Control of the attitude q of a missile by controlling the tin angle f, as shown in Figure P11.16, involves controlling an inherently unstable plant. Consider the

G_p (s) = Q (s) / F (s) = 1 / s² – 5

a. Determine the PD control gains so that the steady-state error for a step command is zero, the closed-loop damping ratio is 0.707, and the dominant closed-loop time constant is 0.1.

b. Use the root locus to evaluate the performance of the resulting controller in light of the specifications z= 0.707 and t = 0.1 if the plant transfer function G_p (s) has an uncertainty D due to fuel consumption, where

G_p (s) = 1 / s² – 5 – D