Solve the following problems:

A feedback control system has the following transfer function:

$T(s)=\frac{14145}{(5+0\mathrm{.}842s+2829)(x+5)}$

a$)$ For a second order system, what pole locations characterize the underdamped system.

b$)$ Using the dominant poles approximation, determine the system undamped natural frequency ${}_n$ and the system damping factor $.$

c$)$ Calculate the system Percent overshoot PO and setting time ${}_s.$ Comment on your answers.

d$)$ How can you improve the system PO$?$

Answers:

a$)$

b$){}_n=$

$,=$

c$)PO=$

$,{}_5=$

d$)$