分数阶PID控制器参数的自适应设计

分数阶比例-积分-微分(proportional-integral-derivative，PID)控制器是整数阶PID控制器在复数域的推广，通过引入两个可调参数λ和μ使得控制器参数整定范围变大，但使得参数设计变得更加复杂。针对分数阶PID控制器的特点，提出了一种参数自适应的改进型差分进化算法整定方法，在目标函数的选取上，针对传统时间与绝对误差乘积准则对超调量控制不足，引入误差与控制信号加权，分别对整数阶和分数阶被控模型进行理论分析和数值仿真，仿真结果证明了该控制器参数设计方法的有效性和准确性。

Self-adjusting design on parameters of the fractional order PID controller

The fractional order proportional-integral-derivative(PID) controller is the expansion of the classical integral order PID controller in complex domain. Two variable parameters λandμ are brought to expand the tuning range, but the controller is made more complicated. For the characteristics of the fractional order PID, a modified differential evolution algorithm with parameter self-adjusting is presented to tune the controller. To choose the objective function, the weighted addition of error and control signal as the disadvantage of overshoot control with integrated time and absolute error criterion are introduced. Theoretical analysis and simulation are carried on with integer order plant and fractional order plant separately. The simulation results illustrate the effectiveness and accuracy of the proposed method.