Algorithm for synthesis of the stable characteristic polynomials for dynamic systems under parametric variations

Abstract

The paper deals with the dynamic systems with perturbed parameters described by the families of the third order characteristic polynomials having coefficients within the given intervals of values. The system dynamics is represented in the form of the root locus portrait. The notion of the root locus field of the family is introduced that is the basis for the system stability condition formulation. Root locus portrait configuration peculiarities of the systems of the kind and graphic-analytical approach to their analysis and synthesis serve as the basis for the system characteristic equation parameters calculation algorithm ensuring its robust stability in case of the given system proven unstable. Algorithm is implemented in the graphic-analytical form. System stability investigation and synthesis, in case of necessity, of the new parameters values are performed on the basis of estimation of the family root locus dominating field location character in the roots plane.