基于H_∞优化设计分数阶PD~μ控制器

H_∞ Design with Fractional-Order PD~μ Controllers

本文针对分数阶时滞系统,利用H∞优化理论,设计分数阶PDμ控制器。首先,给定微分阶次μ,利用图解稳定性准则确定并画出分数阶时滞系统的PDμ控制器在(Kp,Kd)参数平面上的稳定域。然后,在稳定域内计算出满足补灵敏度函数的H∞范数约束的控制器比例增益和微分增益,并确定H∞边界曲线。最后,通过改变H∞控制器的微分阶次,能得到H∞曲线与分数阶次μ之间的关系。

This article focuses on H∞ performance design for fractional-order systems with time-delay,using fractional-order proportional-derivative （PDμ） controllers.First,the stabilizing parameters region in proportional-derivative space of PDμ controller,for a fixed derivative-order,is determined in terms of a graphical stability criterion applicable to frac tional-order time-delay systems.Then,in the stabilizing region,the pairs of proportional and derivative gains of PDμ controller are calculated,it satisfies the H∞-norm constraint of complementary sensitivity function and defines the H∞ boundary curve for a range of frequencies.Finally,by changing the derivative-order of PDμ controller,the relationship between the H∞ curve and the derivative-order is obtained.Examples are followed to illustrate the design procedure.