ERIC ED446898: The Use of the Software MATLAB To Improve Chemical Engineering Education.

9 Pages·2000·0.18 MB·English

by  ERIC

DOCUMENT RESUME
SE 063 523
ED 446 898
Damatto, T.; Maegava, L. M.; Filho, R. Maciel
AUTHOR
The Use of the Software MATLAB To Improve Chemical
TITLE
Engineering Education.
2000-00-00
PUB DATE
NOTE
7p.
Reports Descriptive (141)
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*Chemical Engineering; *Computer Software; Computer Uses in
DESCRIPTORS
Education; Educational Technology; Engineering Education;
Foreign Countries; Higher Education; Undergraduate Study
Brazil
IDENTIFIERS
ABSTRACT
In all the Brazilian Universities involved with the project
"Prodenge-Reenge", the main objective is to improve teaching and learning
procedures for the engineering disciplines. The Chemical Engineering College
of Campinas State University focused its effort on the use of engineering
softwares. The work developed by this project has allowed all Chemical
Engineering undergraduates to deal with commercial softwares which make
engineering calculations and estimates easier. The following works aids
Chemical Engineering Process Simulation and Control improvement through the
use of the commercial software MATLAB. The main concern is to develop some
useful case studies which are able to bring out the important characteristics
for the control structure design and implementation. Beyond the process
simulation and control application, the user has the main concepts related to
control theory readily available in an interactive fashion. The present work
has been divided in two parts. The first one consists of Process Control
fundamental theory so that an undergraduate can either review or have a first
contact with the subject. The second part of the work is an ideal binary
distillation column study where some important aspects of the control theory
have been implemented. (Author)
Reproductions supplied by EDRS are the best that can be made
from the original document.
THE USE OF THE SOFTWARE MATLAB TO IMPROVE CHEMICAL
ENGINEERING EDUCATION
T Damattol
L.M. Maegava2 and R. Maciel Filho3
,
Chemical Engineering College
Campinas State University (UNICAMP)
Campinas, S.P.,Brazil
C.P. 6066, 13083 970
,
The process variables can be divided in 3 groups:
ABSTRACT - In
the Brazilian
all
Universities
manipulated variables, controlled variables and load
Reenge", the
involved with the project "Prodenge
main objective is to improve teaching and learning
variables.
Manipulated variables
procedure for engineering disciplines. The Chemical
They are independent variables which are entering or ,
Engineering College of Campinas State University
leaving the process and can be changed to make the
focused its effort on the use of engineering softwares.
The work developed by this project has allowed all
control.
Controlled variables
Chemical Engineering undergraduates to deal with
They are the variables in which the control will be,.
engineering
commercial softwares
make
which
made. This control can be made either maintaining .11'
The following
calculations and estimates easier.
these variables as constant as possible or making them
work aims Chemical Engineering Process Simulation
;41
and Control improvement through the use of the
follow a desired trajectory. ,
Example: Temperature inside a'reactor.
commercial software MATLAB.
.g
to develop some useful case
Load variables
The main concern is
It is not possible to manipulate with these variables.
studies which are able to bring but the important
Although the effects of the load variables, the control
characteristics for Me control structure design and
system must be prepared to work perfectly.
implementation. Beyond the process simulation and
control application, the user has the main concepts
in an
What is a controller ?
related to control theory readily available
interactive fashion.
The present work has been divided in two parts. The
The construction and operation details of a controller
first one consists of Process Control fundamental
to manufacturer, but its
change from manufacturer
theory so that an undergraduate can either review or
basic functioning is the same.
have a first contact with the subject. The second part
All controller aims to compare the signal which
of the work is an ideal binary distillation column
comes from the transmitter with the set-point and
study where some important aspects of the control
sends a signal to the control valve. The way that the
theory have been implemented
controller compares the process signal with the set
point depends on the type of action wanted. Basically
Part One
there are 3 kinds of actions in a feedback controller:
integral action and derivative
proportional action,
The first part consists of some important
process
action.
