一类变长度棱边多项式鲁棒稳定性半径计算方法

The Method of Calculating Robust Stability Radius of Edge Polynomials with Variable Length

利用变长度棱边多项式的概念,P I控制器鲁棒镇定区间对象族问题归结为4个变长度棱边多项式的同时稳定性问题,这4个变长度多项式可用标称系统(区间对象族的中点)和一个实参数(稳定性半径)表示。将这个同时稳定性问题转化为实的结构奇异值问题。基于这个结果,可用μ工具箱进行优化计算,P I控制器镇定区间对象族的闭环控制系统的稳定性半径被确定。方法是基于扫频的,但扫频是立即的。最后,用数值实例说明所给方法的有效性。

The concept of edge polynomials with variable length is used, the PI controller robust stabilizing control system with interval type plants can be transformed into the problem of simultaneously stability of the four polynomials with variable length, each of the four polynomials with variable length can be described as the nominal plant （i. e. the center of the interval type plants） and a real parameter （i. e. the stability radius）, then the problem can be transformed into the real structured singular values problem. Based on this result,μ toolbox can be used to optimize the result. Stability radius of control system with PI controller stabilizing interval type plants is determined. The proposed approach is based on frequency sweep, but the conversion to frequency sweep test is immediate. Finally, a numerical example is given to illustrate the effectiveness of the approach.