a Q3) Stability analysis: Your team has observed a disturbance in the upstream feed line entering the column. To counteract this, you decide to install a heat exchanger in the feed line to control the temperature (Y) entering the column using a cooling flow (U). The dynamics of this heat exchanger are captured by the following transfer function model: G(s) = 3/(68 +58+4) a) Analyse the heat exchanger transfer function: 0) Determine the poles of this function (i) Plot the poles on the complex plane (ii) Based on the pole locations, describe the general dynamic behaviour of this heat exchanger process. b) Analyse the open-loop stability of this heat exchanger using the three classical stability methods, and make comments about process stability: Routh-Hurwitz method 2 (ii) Assume that the system characteristic equation is given by 652 +55+ K-0 Analyse the open-loop stability using Root-locus method (iii)Assume that the system characteristic equation is given by 692 +58 +4 -K-0 Analyse the open-loop stability using direct substitution method c) A feedback control loop is proposed for this heat exchanger, draw the closed-loop block diagram of this feedback loop labelling clearly all variables. d) Given, GAS)=Kc; Goks)=G(s) = 1; 0 Draw the simplified closed loop block diagram (1) Derive the closed loop characteristic equation