Construction of Root Locus

The root locus construction involves determining the number of branches that equals the number of closed-loop poles. The root locus is symmetrical about the real axis.

The root locus exists on the part of the real axis where the sum of the total number of finite open-loop poles and zeros on the left is odd.

Originating at open-loop poles, the locus traces closed-loop system poles with increasing gain and ends at open-loop zeros, where system poles stabilize with rising gain.

A function that approaches infinity as s approaches infinity has a pole at infinity. If it approaches zero, it has a zero at infinity.

As the root locus moves towards infinity, it approaches certain straight lines known as asymptotes. For a given system, the real-axis intercept and angle are calculated. As the gain increases, the angles start repeating themselves.

Their equation, based on real-axis intercept and angle, reveals the loci's path from poles to infinity.

The locus originates from the open-loop poles and terminates at the open-loop zeros.