Some of them
are presented
definitions.
control
bellow.
Proportional controller (P)
Types of variables
The output signal is compared to the set-point and is
changed proportionally to the input signal error. A
Scientific initiation advised student.
U.S. DEPARTMENT OF EDUCATION
Office of Educational Research and Improvement
2
Advisor.
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DISSEMINATE THIS MATERIAL HAS
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his document has been reproduced as
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originating it.
Minor changes have been made to
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INFORMATION CENTER (ERIC)
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1
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proportional controller just acts when an error is
Proportional Integral Controller (PI)
measured. The equation of this type of controller is:
C)
m(t) =
+ Kc ?(Csp
(I)
integral controller has a proportional plus an
An
where:
integral action. In an integral action the control valve
m(t) = controller output signal which adjusts the
moves based on the time integral of the error. This
control valve
action aims to bring back the system to the set-point
M (t) = controller output signal when the error is zero
and also avoids it to go away from the set point. One
Kc = controller gain
important characteristic of such controller is that, due
C = process signal from transmitter
to the integral action, the response can be very slow.
Csp= set-point signal (process desired signal)
The equation of this type of controller is:
C - C,, = error (e(t))
great advantage of this strategy is
that
allows,
it
1
e(t) dt
M(t) =
+
theoretically, a perfect control. However, in many
applications this is not feasible.
1
(2)
Feedforward / Feedback control
where:
T = integral time
Feedforward control is often used in combination with
of
Proportional Integral Derivative
type
control
Each
feedback control.
compensates the disadvantages of the other one.
Controller (PID)
Ratio control
All of the three actions (proportional, integral and
derivative) are included. The derivative action is an
a special type of feedback control.
The
This
is
action where the
controller aims
to
anticipative
objective is not to control the performance of two
anticipate the future system characteristic based on the
independent variables M, L but to control the ratio
derivative of the error ( the time rate of change of the
Re:
quick and is always in
error). This action is
the
M
R =
opposite direction of the error occurred in the system.
The equation of a proportional integral controller is:
L
a
m = -111 + Kc ? e + edt
de-q
(4)
dt
Some applications of ratio control are, for instance, the
for a distillation
control of a specific reflux ratio
(3)
column or the holding of a fuel air ratio to a furnace at
where:
an optimum value.
T D = derivative time
Part Two
Control Strategies
The second part of this work is
an ideal binary
There are many control strategies. Some of them are
additional
study.
Several
column
distillation
presented bellow.
idealizations were made. These
assumptions and
hypothesis are sometimes valid but they are frequently
Feedback Control
only crude approximations. However, the purpose of
studying this simplified model case is to reduce the
problem to its most elementary form so that the basic
The variable wanted to be controlled is measured and
structure of the equations can be clearly seen.
compared to a desired value (the set- point). The error
First of all,
the column was modeled considering
between the process variable and the set-point
is
of vapor
overflow (whenever a mole
equimolal
turned into an input so that the controller can act in
vaporizes a mole of liquid), which
condenses, it
the system. Therefore, the controller does not make
eliminates an energy equation for each tray. The
any action until an error in the system is detected. It
holdup of vapor is assumed negligible and a simple
is an action to bring the system back to the set-point.
