matlab and simulink 12 labs and every lab 4 questions

Tutorials No 3

All working and MATLAB programs to be kept/typed up in Microsoft

Word, which would be submitted at the end of Term 2

Q1. The input-output relationship of a chemical reaction, → , taking place

in a continuous stirred tank reactor, CSTR, is given by the differential equation

(

) ( )

( )

( )

Q

V Q )(tCao)(tCao

)(tCai

Figure1: Continuous Stirred Tank Reactor

where

Molar concentration of chemical A into CSTR

Molar concentration of chemical A out of and inside CSTR

Volumetric flow rate of A into and out of CSTR

Volume of liquid inside the CSTR

Specific chemical reaction rate

At , ( ) and ( ) are equal to zero. Derive an expression for the time

dependent molar concentration of chemical A, ( ), leaving the CSTR, if the

molar concentration of chemical A, ( ) , into CSTR undergoes a step change

from to at .

Take , and

i. Calculate the steady state value of ( ) from the CSTR.

ii. Calculate the steady state gain, time constant, rise time and settling time of

the chemical reaction.

iii. Plot the variation of ( ) with using MATLAB.

iv. Compare the value of ( ) as → obtained from your MATLAB graph

with the value you obtain from Qii.

v. Compare the time constant obtained from your MATLAB graph with the value

you obtain from Qii.

vi. What is the unit of the steady state gain K?

Label the axes of your MATLAB graph with the correct units.