Answer Happy

QUESTION 3 [25 MARKS] An attitude control system for a missile is shown in Figure 2. a) Comment on the stability of the open loop system and justify your answer. b) Using Block Diagram Reduction or otherwise, show that the closed loop transfer function is Y(s) 10 given by the expression R(5) 5+10K, s +10K, -4 = c) Using the closed-loop transfer function obtained in part (b), determine the values of K, and K, in order that the closed loop system may have a rise time of 0.2 sec and an overshoot of 15% when the system is subjected to a unit-step input. d) Employing the Final-Value Theorem (FVT), determine the steady-state time response of the closed-loop system (i.e. y()) to a unit step input for the gains predicted in part (c). e) Employing Routh's stability criterion or otherwise, determine the range of values for the gains K, and K, for which the closed loop system will be stable. Attitude Dynamics Thrust Angle 8(t) Desired Attitude r(t) 10 $2-4 Actual Attitude y(t) Ks Attitude Rate Sensor K Attitude Sensor Figure 2 (For Question 3)