$2.$ There are inner and outer loops in the given system. Stability and rapid responsiveness are essential for the inner loop. $(9$ points$)$

a$)$ Start with the inner loop and find range of K $1$ to keep the inner loop stable.

b$)$ Select K$1$ in the stable range to achieve the shortest settling time.

c$)$ With the value you have found from part $($b$)$ for K$1$ find the range of value K$2$ in the outer loop in order to keep the system stable.