On modeling root-locus behavior

The purpose of this paper is to establish a mathematical model precisely describing the force interaction within root loci. The concept of generalized root loci is introduced, and its relation with potential flows, such as streamline in fluids and current in electric fields, is revealed. With the help of complex variable theory, the authors derive formula to compute the force applied on root loci and to predict the quantitative variation of applied force when adding a pole or a zero to a root locus or removing one from it. Root sensitivity and root robustness can also be quantitatively measured by using this mathematical model for root loci