As gain K increases, where do system poles move from?

• A. Zeros to poles
• B. Poles to zeros
• C. Left to right
• D. Imaginary to real axis

Answer: (B)

As the gain K increases in a control system, the behavior of the system poles can be analyzed using techniques such as the root locus method. The root locus plot represents the possible locations of the system poles as a gain factor is varied.

In this context, as K increases, the system poles tend to move from their original positions, typically located in the left-half of the complex plane (for a stable system), towards the right-half of the complex plane. This movement can entail transitioning from locations near zeros of the transfer function or even poles, depending on the specific structure of the system. However, the primary focus here is understanding that with an increase in gain, poles will generally migrate towards zeros and can even cross into the right-half plane, which indicates instability.

This characteristic of pole movement is crucial for system stability analysis, as poles in the right-half plane correspond to unstable behavior. Therefore, as gain increases, the trajectory of the poles often leads them from near the zeros and further away from the stability region, reinforcing the importance of gain in control system design.