What parameter varies to show changes in closed-loop poles in Root Locus?

• A. Frequency
• B. Time
• C. Gain (K)
• D. Phase

Answer: (C)

The correct answer, which refers to gain (K), is pivotal in the context of root locus analysis in control systems. The root locus technique visually represents how the poles of a closed-loop system move in the s-plane as the gain (K) varies.

When gain is adjusted, it affects the stability and responsiveness of the control system. In root locus plots, varying K allows us to track how the closed-loop poles transition from their open-loop positions as the feedback gain increases. If K starts at zero, the system behaves according to its open-loop configuration, and as K increases, we can see the closed-loop poles move along predefined paths towards the stability threshold (the imaginary axis).

This movement is integral for designs and analysis in control systems, as the location of these poles directly influences the system's dynamics, including stability, transient response, and steady-state error.

The other parameters listed, such as frequency, time, and phase, do not directly correspond to pole locations as gain does in the root locus context. Frequency may influence system behavior, but it doesn't define how the poles shift. Time is more associated with movement on the response timeline rather than with pole placement. Similarly, phase changes can affect system behavior but do not provide a direct