一类采用分数阶PI~λ控制器的分数阶系统可镇定性判定准则  

Stabilization Criterion for A Class of Interval Fractional-order Systems Using Fractional-order PI~λ Controllers

作　　者：高哲[1] 

机构地区：[1]辽宁大学轻型产业学院,沈阳110036

出　　处：《自动化学报》2017年第11期1993-2002,共10页Acta Automatica Sinica

基　　金：国家自然科学基金(61304094);辽宁省教育厅科学研究一般项目(L2015194;L2015198)资助~~

摘　　要：针对含有一个分数阶项的区间分数阶被控对象,提出了采用分数阶PI~λ控制器的闭环系统可镇定性判定准则.将闭环系统的特征函数分解为扰动函数和标称函数,给出了扰动函数值集顶点的构造方法.根据被控对象分数阶阶次和控制器的阶次,研究了值集形状是否切换和切换频率的计算方法.此外,给出了测试频率区间的上下界,以实现在有限频率区间内判定闭环系统值集与原点的位置关系.在假设值集顶点函数在测试频率区间内不为零和闭环标称系统稳定的情况下,以解析的方式提出了采用分数阶PI~λ控制器闭环系统的可镇定性判定准则.最后,通过对数值算例的可镇定性分析,验证了提出的判定准则的有效性.This study proposes a stabilization criterion for interval fractional-order plants involving one fractional-order term using fractional-order PIλ controllers. The characteristic function of the closed loop system is divided into the nominal function and disturbance function, and the construction method for the vertices of the value set with respect to the disturbance function is investigated. Moreover, the upper and lower limits of the test frequency interval are offered to determine the position relationship between the origin and the value set corresponding to the closed loop system. By supposing that the vertex functions are not equal to zero within the test frequency interval and the closed loop nominal system is stable, the stabilization criterion for closed loop systems using fractional-order PIλ controllers is proposed analytically. Finally, stabilization analyses of numerical examples verify the effectiveness of the proposed criterion.

关 键 词：分数阶系统 区间不确定性 可镇定性 值集 分数阶PIλ控制器 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]