Parametric synthesis of a robust controller on a base of D-partition and method of dominant poles

Abstract

The paper is dedicated to a problem of parametric synthesis of a controller for a control system having interval parameters and affine uncertainty of characteristic polynomial coefficients. Such polynomial can be represented as a sum of productions of interval parameters and polynomials including zero and real poles. The paper proposes a method of synthesizing a linear robust controller placing system poles allocation areas according to desired control quality. The method is based on dividing parameters of a controller in two groups: restricted ones and unrestricted ones. Restricted parameters of a controller provide desired allocation of a dominant pole; unrestricted parameters determine allocation of all other poles of a system. In this case, the right border of an allocation area of a dominant pole defines minimal stability degree of a system synthesized. Values of controller parameters are proposed to be found via D-partition in vertices of a interval parameters’ polytope. An example of the proposed method application is provided.