Question $5$

Refer to Figure Q$4,$ a controller is used to control a system.

a$)$ Determine the type of controller.

b$)$ Determine the transfer function of the system.

c$)$ What are the values of $K_p$ and $K_d,$ to meeting the following requirements: damping ratio of $=0\mathrm{.}3,{}_n=70ra\frac{d}{s}?$

d$)$ If the damping ratio $$ is double, does it have any effect on the $K_p$ value? Why?

Hint: you may use the following relationship for the system:

$\frac{Y(s)}{R(s)}=\frac{k{}_n^2}{s^2+2{}_{n}s+{}_n^2}$

Question $6$

a$)$ What is the Characteristic equation, system poles and system zeros of the following transfer function?

$G(s)=\frac{(s+5)(s-14)}{s^3-5s^2-6s}$

b$)$ Given a power machine that transfer function its work done output force and power input $V$ of

$G(s)=\frac{215{10}^{-3}}{2s+4}\frac{N}{W}$

i$)$ Find the response of the system when apply to a step input of $140$W$.$

ii$)$ Find the time taken to reach $90\%$ of the steady$-$state value.