Final answer:
The response of a closed-loop system to a unit step input requires analyzing the poles for settling time and percent overshoot. Neglecting a pole simplifies the system analysis but may lead to inaccuracies in predicting system behavior, notably in settling time and overshoot.
Step-by-step explanation:
To determine the response of a closed-loop transfer function T(s) = Y(s)/R(s) = 77(s+2)/(s+7)(s^2+4s+22) to a unit step input, we need to consider the dynamics of the system, specifically the natural frequency and damping ratio, to find the settling time (Ts) and the percent overshoot (P.O.). Using the 2% criterion for the settling time, we analyze the poles of the transfer function and use standard second-order system approximations to find these parameters.
When we neglect the real pole at s = -7, we are simplifying the system by considering it as a second-order system without the influence of the slower pole. We can compare this approximate result to the actual system response to evaluate the impact of neglecting this pole. Generally, the true system behavior may be different in terms of both settling time and percent overshoot when a pole is ignored, even more so if the neglected pole has a significant influence on the system dynamics.
In the context of overshoot and settling time, the concept of a characteristic time constant and the dependence on damping are highlighted. The underdamped case will show some overshoot, while an overdamped system generally experiences less or no overshoot, but with a longer settling time.