A first$-$order plant is controlled using PI controller as shown below. You are to design the controller so that the closed$-$loop poles lic within the shaded region shown in the Figure below.

a$.$ What conditions ${}_n$ and $$ of the closed$-$loop system need io satisfy in order for the closedloop poles to lie in the shaded rep:on$.$

b$.$ Let $K_a==2.$ Find values for K and $K_1$ so that the poles of the closed$-$loop system lie within the shaded region.

c$.$ Prove that no matter what the values of $K_{}($with $K_{}0)$ and $$ are, the controller provides enough flexibility to place the poles anywhere in the complex plane.

a$)$