Characterization and computation of robust root loci for systems having parametric uncertainties
Chyi Hwang, Shih-Feng Yang · Journal of the Chinese Institute of Engineers · 2011
Given an nth-degree polynomial p(s; q ) whose coefficients are continuous functions of m-dimensional real vector , the robust root locus (RRL) of the polynomial set is defined as where R and C denote the sets of real number and complex numbers, respectively. By exploiting the notion of generalized principal points of Q associated with a continuously differentiable mapping , we present in this article a necessary condition for (s, q ) satisfying as well as s being on the boundary of the RRL . For a general parameter dependency of the polynomial p(s; q ), this condition renders analytic manifolds of dimension one in the domain . Hence, the boundary of each section of the RLL can be accurately constructed via tracing the manifolds using a path-following algorithm. This approach to the construction of the RRL is applicable to the case where the parameter domain boundary admits an analytic description. As compared with other existing methods of RRL generation algorithms, the proposed approach has the advantages of having more computational efficiency, more solution accuracy, and wider application scope. To illustrate the proposed approach of generating robust root loci, examples with three different parameter domains including a box, a diamond, and an ellipsoid parameter domain are given.