分数阶P（ID）^u控制器和分数阶超前滞后校正器的设计

Design for two types of fractional-order controllers：P（ID）^u controller and lead-lag compensator

本文提出分数阶P(ID)μ控制器和分数阶超前滞后校正器及其扩展频域设计方法。Podlubny分数阶PIλDμ控制器从控制角度难以直观分析且设计复杂,其冗余参数成为获得有效控制性能的障碍。本文利用分数阶扩展频域法,从分数阶系统零极点的角度考虑分数阶控制器,直接分析系统性能与分数阶控制器参数的对应关系,得出提出更为简易合理的P(ID)μ控制器和具有可分离特性的分数阶超前滞后校正器,同时给出频域设计的具体步骤并举例说明。

Fractional-order P（ID）^μ controllers and fractional lead-lag compensators with their extended frequency domain design methods are provided. Fractional PI^λD^μ controller with its complicated design by Podlubny is hard to analysis directly from conception of control. Its redundant parameters become the barrier to obtain efficient control performances. Here, using fractional-order extended frequency domain analysis method, considering fractional controller from the sight of system zeros or poles to analyze corresponding relationship between system performance and parameters of fractional controller, the authors provide a simply realized and reasonable type of PI^λD^μ fractional controller and a kind of separable fractional lead-lag compensator. Also their design methods are concluded through an illustrative example.