S. Y. B.
Tech (ECE)
S. Y. B. Tech Semester: IV Subject: Control Systems
Name: Class:
Roll No: Batch:
Experiment No: 01
Name of the Experiment: To obtain pole, zero and gain value of a transfer function.
Performed on: Marks Teacher’s Signature with date
Submitted on:
Aim: To obtain pole, zero and gain value of a transfer function
Prerequisite:
knowledge of various types of signals
Idea about software MATLAB
Objective:
To obtain
I. Pole, zero, gain values from a given transfer
function
II. Transfer function model from pole, zero,
gain values
III. Pole, zero plot of a transfer function
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THEORY:
A transfer function is also known as the network function is a
mathematical representation, in terms of spatial or temporal
frequency, of the relation between the input and output of a (linear
time invariant) system. The transfer function is the ratio of the
output Laplace Transform to the input Laplace Transform
assuming zero initial conditions. Many important characteristics of
dynamic or control systems can be determined from the transfer
function. The transfer function is commonly used in the analysis of
single-input single-output electronic system, for instance. It is
mainly used in signal processing, communication theory, and
control theory. The term is often used exclusively to refer to linear
time-invariant systems (LTI). In its simplest form for continuous
time input signal x(t) and output y(t), the transfer function is the
linear mapping of the Laplace transform of the input, X(s), to the
output Y(s).
Zeros are the value(s) for z where the numerator of the transfer
function equals zero. The complex frequencies that make the
overall gain of the filter transfer function zero.
Poles are the value(s) for z where the denominator of the transfer
function equals zero. The complex frequencies that make the
overall gain of the filter transfer function infinite.
The general procedure to find the transfer function of a linear
differential equation from input to output is to take the Laplace
Transforms of both sides assuming zero conditions, and to solve
for the ratio of the output Laplace over the input Laplace.
The transfer function provides a basis for determining important
system response characteristics without solving the complete
differential equation. As defined, the transfer function is a rational
function in the complex variable ‘s’ that is It is often convenient to
factor the polynomials in the numerator and the denominator, and
to write the transfer function in terms of those factors:
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where, the numerator and denominator polynomials, N(s) and D(s).
The values of s for which N(S) = 0, are known as zeros of the system. i.e; at
s= .
The values of s for which D(S) = 0, are known as poles of the system. i.e; at s =
.
PROCEDURE:
Enter the program in the editor window.
If the program is typed in command window, the functions should be typed
without semi-colon.
Enter the values in the numerator & denominator depending on order of the
system.
The syntax used to get transfer function is tf.
Finally save the program and run it.
CALCULATIONS:
CONCLUSIONS:
Post lab questions:
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1. What do you mean by poles?
2. What is a transfer function?
3. What is the significance of transfer function?
Example: To obtain pole, zero & gain values of following transfer function.
TF= (s^2 + 4 s + 3)/( 3 s^3 + 19 s^2 + 27 s + 35)
Matlab Code:
num = [1 4 3]
den= [3 19 27 35]
g = tf(num,den)
[z,p,k] = tf2zp(num,den)
pzmap(g)
Output :
Transfer function:
s^2 + 4 s + 3
---------------------------------------
3 s^3 + 19 s^2 + 27 s + 35
z=
-3
-1
p=
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-5.0000
-0.6667 + 1.3744i
-0.6667 - 1.3744i
k=
0.3333
Pole Zero Plot:
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