4. Consider the following block diagram. r(s) 2 G (8) G(s) y(s) L(s) Given the closed-loop transfer function Get(s) = y(s) 20(10-5) T(S) (s+905+100) If Ge(s) = 1, a) Find the plant transfer function G, (s). b) Draw the asymptotic Bode magnitude and phase plots of G,(s). c) Find the gain crossover frequency and phase margin. For the above plant, consider the controller transfer function as kc(s + 100) Ge(s) = (s + 10) d) Draw the asymptotic Bode magnitude and phase plots of the outer-loop transfer function, L(s). Find the value of k, such that gain crossover frequency is 5 rad/s. e) Find the corresponding phase margin. [2] [8] [4] [4] [2]