For a system in unity feedback configuration with forward transmittance [ G(s)=frac{K}{s^{2}}, ] a cascade compensator is

Question:

For a system in unity feedback configuration with forward transmittance

\[
G(s)=\frac{K}{s^{2}},
\]

a cascade compensator is to be designed to achieve settling time of 1.6 seconds and peak overshoot of $16 \%$. If the compensator zero is located at $s=-1$, do the following:

(a) Locate the dominant roots

(b) Locate the compensator pole

(c) Find the system gain required to meet design specifications.

(d) Find the appropriate error coefficient.