Placing Poles Allocation Areas of Interval Control System with Desired Root Quality Indices

The paper is dedicated to the problem of placing roots of interval system characteristic polynomial the coefficients of which are included in a parametric polytope, according to desired control quality. To provide applicable values of stability degree and oscillability degree, a pair of dominant poles is placed in desired areas of a complex plane. Other poles of the system, which are unrestricted poles, are placed in a desired allocation area, the border of which is defined to observe the poles dominance principle. In order to place poles according to desired control quality, a set of parametric polytope's vertices, which determine poles allocation, is found on the basis of angular properties of interval root locus. The parameters of a controller providing desired allocation of dominant and unrestricted poles are found with the help of D-partition basing on the previously obtained vertex polynomials.