分数阶PI^λD^μ控制器的一种状态空间实现

A State-Space Realization of Fractional Order PI^λD^μ Controller

首先回顾了分数阶微积分、分数阶系统和分数阶PI^λD^μ控制器的数学描述，对于一类分数阶SISO被控对象，提出了一种基于整数阶微分算子的分数阶PI^λD^μ控制器的S平面状态空间实现。同时，在Matlab Simulink仿真平台实现了基于Oustaloup连续滤波器法的分数阶微分算子和该状态空间实现，并基于遗传算法整定了状态空间参数。仿真结果验证了该状态空间的有效性与正确性。

This paper outlines the mathematical descriptions of fractional calculus, fractional regulated systems and fractional order PI^λD^μ controller. For a class of fractional order SISO regulated system, the paper also puts forward a state space description of fractional order PI^λD^μ controller on s-plane based on the integer-order derivative integrator. Meanwhile, it realizes the Oustaloup fractional derivative integrator and the presented state space on the Maltab Simulink platform, finally tunes the parameters of fractional order PieD＇controller based on Genetic Algorithm. The simulation results verify the correctness and effectiveness of the presented state space.