Effect of fractional-order PID controller on the dynamical response of linear single degree-of-freedom oscillator with displacement feedback
NIU Jiang-chuan
SHEN Yong-jun
YANG Shao-pu
LI Su-juan
Abstract：The free vibration of a linear single degree-of-freedom (SDOF) oscillator with fractional-order proportional-integral-derivative (PID) controller based on displacement feedback is investigated by the averaging method, and the ap-proximate analytical solution is obtained. The effects of the parameters in fractional-order PID controller on the dynamical properties are characterized, where the proportional component is characterized in the form of equivalent linear stiffness, the integral component is characterized in the form of equivalent linear negative damping and equivalent linear stiffness, and the differential component is characterized in the form of equivalent linear damping and equivalent linear stiffness. Those equivalent parameters could distinctly illustrate the effects of the parameters in fractional-order PID controller on the dynamical response. A comparison of the approximate analytical solution with the numerical results is made, and their satisfactory agreement verifies the correctness of the approximate results. The system stability is analyzed based on the approximate analytical solution and the characteristic equation of the fractional-order system. Finally, the effects on system control performance of fractional-order PID controller for linear SDOF oscillator with displacement feedback are analyzed by the time response performance metrics parameters,when the coefficients and orders of fractional-order PID controller are changed.
Keywords：fractional-order PID controlcontrol system stabilitydisplacement feedbackaveraging method
Publication Date：2016-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 1265-1271 )