Class TransferFunction

Initialization of TransferFunction object

This method initialize a TransferFunction object.

Overrides: object.__init__

String representation

This method returns the string representation of the transfer
functions. For example:

    Transfer Function:
    .
    .     1      
    ------------
    s^2 + 2s + 3

Overrides: object.__str__

Operation of addition

This method returns a TransferFunction object with the result of the addition of the TransferFunction 'self' and the TransferFunction 'tf'. For example:

>>> a = TransferFunction([1], [1, 2, 3])
>>> b = TransferFunction([1], [2, 3, 4])
>>> c = a + b
>>> print c
Transfer Function:
.
.        3s^2 + 5s + 7         
------------------------------
2s^4 + 7s^3 + 16s^2 + 17s + 12
.
>>> type(c)
<class 'controlsystems.types.TransferFunction'>

Operation of subtraction

This method returns a TransferFunction object with the result of the subtraction of the TransferFunction 'self' and the TransferFunction 'tf'. For example:

>>> a = TransferFunction([1], [1, 2, 3])
>>> b = TransferFunction([1], [2, 3, 4])
>>> c = a - b
>>> print c
Transfer Function:
.
.         s^2 + s + 1          
------------------------------
2s^4 + 7s^3 + 16s^2 + 17s + 12
.
>>> type(c)
<class 'controlsystems.types.TransferFunction'>

Operation of multiplication of polynomials

This method returns a TransferFunction object with the result of the multiplication of the TransferFunction 'self'and the TransferFunction 'tf'. for example:

>>> a = TransferFunction([1], [1, 2, 3])
>>> b = TransferFunction([1], [2, 3, 4])
>>> c = a * b
>>> print c
Transfer Function:
.
.              1               
------------------------------
2s^4 + 7s^3 + 16s^2 + 17s + 12
.
>>> type(c)
<class 'controlsystems.types.TransferFunction'>

Simplify Transfer Functions

This method returns a TransferFunction object with the transfer function simplified. For example:

>>> a = TransferFunction([3], [3, 6, 9])
>>> print a
Transfer Function:
.
.      3      
-------------
3s^2 + 6s + 9
.
>>> b = a.simplify()
>>> print b
Transfer Function:
.
.     1      
------------
s^2 + 2s + 3
.
>>> type(b)
<class 'controlsystems.types.TransferFunction'>

Attention: This method is far from perfect, and don't simplify all possible expressions, but it's usable.

Operation of multiplication between numbers and transfer functions

This method returns a TransferFunction object with the result of the multiplication of the TransferFunction 'self' and the number 'a'. For example:

>>> a = TransferFunction([1], [1, 2, 3])
>>> b = a.mult(5)
>>> print b
Transfer Function:
.
.       5       
---------------
5s^2 + 10s + 15

>>> type(b)
<class 'controlsystems.types.TransferFunction'>

Operation of division of a transfer function per a number

This method returns a TransferFunction object with the result of the division of the coefficients of the TransferFunction 'self' and the number 'a'. For example:

>>> a = TransferFunction([3], [3, 6, 9])
>>> print a
Transfer Function:
.
.      3      
-------------
3s^2 + 6s + 9
.
>>> b = a.div(3)
>>> print b
Transfer Function:
.
.     1      
------------
s^2 + 2s + 3
.
>>> type(b)
<class 'controlsystems.types.TransferFunction'>

Feedback with unit gain

This method returns a TransferFunction object with the result of the unit gain feedback of the transfer function. For example:

>>> a = TransferFunction([1], [1, 2, 3])
>>> b = a.feedback_unit()
>>> print b
Transfer Function:
.
.         s^2 + 2s + 3        
-----------------------------
s^4 + 4s^3 + 11s^2 + 14s + 12
.
>>> type(b)
<class 'controlsystems.types.TransferFunction'>

Attention: This method is far from perfect, and don't simplify the expressions, but it's usable.