Which one of the following conditions is justifying a second-order approximation ?

Solution:

Second-order approximation of higher-order systems:
Certain higher-order systems can be approximated as second-order systems and can be characterized by the parameters in the preceding section.

The conditions are as follows:

• Higher-order poles are much farther into the left half of the s-plane than the dominant second-order pair of poles. The response that results from a higher-order pole does not appreciably change the transient response expected from the dominant second-order poles.
• Closed-loop zeros near the closed-loop second-order pole pair are nearly canceled by the close proximity of higher-order closed-loop poles.
• Closed-loop zeros not canceled by the close proximity of higher-order closed-loop poles are far removed from the closed-loop second-order pole pair.