FAKULTI TEKNOLOGI DAN KEJURUTERAAN
ELEKTRONIK DAN KOMPUTER
UNIVERSITI TEKNIKAL MALAYSIA MELAKA
CONTROL PRINCIPLES
BEEE2364 SEMESTER 1 SESI 20232024
LAB 5: BLOCK REDUCTION METHOD
NO. STUDENTS' NAME MATRIC. NO.
1.
2.
3.
PROGRAMME 2 BERT
SECTION /
GROUP
DATE
1.
NAME OF
INSTRUCTOR(S)
2.
EXAMINER’S COMMENT(S) TOTAL MARKS
Page 1 of 10
Rev Date Author(s) Description
.
No.
1.0 30 JAN 1. Izadora binti Mustaffa 1. Update to new UTeM logo
2019 2. Update faculty's name
3. Change "course" to
"programme"
4. Remove verification stamp
2.0 28 FEB Izadora binti Mustaffa 1. Change content of the
2019 laboratory sheet
3.0 19 NOV Amar Faiz Zainal Abidin 1. Change content of the
2019 laboratory sheet
4.0 17 MAY Farees Ezwan Bin Mohd 1. Remove Part 2
2021 Sani (Electro-Mechanical system)
5.0 18 MAY Hafez Sarkawi Streamlined Procedure 4.0.
2021
6.0 29 DEC Ts. Dr. Hafez Sarkawi 1. Revised the new faculty name.
2023 2. Revised the Sysnopsis &
Theory and Procedure.
Page 2 of 10
1.0 OBJECTIVES
To find transfer function for a given complex block diagram using MATLAB.
2.0 EQUIPMENT/COMPONENTS
i) Computer
ii) MATLAB Software
3.0 SYNOPSIS & THEORY
A control system consists of the inter-connection of subsystems. A more complicated system
will have many inter-connected subsystems. To analyze the system response, the multiple
subsystems need to be represented as a single transfer function. The reduction of the multiple
subsystems can be done using block reduction method.
The basic components of a block diagram
The following are some of the rules in block reduction method.
a) Cascade form
Page 3 of 10
b) Parallel form
c) Parallel form
d) Feedback form
Page 4 of 10
e) Block diagram equivalent forms for moving a block to the left past a summing junction
f) Block diagram equivalent forms for moving a block to the right past a summing junction
g) Block diagram equivalent forms for moving a block to the left past a pickoff point
h) Block diagram equivalent forms for moving a block to the right past a pickoff point
Page 5 of 10
4.0 PROCEDURE
1) Open MATLAB software. Open New Script.
2)
(
For the block diagram shown in Figure 1, the overall transfer function TF=
)
C ( s)
R (s )
of the
7 1
system can be found by using Block Reduction Method. For G 1= , G 2= ,
s 2 s+ 3
s−1 3 7 7 7 s−8
G 3= , G 4= , G 5= 2 , G 6= 2 , G 7= , H 1=s and
s+2 s +3 s +7 s−1 s +1 72 s−1
H 2=7 s, the MATLAB coding based on Block Reduction Method is given in the following:
MATLAB Coding:
%--------------------------------------------------------------------------
% Declare individual block's transfer function
s = tf('s')
G1 = 7/s
G2 = 1/(2*s+3)
G3 = (s-1)/(s+2)
G4 = 3/(s+3)
G5 = 7/(s^2+7*s-1)
G6 = 7/(s^2+1)
G7 = (7*s-8)/(72*s-1)
H1 = s
H2 = 7*s
%--------------------------------------------------------------------------
% Define all Block Reduction Model according to the steps
A = G1 * G2
B = feedback(G3, H1, -1)
C = feedback(G4, H2, +1)
D = G5 + G6 - G7
TF = A * B * C * D
Page 6 of 10
Figure 1
3) Write down the output you observed. Describe the MATLAB functions listed in Table 1:
Table 1
Line Details
MATLAB
s = tf('s')
Command
1 MATLAB
Output
Explanation
MATLAB
G1 = 7/s
Command
2 MATLAB
Output
Explanation
MATLAB
G2 = 1/(2*s+3)
Command
3 MATLAB
Output
Explanation
MATLAB
G3 = (s-1)/(s+2)
Command
4 MATLAB
Output
Explanation
5 MATLAB G4 = 3/(s+3)
Command
Page 7 of 10
MATLAB
Output
Explanation
MATLAB
G5 = 7/(s^2+7*s-1)
Command
6 MATLAB
Output
Explanation
MATLAB
G6 = 7/(s^2+1)
Command
7 MATLAB
Output
Explanation
MATLAB
G7 = (7*s-8)/(72*s-1)
Command
8 MATLAB
Output
Explanation
MATLAB
H1 = s
Command
9 MATLAB
Output
Explanation
MATLAB
H2 = 7*s
Command
10 MATLAB
Output
Explanation
MATLAB
A = G1 * G2
Command
11 MATLAB
Output
Explanation
MATLAB
B = feedback(G3, H1, -1)
Command
12 MATLAB
Output
Explanation
Page 8 of 10
MATLAB
C = feedback(G4, H2, +1)
Command
13 MATLAB
Output
Explanation
MATLAB
D = G5 + G6 - G7
Command
14 MATLAB
Output
Explanation
MATLAB
TF = A * B * C * D
Command
15 MATLAB
Output
Explanation
4) Based on the knowledge gathered from Procedure 4.0 (2) above, find the overall transfer
function TF=
( C ( s)
R (s ))for the block diagrams in Figure 2, Figure 3 and Figure 4. Use the
following transfer functions:
1 1 1 1 1 1 1
G 1 ( s )= , G 2 ( s )= , G 3 ( s )= , G 4 ( s )= ,G 5 ( s )= ,G6 ( s )= , G 7 ( s )= .
s +1 s+ 2 s+3 s+4 s +5 s+6 s+ 7
Figure 2
Page 9 of 10
Figure 3
Figure 4
Page 10 of 10
