EP 314LAB 4 Introduction to MATLAB

Open Loop Analysis

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

=

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.

1 =

1

+ 1;

Q3. Illustrate the y(s) profile if unity input step is applied for u.

1

=

0.5

0.5 + 1

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

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

Contents:

1. Block Diagram

2. Transfer Function

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

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

Solution Case Study No. 1

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

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:

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

Sample on block diagram setting

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.

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.

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