transfer function

1. MAJOR
ASSIGNMENT
MODELING OF SENSITIVITY OF
TRANSFER FUNCTION
SUBMITTED BY :
MAHENDRA PATEL
SUBMITTED TO :
MR. SOMESH CHATURVEDI

2. Transfer Function Definition
 The transfer function is sometimes defined
as:
– The Laplace transform of the time impulse
response with zero initial conditions.
 The development directly above is where this
definition comes from.
2

3. Transfer Function
G(s) is called the transfer function, and
represents the input-output relation for a
given system in the s-domain.
The above equation is an important formula,
but note that it may not necessarily be the
easiest way to obtain the transfer function
from the state and output equations.
3

4. Concept
 Consider a single input, single output linear
system:
4

5. Where,
 A is an n-by-n matrix, b is a n-by-one vector,
c is a one-by-n vector, and d is a scalar.
 Taking the Laplace transform of the state
and output equations, we get:
5

6. We get
6

7.  Let x0 = 0. We are interested in finding the
input-output relation, which is the relation
between Y(s) and U(s).
7

8. 8

9. In Time Domain
9

10. In Laplace Domain
Convolution in the time domain = Product in the Laplace domain.
10

11. Notion of Poles and Zeros
 In the above, the transfer function G(s) was
found to be a fraction of two polynomials in s.
11

12.  The denominator, D(s), comes from the
determinant of (sI-A), which appears from
taking the inverse of (sI-A).
12

13. Values of “s”
 These values of s have the same importance
in the present discussion.
 Values of s that make the numerator, N(s),
go to zero are called zeros since they make
G(s) = 0. Values of s that make the
denominator, D(s), go to zero are called
poles; they make G(s) = ¥.
13

14. Transfer Function Analysis
14

15. Alternatively put,
 The poles are the roots of D(s), and the
zeroes are the roots of N(s).
15

16. Realization condition
 The realization condition states that the order
of the numerator is always less than or equal
to the order of the denominator.
16

17. THANKYO
U
17