Problem $3$

Given the system shown halnum

Figure $2$ A block diagram for Problem $3$

$($a$)$ Design the value of K $1,$ as well as a in the feedback path of the minor loop, to yield a settling time of $4$ seconds with $\backslash (5\backslash \%\backslash )$ overshoot for the step response.

$($b$)$ Design the value of K to yield a major$-$loop response with $\backslash (10\backslash \%\backslash )$ overshoot for a step input.

$($c$)$ Use MATLAB or any other computer program to simulate the step response to closed$-$loop system.

$($d$)$ Add a PI compensator to reduce the major$-$loop steady$-$state error to zero and simulate the step response using MATLAB or any other computer program. The PI controller will replace the gain K$.$