引用本文: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.[点击复制]
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 with displacement feedback[J].Control Theory and Technology,2016,33(9):1265~1271.[点击复制]
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
摘要点击 3319  全文点击 2137  投稿时间：2015-11-17  修订日期：2016-06-04
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DOI编号  10.7641/CTA.2016.50911
  2016,33(9):1265-1271
中文关键词  分数阶PID控制  控制系统的稳定性  位移反馈  平均法
英文关键词  fractional-order PID control  control system stability  displacement feedback  averaging method
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(GCC2014 053)和河北省高层次人才项目(A201401001)资助.
作者单位E-mail
牛江川 石家庄铁道大学机械工程学院 menjc@163.com 
申永军* 石家庄铁道大学机械工程学院 shenyongjun@126.com 
杨绍普 石家庄铁道大学机械工程学院  
李素娟 石家庄铁道大学信息科学与技术学院  
中文摘要
      研究了基于位移反馈分数阶PID控制的单自由度线性振子的自由振动, 通过平均法得到了系统的一阶近似 解析解. 发现分数阶PID控制器的比例环节以等效线性刚度的形式影响系统的动力学特性, 积分环节以等效线性负 阻尼和等效线性刚度的形式影响系统的动力学特性, 微分环节以等效线性阻尼和等效线性刚度的形式影响系统的 动力学特性. 对近似解析解和数值解进行了比较, 二者吻合良好, 验证了近似解析解的正确性. 从近似解析解和分 数阶系统的特征方程两个角度对系统的稳定性进行了分析. 最后利用系统的时间响应性能指标分析了位移反馈分 数阶PID控制器的系数和分数阶阶次变化时, 对单自由度线性振子控制性能的影响.
英文摘要
      The free vibration of a linear single degree-of-freedom (SDOF) oscillator with fractional-order proportionalintegral- derivative (PID) controller based on displacement feedback is investigated by the averaging method, and the approximate 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.