Semi-analytic approach to root locus

The graphical method of constructing root locus is very well known. The analytical methods of obtaining root locus equations developed in the Soviet Union merit utilization due to the flexibility inherent in the manipulation of algebraic expressions. Arrays are developed whereby these algebraic expressions can be obtained from a knowledge of the open loop transfer function. Breakaway points on the real axis and intersection with the imaginary axis can be obtained directly from these arrays. Finally, arrays are formulated for the case where one of the parameters of the open loop transfer function varies.