linear relationship between the liquid holdup, (MN)
and the liquid flow rate leaving the tray, LN is also
Feedforward Control
a pure
considered. A further assumption made is
binary system with constant molar relative volatility
a through the column and perfect 100 percent efficient
The variable is measured and a corrective action is
trays. The variables used to model the column are
taken before it upset the process. It is basically an
action to maintain the system in the set-point. The
presented bellow:
3
where:
N, = feed tray of the column
F = feed rate (moles/s)
erro =
-XD
XD
set-point
The initial conditions given for the column are:
xF = composition of liquid in the feed tray
= 20
= holdup of liquid in the reflux drum (moles)
NT
MD
xD= composition of the liquid in the drum
set-point = 0.98
XD
= top tray of the column
XB set-poant = 0.02
NT
yNT = composition of vapor in the top of the column
XF set-point = 0.5
NF=10
R = rate of reflux (moles/s)
D = rate of overhead distillate
product removed
MD0=100 moles
MB0=100 moles
(moles/s)
M0=10 moles
B = rate of liquid bottoms product removed (moles/s)
Ro=128.01 molests
xB = liquid composition in the base of the column
V = rate of vapor generated in the reboiler of the
Vo=178.01 moles/s
F=100 moles/s
column (moles/s)
MB = holdup in the reboiler (moles)
11=0.1
a=2
MN = holdup on each tray (moles)
The constants of the 2 controller are:
xN = composition of liquid in each tray
yN = composition of vapor in each tray
KcD=1000
p= hydraulic constant of the trays
KCB=1000
Ro = initial reflux rate
TD=5
TB=1.25
MN = constant
To make the control of the given column, a program
and a
are 4
equations per tray:
a
total
There
was made in the software MATLAB. The program
component continuity, a liquid hydraulic equation and
asks the student a perturbation
the the
in
in
a vapor-liquid equilibrium equation. These equations
composition of the feed stream. The program is listed
are presented bellow.
bellow:
Vapor-liquid equilibrium equation:
% initial variables
a ?x,,
NT=20;NF=10;MD0=100;MB0=100;MO=10;
Yr,
R0=128.01;V0=178.01;F=100;BETA=0.1;
+ (a 1)?xn
ALFA=2;
% CONTROLLER CONSTANTS
(5)
Liquid hydraulic equation:
KCD=1000;KCB=1000;
M 17
TAUD=5;TAUB=1.25;
LN = EN +
ERINTB=0;ERINTD=0;
N N
% Perturbation
Z=input('Enter with a perturbation between 0 and 1
(6)
Z=');
Total continuity:
% INITIAL VALUES OF X
d(M
)
XB=0.02;
LN
L'N+I
N
dt
X=[0.035 0.05719 0.08885 0.1318 0.18622 0.24951
0.31618 0.37948 0.43391 0.47688 ...
(7)
Component continuity:
0.51526 0.56295 0.61896 0.68052 0.74345 0.80319
0.85603 0.89995 0.93458 0.96079];
XD=0.98;
d(MN ?xN)
Vyipitial conditions
LN ?xN + V ?yN_,
LN+I ?xN +l
dt
for'SI=1:NT
M(N)=MO;
(8)
MX(N)=M(N)*X(1,N);
A feedback control was made through 2 controllers PI
LO(N)=RO+F;
which change the reflux R and the vapor V to control
if N>NF
bottom
composition
and
distillate
overhead
xp
LO(N)=RO;
composition xB. The equations for each controller are:
1
end;
end;
err, ?dt,/
KcB ? err, +
V = Vo
Time=0;DELTA=0.005;ERINTD=0;ERINTB=0;i=1
(9)
while Time<12
where:
% LIQUID HYDRAULIC EQUATION AND VLE
