Note:

Since your definitions related with variables and

assumptions may change, please define your systems.

Please show your control structure in detail by using the

rules of documentation.

Write down your assumptions in detail related with each

problem statement.

Please define the variables you named with letters.

In the block diagram representation, do not forget to derive

each transfer function by yourself and indicate your assumptions.

In a well$-$mixed, continuous heating tank with one input

stream and one output stream, the temperature of the fluid in the

tank is to be kept constant against changes in input temperature.

For this system

a$.$ show the system in a plot $(3$p$)$

b$.$ define the aim, the system and clearly indicate your

assumptions $(7$p$)$

c$.$ derive the model equation which gives the change in system

temperature with respect to time $($considering the rules of

modeling and clearly indicating your variable analysis, as

controlled, manipulated, measured, input, output, etc.$)(10$p$)$

d$.$ solve the derived model equation $($find the function where

temperature change with respect to time is given$)(10$p$)$

e$.$ design and show a feedback control structure on this system

$($for the control of the temperature$)(5$p$)$

f$.$ considering the control structure $($in part e$)$ prepare the block

diagram. $($In this block diagram you should select a specific

mechanism for the controller and you should derive all the

transfer functions for basic units of the system$).(20$p$)$

Write down the equation used for the calculation of "Degrees

of Freedom" and explain its meaning and importance for process

control studies. $(10p$

Explain the use, importance and selection of measuring

elements in process control. $(10$p$)$

Consider a heating system, where heat transfer with

radiation $(Q(t)=A{T}^4)$ takes place. For this system, in order to

derive the model equation, which gives the change of temperature

with respect to time, and to derive the transfer function linearize

the radiation term. $(10$p$)$

In a water treatment system four non$-$ interacting tanks are

used in series. For this system evaluate the transfer function which

relates the liquid height in the fourth tank to liquid height in the

first tank. $($Indicate your assumptions clearly, sketch the system

indicating the streams, show your derivation of the transfer

function for the first tank in detail and show the derivation of the

desired transfer function in detail.$)(15$p$)$

$($Bonus$,5$p$)$ For the equation $(x(t)=(\frac{4}{3})e^{-t}-(\frac{1}{3})e^{-4t})$ show the

use of Laplace transform for the solution.

$($Bonus$,5$p$)$ Driving an automobile safely requires large

amounts of individual skills and especially the ability to utilize

feedback and feed forward control systems efficiently. If the

objective of the driver is to keep the automobile at a constant

speed, develop a suitable control structure to be used by the

driver. Show the control structures on a control loop by indicating

sensor$,$ controller etc. and define the system variables.