National Instruments 370753C-01 Manual De Usuario

One way of representing continuous-time finite-dimensional linear 
time-invariant systems is with the transfer function:

with num(s) and den(s) being polynomials in s. They can be specified either 
by their roots or their coefficients. Transfer functions are defined using the 
Laplace transform operators for continuous time and the forward shift 
operator z for discrete time. Both forms of transfer functions are written 
with positive coefficients, each higher order terms having successively 
larger coefficients.

Discrete systems are defined analogously, using the z variable instead of s. 
Xmath does not automatically perform cancellations of polynomial roots 
appearing in both the numerator and the denominator of a transfer function. 
If you want to cancel common roots in a transfer function, use the function 

cancel( )

. For state-space systems, refer to the 

minimal( )

 function. 

For more information, refer to the 

 section of 

To illustrate how you arrive at a particular transfer function, if you have a 
system differential equation that takes the form:

(2-1)

Laplace-transforming equation (assuming zero initial conditions) yields:

(2-2)

Collecting terms, you can find the transfer function from U(s) to Y(s), H(s):

(2-3)

The roots of the numerator polynomial are the zeros of the transfer 
function, and the roots of the denominator are its poles. In some 
circumstances, you might want to construct a transfer function based on 
where you know the pole and zero locations to be. For example, you can 

( )

( )

( )

------------------

=

y·· 6y· 8y

+

+

2u· u

–

=

2

( ) 6sY s

( ) 8Y s

( )

+

+

2sU s

( ) U s

( )

–

=

( )

( )

-----------

( )

2s 1

–

2

6s 8

+

+

--------------------------

=

=