errs = XB set-point -XB
1
for N=1:20
Y(N)=ALFA*X(1,N)/(1+(ALFA-1)* X(1,N));
R = R D + KeD ? errD +
err0 9dt-V
L(N)=LO(N)+(M(N)-M0)/BETA;
ID
end;
YB=ALFA*XB/(1+(ALFA-1)*XB);
(10)
4
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end;
% 2 CONTROLLERS FEEDBACK P1
MDOT(NT)=R-L(NT);
ERRB=0.02-XB;
MXDOT(NT)=V*(Y(NT-1)-Y(NT))+R*XD-
ERRD=0.98-XD;
L(NT)*X(1,NT);
V=VO-KCB*(ERRB+ERINTB/TAUB);
XDDOT=V*(Y(NT)-XD)/MDO;
R=RO+KCD*(ERRD+ERINTD/TAUD);
% Euler Integration
D=V-R;
Time=Time+DELTA;
B=L(1)-V;
XB=XB+DELTA*XBDOT;
if R<0 disp('level too low or unreal composition ')
for N=1:NT
end;
M(N)=M(N)+MDOT(N)*DELTA;
if V<0 disp("level too low or unreal composition ')
MX(N)=MX(N)+MXDOT(N) *DELTA;
end;
X(1,N)=MX(N)/M(N);
if D<0 disp('level too low or unreal composition ')
end;
end;
XD=XD+XDDOT*DELTA;
if B<0 disp('level too low or unreal composition')
ERINTD=ERINTD+ERRD*DELTA;
end;
ERINTB=ERINTB+ERRB*DELTA;
% CALCULATION OF DERIVATIVES
A(i,:)=[ Time XB X(1,10) XD R V];
XBDOT(L(1)*X(1,1)-V*YB-B*XB)/MBO;
i=i+1;
MDOT()=L(2)-L(1);
end;
MXDOT()=V*(YB-Y(1))+L(2)*X(1,2)-L(1)*X(1,1);
figure(1);plot(A(:,1),A(:,2);c-'),xlabel(Time
for N=2:NF-1
[hr]'),ylabel('XB');grid;
MDOT(N)=L(N+1)-L(N);
figure(2);plot(A(:,1),A(:,3),'r-'),xlabel('Time
MXDOT(N)=V*(Y(N-1)-Y(N))+L(N+1)*X(1,N+1)-
[hr]'),ylabel('XF');grid;
L(N)*X(1,N);
figure(3);plot(A(:,1),A(:,4),'g-'),xlabel('Time
end;
[hr]'),ylabel('XD');grid;
% FEED TRAY
figure(4);plot(A(:,1),A(:,5),'b-'),xlabel('Time
MDOT(NF)=L(NF+1)-L(NF)+F;
[hr]'),ylabel('R (moles/hr)');grid;
MXDOT(NF)=V*(Y(NF-1)-
figure(5);plot(A(:,1),A(:,6),'m-'),xlabel('Time
Y(NF))+L(NF+1)*X(1,NF+1)-L(NF)*X(1,NF)+F*Z;
[hr]'),ylabel('rate of vapor (moles/hr)');grid;
for N=(NF+1):(NT-I)
For a step perturbation in the composition of the feed
MDOT(N)=L(N+1)-L(N);
the program gives the
stream from 0.5
0.55,
to
MXDOT(N)=V*(Y(N-1)-Y(N))+L(N+1)*X(1,N+1)-
following graphics:
L(N)*X(1,N);
5
Figure 1. Graphic of composition .x13 X time (hours)
0.9808
0.9807
0.9806
0.9805
0.9804
.....
.....
........ .. .
0.9803
0.9802
0.9801
-
0.98
14
0
12
6
2
10
4
8
Figure 2. Graphic of composition xi, X time (hours)
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Observing the graphics it can be seen that, after the
output
perturbation, the control acts in the system and the
Reenge" was encouraged as well as the undergraduates'
compositions stabilize.
contribution.
Other activities
References
All of the present work will be accessible to
all
Luyben, W.L; "Process Modeling, Simulation
1)
Chemical Engineering undergraduates of. UNICAMP
and Contro for Chemical Engineers"; 2" Edition;
create a deep interaction
through home-pages to
Mc Graw-Hill, 1974.
between the students and the studied subjects.
Seborg, Dale E., Thomas F. Edgar and Duncan
2)
Moreover, 2 performances regarding this work were
A. Mellichamp; "Process Dynamics and
made to
professors of Chemical Engineering
all
Control"; 151 Edition; John Wiley and Sons,
of UNICAMP.
the
both
lectures
College
In
1989.
participation of all professors in the project "Prodenge-
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