GEOMETRICAL CONSTRUCTION OF THE ROOT LOCUS FOR A THIRD ORDER SYSTEM.

The problem of plotting the root locus of the equation (s**3 plus a//2s**2 plus a//1s plus s plus a//0) plus K equals 0 is encountered in the analysis and design of control systems. The locus branches off the real axis, for a//i real and K a real variable, are known to be hyperbolic. The author's setsquare and compass method (which is believed to be original) permits construction of the locus by simple geometrical operations, thus eliminating the search process inherent in W. R. Evans' method. It requires only one preliminary calculation of a square root. Through this simple demonstration of its utility, the analytical approach to root locus may be seen as a complement to Evans' graphical approach.