Part C (30%) The planar equations of motion for the missile is given by the following: W F = Zau m(w - qu) W EMy Ma + M88 = Jyyq roketsan 9 2 Fig. 4 Flight variables m = 50 kg: Mass Jyy = 10 kg-m: Moment of inertia u = 200 m/s: Longitudinal speed Za = -10000 N/rad: Force derivative wrt. a EF: Total lateral force EM,: Total moment w: Lateral speed q: Pitch rate 8: Fin angle (control input) M = -1000 N-m/rad: Moment derivative wrt. a M8 = 1500 N-m/rad: Moment derivative wrt. 8 Obtain the transfer function relating the fin angle to the pitch rate. Assuming the gyro is ideal, design' a pitch-rate autopilot for a max. settling time of 1 s. Note that the steady-state error does not need to be zero here. Why might this be? Test your design using various inputs. Comment on the results. Test the performance of your design against wind disturbance. Comment on the results.