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

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (24) : 88-95.

NIU Jiang-Chuan SHEN Yong-Jun YANG Shao-Pu LI Su-Juan

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Abstract

The free vibration of a linear single degree-of-freedom (SDOF) oscillator with fractional-order PID controller of velocity feedback is investigated by the averaging method, and the approximately analytical solution is obtained. The effects of the parameters in fractional PID controller on the dynamical properties are characterized. The proportional component of fractional-order PID controller is characterized in the form of equivalent linear damping. The integral component of fractional-order PID controller is characterized in the form of equivalent linear damping and the equivalent linear stiffness. The differential component of fractional-order PID controller is characterized in the form of equivalent linear damping and the equivalent linear negative stiffness. Those equivalent parameters could distinctly illustrate the effects of the parameters in fractional PID controller on the dynamical response. A comparison of the analytical solution with the numerical results is made, and their satisfactory agreement verifies the correctness of the approximately analytical results. The effects on system control performance of the coefficients and the orders in fractional-order PID controller are analyzed by time response performance metrics parameters. Finally, the superiority of the fractional-order PID controller based on velocity feedback is demonstrated through the control of a SDOF quarter vehicle suspension model.

Key words

fractional-order PID control / averaging method / approximately analytical solution

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NIU Jiang-Chuan SHEN Yong-Jun YANG Shao-Pu LI Su-Juan. Effect of fractional-order PID Controller on the dynamical response of linear single degree-of-freedom oscillator[J]. Journal of Vibration and Shock, 2016, 35(24): 88-95

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