Given the transfer function of a system as: Y(s) 15s + Ks+111 %3D for K20, with two zeros and three poles. U(s) s' +15s +73s +111 For U(s) = (a unit step input) and with zero initial conditions. a) 20 points: Find y(t) vs. t in terms of K (Find the exact solution with no imaginary terms) b) 20 points: Using y(t) of (a), find E(K) = [ (v()-u(1))' dt in terms of K (Find the exact solution with no imaginary terms). c) 20 points: From part (b), use calculus to find the minimum value of E(K) and the corresponding value of K. a- y(t) = I+ (01K - 8.2) + 7.2 [e cost + 4.64 sint ]