SGGS Institute of Engineering and Technology, Vishnupuri, Nanded, India.
ISA Trans. 2011 Oct;50(4):538-47. doi: 10.1016/j.isatra.2011.06.002. Epub 2011 Jul 16.
In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques.
本文讨论了模糊参数不确定系统的稳定性裕度、增益和相位裕度的确定。研究了系数由模糊函数描述的不确定线性系统的稳定性分析。提出了一种用于确定 FPUS 稳定性裕度的复杂度降低技术。该方法取决于特征多项式的阶数。为了找到阶数小于 5 的区间多项式的稳定性裕度，并不总是需要确定和检查所有四个 Kharitonov 多项式。结果表明，对于阶数为五、四和三的 FPUS，分别只需要三个、两个和一个 Kharitonov 多项式来确定稳定性裕度。只有对于第六阶和更高阶的多项式，才需要完整的 Kharitonov 多项式来确定稳定性裕度。因此，对于较低阶系统，计算大大减少。该思想已扩展到确定模糊区间多项式的稳定性裕度。还表明，可以在不使用图形技术的情况下，通过解析方法确定 FPUS 的增益和相位裕度。
