Download - computer lab for pdc( chemical engineering)
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EP 314LAB 4 Introduction to MATLAB
Open Loop Analysis
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EP314 Lab Timeline
LAB 1 & 2 -Introduction to MATLAB
Interface, code, function, graph, Simulink, etc.
LAB 3, 4 & 5 - Modelling of Chemical Process
ODE, Transfer Function, Open Loop Analysis, Sensitivity analysis, etc.
LAB 6 ,7,8 & 9 - Closed Loop and Controller Design
Block diagram, controller design, Performance Analysis, Criteria of Good controller, Stability Analysis, etc.
NO LAB
LAB 10 - Advanced Control System
Feedforward, Cascade and Ratio controls.
we
ek
2 3 4 5 6 7 8 9 10 11 12
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=
1
+ 1
Q1. Illustrate the y(s) profile if unity input step is applied for u.
-
=
1
2 + + 1
Q2. Illustrate the y(s) profile if unity input step is applied for u.
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1 =
1
+ 1;
Q3. Illustrate the y(s) profile if unity input step is applied for u.
1
=
0.5
0.5 + 1
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1 =
1
+ 1;
Q3. Illustrate the y(s) profile if unity input step is applied for u.
1
=
0.5
0.5 + 1
%Create NEW m-file and run the code as follows;
%Transfer Fcn1
Kp1 = 0.5;
Tau1 = 0.5;
%Transfer Fcn2
Kp2 = 1;
Tau2 = 1;
sim('exq3',10)
plot(t,y)
Save Simulink model as: exq3.mdl
Alternative Solution
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1
=
1
2 + 0.7 + 1;
Challenge: Illustrate and compare the y1, y2 and y3 profiles if unity input step is applied for u.
2
=
1
2 + 2 + 1;
3
=
1
2 + 3 + 1
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Contents:
1. Block Diagram
2. Transfer Function
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Case Study 1: Two-Tank Liquid System
=2
1
Find transfer function, G(s):
-
1
= 1
111 +
1
11
Laplace Transformation for Tank 1
Step 2: Take Laplace transform on both sides
{1
} = {1
111 +
1
11}
11 + 1
111() =
1
11()
Step 1: Take deviation from steady state
1
= 1
111 +
1
11
Step 3: Rearranges to standard form
Solution Case Study No. 1
1
1()=
111 + 1
-
Laplace Transformation for Tank 2
Step 2: Take Laplace transform on both sides
{2
} = {1
121
1
222}
Step 1: Take deviation from steady state
Step 3: Rearranges to standard form
Solution Case Study No. 1
2
=1
121 +
1
22
1
222
2
=1
121
1
222; 2
22 + 1
222() =
1
121()
2
1()=
2/122 + 1
-
1 =1
1()=
111 + 1
2 =2
1()=
2/122 + 1
1 2 1 1 2
TF Tank 1 TF Tank 2
Overall Transfer function
Transfer function for tank 1
Transfer function for tank 2
By applying chain rule, the TF for G(s) can be written as:
=2
1()=
1(11 + 1)
2/1(22 + 1) final answer
Solution Case Study No. 1
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MATLAB/Simulink Block Diagram
Solution Case Study No. 1
%Create NEW m-file and run
the code as follows:
U1 = 1; U2 = 0; R1 = 0.5;
R2 = 2/3; A1 = 1; A2 = 0.5;
sim('casestudy1',5)
plot(t,h1,'b',t,h2,'r')
casestudy1.mdl
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Solution Case Study No. 1
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Case Study 2: Two-Tank Liquid System
=2
1
Find transfer function, G(s):
1 =1 21
3 =22
1 = ( 1)
-
1
= 1 211
+1
11
Laplace Transformation for Tank 1
Step 2: Take Laplace transform on both sides
{1
} = {2 111
+1
11}
11 + 1
111 =
1
112 +
1
11
Step 1: Take deviation from steady state
1
= 1 211
+1
11
Step 3: Rearranges to standard form
Solution Case Study No. 2
1 =1
11 + 12 +
111 + 1
1
-
Laplace Transformation for Tank 2
Step 2: Take Laplace transform on both sides
Step 1: Take deviation from steady state
Step 3: Rearranges to standard form
Solution Case Study No. 2
2
=1 212
2
22
2
1()=
/
1 + 1
2
=1 212
222
{2
} = {112
212
222
} 2 =112
1
11+
1
222()
2
1 =
+
=1
12; =
1
11+
1
22
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Overall Transfer function
Transfer function for tank 1
Transfer function for tank 2
By applying chain rule, the TF for G(s) can be written as:
Solution Case Study No. 2
1 =1
11 + 12 +
111 + 1
1
2
1()=
/
1 + 1
1 = 1 2 + 1 11
2 = 2()1()
11
2 1
1
2
TF Tank 1
1 2
+
+
TF Tank 1
TF Tank 2
2 = 2 1 2 + 1 11
2 = 1 2 2 + 1 2 11
(1 1 2 )2 = 1 2 11
2
1()=
1 2 11 1 2
2 = 2()1()
Answer:
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MATLAB/Simulink Block Diagram
Solution Case Study No. 2
%Create NEW m-file and run the
code as follows:
U1 = 1; R1 = 2; R2 = 2; A1 = 1;
A2 = 1;
%G1
num1 = [1];
den1 = [R1*A1 1];
%G2
alpha = [1/(R1*A2)];
betta = 1/(R1*A1) + 1/(A2*R2);
num2 = alpha/betta;
den2 = [1/betta 1];
sim('casestudy2',35)
subplot(2,1,1)
plot(t,H1,'b'),hold on
plot(t,H2,'r'),hold off,grid
legend('H1','H2')
subplot(2,1,2)
plot(t,U1),grid
casestudy2.mdl
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Sample on block diagram setting
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LAB 4 (Group 1): Multiple Tanks Process
1 2
3
Given;
1 0 = 2 0 = 3 0 = 0
1 =(12)
1; 2 =
2
2; 3 =
3
3
= 0.5 1
Q1. Illustrate profile for H1, H2 and H3.
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LAB 4 (Group 2) : Multiple Tanks Process
1
2 3
Given;
1 0 = 2 0 = 3 0 = 0
1 =1
1; 2 =
23
2; 3 =
3
3
= 1.5 2
Q1. Illustrate profile for H1, H2 and H3.
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Individual Assignment (5%)Due: 1 week (From 1 June to 8 June, 2015 5:00PM)
Method: Printed report
RubricIn the report: 1 2 3 4 5
Show Transfer Function derivation
NO transfer function OR Wrong Transfer function
Only Overall Transfer Function
Complete derivation with appropriate step and order
Show FigureNO Figure OR Wrong Figure
Only H1, H2 and H3 profile
Complete with labels, lagend, all signals shown in good representation
MATLAB/Simulink code
NO Code OR Similar code
Only Simulink Code
Provided mfile code with simulink diagram. The signals are labeled at every line and mfile is written in good order
Description NO descriptionDescribe in moderate manner
Describe the observation of the height profiles in concise manner