How does the root locus help in control design?

• A. It plots frequency response of the system.
• B. It shows how closed-loop pole locations move as the feedback gain changes.
• C. It determines the time constant of the system.
• D. It predicts noise in the sensor.

Answer: (B)

The root locus is a graphical way to see how the closed-loop poles move as the feedback gain changes. For a standard negative-feedback system with forward path G(s) and feedback H(s), the closed-loop poles are the roots of 1 + K G(s)H(s) = 0. As the gain K varies, those poles trace out paths in the complex s-plane. This visualization lets you assess stability (do the poles stay in the left-half plane as K changes?) and connect pole locations to transient response (real parts relate to decay rate, imaginary parts to oscillation). By selecting a gain where the locus places the dominant poles in a region that gives the desired settling time and damping, you achieve the required performance. It’s not about frequency response plots, time constants directly, or sensor noise predictions—the root locus specifically tracks how closed-loop pole positions respond to changes in gain.