Figure 1 shows a system that controls the roll angle of an airplane, with frictional losses ignored. If proportional control were used, the two poles at s = 0 would split off at +90 angles, and the system would be marginally stable for all values of gain. Instead, we need to add a controller that draws those poles to the left, thus stabilizing the system and increasing its speed. If we place a pole far to the left and a zero closer to the origin, then the locus from the pole will move right toward the zero, and the centroid of roots rule requires that the two complex poles move toward the left. Thus, a practical PD controller is implemented. You wish to fulfill the following design criteria: 11. Acceleration error constant, Ka, equal to 10. Damping factor,