Explain the meaning, importance and use of Degrees of

Freedom in process control modeling studies. $(10)$

In a system where three non$-$interacting tanks are used in

series find the transfer transfer function which relates

liquid height in the third tank to input flow rate to the

first tank. $(15)$

In a well mixed closed tank, liquid is heated with

saturated steam which flows through a coil $($yay$,$bobin$)$

immersed $($daldirmak$)$ in the liquid. If the temperature of

this system is to be controlled by a feedback control

structure;

a$)$ Plot the system, indicate system information and list

your assumption $(10)$

b$)$ Derive and solve the model equation $(15)$

c$)$ Develop the block diagram which represents the

system $(10)$

d$)$ Depending on your system selection $($ batch,

continous etc. $)$ give an example from food industry

which is represented by your system $(5)$

In a CSTR Vitamin B$1($ thiamin $)$ production takes place.

Thiamin is produced when thiazole and pyrimidine

derivative makes a reaction. Thiamin production from

thiazole is a first order reaction. Mixture of thiazole and

pyramidine is fed to a CSTR which kept at $25C$ and

output steam is further processed in order to purify

thiamin. Thiamin is not stable in a neutral or alcaline

conditions, for this reason $pH$ of CSTR is continously

controlled to maintain acidic conditions.

a$)$ Show the CSTR with all streams in a plot $(10)$

b$)$ Construct a control structure for $pH$ control and

indicate controlled, manipulated and disturbance

variables $(10)$

c$)$ Prepare the model equation where chance of thiamin

concentration with respect ot time is given $(10)$

Explain the importance of documentation in process

control studies. $(5)$

$($ Bonus $)$ In a pneumatic control system error is given

$(t)=t^{{?}^{{?}^{?}}}2+2t.$ For PID system, derive the transfer function.