society卷 / 35期
关键词：
Approximately analytical solution; Averaging method; Fractional-order PID control;
D O I：
10.13465/j.cnki.jvs.2016.24.015
中图分类号：
学科分类号：
摘要：
The free vibration of a linear single degree-of-freedom (SDOF) oscillator with a fractional-order PID controller of velocity feedback was investigated by the averaging method, and the approximately analytical solution was obtained. The results indicate that the effects of the parameters in the fractional-order PID controller on the dynamical properties are characterized. The proportional component of the fractional-order PID controller is characterized in the form of equivalent linear damping. The integral component of the fractional-order PID controller is characterized in the form of equivalent linear damping and equivalent linear stiffness. The differential component of the fractional-order PID controller is characterized in the form of equivalent linear damping and equivalent linear negative stiffness. Those equivalent parameters could distinctly illustrate the effects of the parameters in the fractional-order PID controller on the dynamical response. A comparison of the analytical solution with numerical results is made, and their agreement verifies the correctness of the approximately analytical results. The effects on system control performance of the coefficients and the orders in the fractional-order PID controller were analyzed by time response performance metrics parameters. Finally, the parameters tuning of the fractional-order PID controller based on velocity feedback was demonstrated through controlling a SDOF quarter vehicle suspension model. © 2016, Editorial Office of Journal of Vibration and Shock. All right reserved.
引用
收藏
页码：88 / 95
页数：7
相关论文
共 25 条
  • [1] Petras I., Fractional-order Nonlinear Systems, (2011)
  • [2] Podlubny I., Fractional Differential Equations, (1999)
  • [3] Shen Y.J., Yang S.P., Xing H.J., Et al., Primary resonance of duffing oscillator with fractional-order derivative, Communication in Nonlinear Science and Numerical Simulation, 17, 7, pp. 3092-3100, (2012)
  • [4] Rossikhin Y.A., Shitikova M.V., Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass systems, Acta Mechanica, 120, 1-4, pp. 109-125, (1997)
  • [5] Yang S.P., Shen Y.J., Recent advances in dynamics and control of hysteretic nonlinear systems, Chaos Solitons and Fractals, 40, 4, pp. 1808-1822, (2009)
  • [6] Chen J.H., Chen W.C., Chaotic dynamics of the fractionally damped van der Pol equation, Chaos, Solitons and Fractals, 35, 1, pp. 188-198, (2008)
  • [7] Zhang C., Gao J., Xu L., Chaos in fractional-order Liu system and a fractional-order unified system and the synchronization between them, Acta Physica Sinica, 56, 9, pp. 5124-5130, (2007)
  • [8] Wu G., Huang H., Ye G., Semi-active control of automotive air suspension based on fractional calculus, Transactions of the Chinese Society for Agricultural Machinery, 45, 7, pp. 19-24, (2014)
  • [9] Sun H., Jin C., Zhang W., Et al., Modeling and tests for a hydro-pneumatic suspension based on fractional calculus, Journal of Vibration and Shock, 33, 17, pp. 167-172, (2014)
  • [10] Podlubny I., Fractional-order systems and PI<sup>λ</sup>D<sup>μ</sup> -controllers, IEEE Transactions on Automatic Control, 44, 1, pp. 208-214, (1999)
123