Figure 18.101 : System with negative feedback
an output of H(s)Y(s).
Thus the feedback signal is
H(s)Y(s). The error is the
difference between the system input signal X(s) and
the feedback signal and is thus:


X s ( ) 
� 
H s Y s ( ) ( ) 
and so:
For a system with positive feedback ( Figure 18.102 ), the feedback
signal is H(s)Y(s) and thus the
input to the G(s) system is X(s)
�H(s)Y(s). Hence:


X s ( ) 
� 
H s Y s ( ) ( ) 
Input 
�

Error



G(s) 
X(s) 
Y(s) 
� 
Feedback 

4
Example 18.18
Determine the overall transfer function for a control system ( Figure
18.103 ) which has a negative feedback loop with a transfer function 4
and a forward path transfer function of 2 / ( s�
2).
Solution
The overall transfer function of the system is: