The root-locus plot of a closed-loop system with unity negative feedback and transfer function πΎπΊ(π ) in the forward path is shown in the figure. Note that πΎ is varied from 0 to ∞. Select the transfer function πΊ(π ) that results in the root-locus plot of the closed-loop system as shown in the figure.
Since five Root Locus branches originate from the same point, the system must have five coincident open-loop poles at that location. This is because Root Locus branches always start from open-loop poles, and the number of Root Locus branches equals the number of open-loop poles (or zeros, whichever is greater).
Hence, the system has five repeated real poles, which corresponds to Option (A): 1/(s+1)^5