DEPARTMENT OF MECHATRONICS

ENGINEERING

UNIVERSITY OF ENGINEERING AND TECHNOLOGY,

PESHAWAR
MTE-328L CONTROLL SYSTEMS LAB, 6th SEMESTER
LAB REPORT 4
SUBMITTED BY: TAIMOOR KHAN
REG NO.: 20PWMCT0739
SUBMITTED TO: PROFF DR. RYAZ AKBAR SHAH
SUBMISSION DATE: 05-04-2023
LAB TITLE  “INTRODUCTION TO CONTROL SYSTEM
TOOLBOX”
LAB REPORT RUBRICS:
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LAB NO.4
LAB TILTLE
“INTRODUCTION TO CONTROL SYSTEM TOOLBOX”

OBJECTIVES
 How to create create Transfer Function model of different systems .
 To know about the representation of the system in MATLAB.
 To know about the step and impulse response of a system.
 To know about the linear System Analyzer.

THEORY
TRANSFER FUNCTION
A transfer function represents the relationship between the output signal of a control system and
the input signal, for all possible input values.[1]
A transfer function is a convenient way to represent a linear, time-invariant system in terms of its
input-output relationship. It is obtained by applying a Laplace transform

Advantages
Transfer function is a mathematical representation that describes how an input signal is
transformed into an output signal in a system.
The transfer function provides important information about the system's frequency response,
stability, and performance.

IN LAB TASKS
SIMPLE TRANSFER FUNCTION
COMMANDS
num = [5 4 1];
den = [1 2 4];
final = tf(num,den)

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COMMANDS
zeta = 0.25;
w0 = 3;
h = tf(w0^2,[1,2*zeta*w0,w0^2])

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Transfer function of the DC motor
If we want to create the transfer function of aDC motor directly so we can do so
 COMMANDS
s = tf('s');

sys_tf = 1.5/(s^2+14*s+40.02)

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Parallel connection of systems
Parallel connections of the system can be solved by two ways
1.Simple addition method
2.Parallel command method

1.Simple addition method

 COMMAND
num1= [1 2];
dnum1=[2 1 3];
sys1=tf(num1, dnum1)
num2= [1];
dnum2=[1 1];
sys2=tf(num2, dnum2)
fsys= (sys1+sys2)

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2.Parallel command method
 COMMAND
num1= [1 2];
dnum1=[2 1 3];
sys1=tf(num1, dnum1)
num2= [1];
dnum2=[1 1];
sys2=tf(num2, dnum2)
sys= parallel(sys1,sys2)

From above figure it is clear that the result of both methods are same so we can use any of that.

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Series connection of systems
Series connections of the system can be solved by two ways
1.Simple multiplication method
2.Series command method

1.Simple multiplication method

 COMMAND
a= [1 2];
b=[2 1 3];
sys1=tf(a,b)
c= [1];
d=[1 1];
sys2=tf(c,d)
fsys= (sys1*sys2)

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2.Series command method
 COMMAND
a= [1 2];
b=[2 1 3];
sys1=tf(a,b)
c= [1];
d=[1 1];
sys2=tf(c,d)

sys= series(sys1,sys2)

From the above figure it is clear that the transfer function will be same in both cases

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ZERO POLE GAIN COMMAND
 It creates a continuous-time zero-pole-gain model
 With zeros and poles specified as vectors and the scalar value of gain
K is called the gain.

 COMMAND
z=[5 2 7]
p=[-4 -1 -9];
k=6;
zpk=zpk(z,p,k)

STEP INPUT FUNCTION

Step input function is used to generate step response of LTI systems.
Y=step(sys,t)
Plot(t,y)
 COMMAND

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IMPULSE INPUT FUNCTION
Impulse input function is used to generate impulse response of LTI systems.
y=impulse(sys,t)
Plot(t,y)

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LINEAR SYSTEM ANALYZER
We have made the system in the simulink and analyze it which is shown below;

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 POST LAB TASKS
TASK 1

 COMMAND
clear all
m=[2];
n=[1];
o=[1 1];
p=[1 2];
tf1=tf(o,p);

j=[1];
k=[1 10];
tf2=tf(j,k);

r=[1 0 1];
s=[1 4 4];
tf3=tf(r,s);

a=[1 1];
b=[1 6];
tf4= tf(a,b);

fsys=tf1+tf2+tf3

d=feedback(n,tf4)
e=feedback(tf1,tf3+tf4)

h=feedback(tf2+tf3,m)
g=feedback(tf1+tf2+tf3,n)

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SIMULINK DESIGN

PLOT

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TASK 2
 COMMAND
clear all
t=0:0.1:15;
r=[2 5 1];
s=[1 2 3];
tf1=tf(r,s);

g=[5 10];
h=[1 10];
tf2=tf(g,h);
fsys=feedback(tf1,tf2)
sgnal=step(fsys,t)
plot(t,sgnal)
PLOT

SIMULINK DESIGN

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PLOT

REFERENCES
1. https://www.electrical4u.com

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