1. The distillation column in Fig. 1 has the following transfer function model: D(s)Y(s)=100s+12e20s,F(s)Y(s)=60s+10.5e30s with Gm=Gv=Gt=1. Note: D is MV and F is DV (a. 25 pts.) Design a feedforward controller based on a steady-state analysis. (xsp= Figure 1: Distillation column 0.1mol/m3,ysp=0.08mol/m3) (b. 25 pts.) Design a feedforward controller based on a dynamic analysis. (c. 25 pts.) Design a PI feedback controller based on the Direct Synthesis (DS) approach with cl=20. (d. 25 pts.) Given the controller designed in the part c, and setpoint ysp(t)=S(t), calculate the ISE