Given the following open-loop plant: G(s)=\frac{20(s+2)}{s(s+5)(s+7)} design a controller to yield a 10% overshoot and a settling time of 2 seconds. Place the third pole 10 times as far from the imaginary axis as the dominant pole pair. Use the phase variables for state-variable feedback.

Fig: 1

Fig: 2

Fig: 3