Control of the attitude θ of a missile by controlling the fin angle φ, as shown in Figure P11.16, involves controlling an inherently unstable plant. Consider the specific plant transfer function a....

Control of the attitude θ of a missile by controlling the fin angle φ, as shown in Figure P11.16, involves controlling an inherently unstable plant. Consider the specific plant transfer function

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 ζ = 0.707 and τ = 0.1 if the plant transfer function G_p(s) has an uncertainty  due to fuel consumption, where