Optimization of the pole location of automatic control systems with a reduced-order controller

An optimization approach to finding the parameters of reduced-order controllers is proposed. It is shown that numerical estimation of the location of the characteristic roots in the complex plane allows the set of the roots to be divided into parts, in each of which, real coordinates for the roots are introduced. The resulting structure of the root simplex is similar to a geometrical complex. The structure of the regions and boundaries of the simplex is represented by graphs and digraphs. The roots are moved to the desired region by minimization of the same estimate of the objective function depending on the controller parameters. Critical regions are represented by reduced graphs