Exercise 5.9 a The eect of a concentration disturbance must be reduced by a factor of  at the frequency  radmin The disturbances should be dampened by use of buer tanks and the objective is to minimize the total volume How many tanks in series should one have What is the total residence time

b The feed to a distillation column has large variations in concentration and the use of one buer tank is suggest to dampen these The eect of the feed concentration d on the product composition y is given by scaled variables time in minutes Gd s

 es
s that is after a step in d the output y will after an initial delay of  min increase in a ramplike fashion and reach its maximum allowed value which is  after another minutes  Feedback control should be used and there is a additional measurement delay of  min What should the residence time in the tank be

c Show that in terms of minimizing the total volume for buer tanks in series

it is optimal to have buer tanks of equal size

d Is there any reason to have buer tanks in parallel they must not be of equal size because then one may simply combine them 

e What about parallel pipes in series pure delay  Is this a good idea

Buer tanks are also used in chemical processes to dampen liquid owrate disturbances or gas pressure disturbances This is the topic of the following exercise