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

发布时间：2018-08-12 08:47

【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.
[Abstract]:For an interval fractional order controlled plant with a fractional order term, a stabilization criterion for closed loop systems using fractional order PI位 controller is proposed. The eigenfunction of closed loop system is decomposed into perturbation function and nominal function. The method of constructing vertex of perturbation function value set is given. According to the fractional order of the controlled object and the order of the controller, the calculation method of whether the shape of the value set is switched and the switching frequency is studied. In addition, the upper and lower bounds of the test frequency interval are given to determine the position relationship between the value set and the origin of the closed-loop system in the finite frequency range. Under the assumption that the vertex function of the set of values is stable in the closed loop nominal system without zero sum in the test frequency range, a stabilization criterion for the closed-loop system using fractional order PI- 位 controller is proposed in an analytical manner. Finally, the validity of the proposed criterion is verified by qualitative analysis of numerical examples.
【作者单位】：辽宁大学轻型产业学院;
【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~~
【分类号】：TP273

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