控制理论与应用2016，Vol.33Issue(9)：1265-1271,7.DOI:10.7641/CTA.2016.50911
位移反馈分数阶PID控制对单自由度线性振子的影响
Effect of fractional-order PID controller on the dynamical response of linear single degree-of-freedom oscillator with displacement feedback
摘要
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.关键词
分数阶PID控制/控制系统的稳定性/位移反馈/平均法Key words
fractional-order PID control/control system stability/displacement feedback/averaging method分类
数理科学引用本文复制引用
牛江川,申永军,杨绍普,李素娟..位移反馈分数阶PID控制对单自由度线性振子的影响[J].控制理论与应用,2016,33(9):1265-1271,7.基金项目
国家自然科学基金项目(11372198),河北省高等学校创新团队领军人才计划项目(LJRC018),河北省高等学校高层次人才科学研究项目(GCC2014053)和河北省高层次人才项目(A201401001)资助 （11372198）
