A Scanning Method for Drawing Root Loci for Sample-Data Feedback Systems

Procedures that are efficient in classical manual computing techniques are frequently inefficient for use on digital computers; for example, as pointed out by Polak, the Nyquist criterion we have had for years turns out to be quite incompatible in CAD. Similarly, the Evans root locus method is not quite compatible with modern design technique either, when we examine it carefully from the CAD point of view. This paper presents a scanning method and a graphical procedure for drawing the root locus. The problem of complex-root finding is converted into a real-root-finding one and a higher order polynomial complex factoring problem is reduced to a much lower order polynomial real-root-finding problem on the one hand, the Evans rules are complemented for drawing the discrete root locus on the other. Not only all the critical information required in the Evans method can be easily found for the discrete case, but also the detailed picture of the root locus is obtained accurately through the scanning.