What is the effect of adding poles to a system?

• A. System stability increases
• B. The root locus shifts away from the imaginary axis
• C. System becomes more oscillatory and relative stability decreases
• D. The range of K increases

Answer: (C)

Adding poles to a system typically impacts its behavior in terms of stability and oscillation. When additional poles are introduced, especially if they are located closer to the imaginary axis in the s-plane, the system's response can become more oscillatory. This happens because adding poles can introduce new dynamics, which can lead to longer settling times and an increase in oscillations around the setpoint.

Furthermore, with more poles, the relative stability of the system often decreases, as the poles may move the system's roots further into the left-half plane or even to the right-half plane, which can result in a less damped response. This makes the system more sensitive to disturbances and can make it less reliable overall. As the system becomes more oscillatory, it indicates a reduction in stability margins, further highlighting the negative effect of adding additional poles in terms of relative stability. Thus, the correct inference from this scenario is that the system becomes more oscillatory and the relative stability decreases.