Consider the closed-loop system shown below: The loop has two proportional controllers. Kc and Kc2 (a) For what range of the controller gain K is the inner loop stable? (Hint: Use the characteristic equation only for the inner loop only and check the Routh's criteria for stability). (b) Let the controller gain K be 0.2. Calculate the closed-loop transfer function from D to Y. Assuming R= 0. (c) Calculate the range of the controller gain Kc2, that makes the overall closed loop system (Y/D) stable. Use Routh's test again. D R+ K 1 (S-1) Ka 10 16 2 (5s + 1)(8s + 1)