Problem $5(10$ Points$)$: The system shown below uses proportional control combined with a with velocity

feedback loop.

Suppose that $=20$ and c $=10.$ What gains, $$p and $2,$ are necessary to ensure the following:

i$.$ Zero steady$-$state error due to a unit step command $(\backslash$theta r$)$

ii$.$ A steady$-$state error due to a unit$-$step disturbance $($d$)$ to be no greater than $0\mathrm{.}1$ in magnitude

iii. A time constant of $\backslash$tau $=0\mathrm{.}1$ secondsSuppose that I$=20$ and c$=10.$ What gains, K$\_($p$)$ and K$\_(2)\backslash$Theta $\_($r$)$ T$\_($d$)\backslash$tau $=0\mathrm{.}1$ seconds