A mass/momentum balance on the suction flowrate resulted in the following approximate linear model for the suction pressure Ps (s) : P,(s) = -Fc (s) + F(s); Ps (t) is in psig. 1 -0.5 (4s+1) (3s+1) Where Fi(s) and Fe(s) are, respectively, the inlet and outlet compressor flows expressed in liter/second. The time constants are in seconds. The response of the compressor flow to the controller output signal M(s) (CO) is given by: 0.4 2s+1 1.5 4s+1 Fc(s) = M(s), M(s) is the input to the compressor (final control element). The pressure transmitter has a range of 5 to 25 psig and negligible time constant. a. Write down the transmitter transfer function H (s). b. Draw the block diagram for the closed loop. Show all the process units (i.e., with unit name) and associated variables. c. Draw the unit feedback diagram for the closed loop. Write down the closed-loop transfer function and the characteristic equation. Must the controller be direct acting or reverse acting? Justify your answer. d. Calculate the ultimate gain and period, assuming a proportional controller. e. Design a PI controller and PID controller using a suitable design method using the result in d) above. f. Calculate the offset caused by a change of 0.50 liter/s in the inlet flow for each controller (P and PI) and comment on the results.