Question: For experiment $3,$ you chose the controller zero to be at $-30$ and adjusted the other gain. So$,$ the PI controller that you used can be written as $()=+30$ where $$ is the gain. Using root locus of $$ show how the closed$-$loop poles will change as you adjust the gain $$ from $0$ to infinity. Explain based on rootlocus what will happen to the settling time and overshoot as you change the gain $$ from $0$ to infinity. $(2$ points$)$

Hint: Settling time depends on the real part of the closed loop pole, and overshoot depends on the angle the closed loop poles make with negative real axis.