a) Obtain the transfer function between Y(s) and U(s) and put in standard gain/time constant form. (5 pts) b) Derive an approximate first-order-plus- time-delay transfer function model using Taylor-series expansion. Calculate gain, time constant and time delay. (5 pts) Write approximated transfer function. (5 pts) c) Derive an approximate second-order-plus- time-delay transfer function model by Skogestad's half rule. Calculate gain, time constants and time delay. (10 pts) Write approximated transfer function. (5 pts) U(S) Y(s) 14(0.3 -0.93) (3s + 1)(4s + 1) 1 12s + 1 e-1.18