Page 36 - Servo Motors and Industrial Control Theory -

28 2 Feedback Control Theory Continued

Fig. 2.7 The exact root 30
locus of the system for dif-
ferent gain K
18

Y1 6
Y2
30 18 6 6 18 30
Y3 6

18

30
X1, X2, X3,

be seen that the root locus sketched manually is similar to each other. The value of
roots at gain k = 500 are given below.

=
K : 500
 520 + 50· K
 204 + K 
F:  
=
 25 
  1  

G : polyroots (F)=

 − 29.947 
+
G =  2.474 29.087i 
 
−
 2.474 29.087i
The locus is shown in Fig. 2.7.
The root locus is plotted by calculating the roots at different values of gain. For
each gain the roots were put in an array and then the results were plotted on the
graph. Each root is shown by a cross. Because of many gains the roots were put in
three arrays and then plotted. It can be seen that the two root locus are similar. In
fact there is no need to plot the root locus because trying few gains it is possible to
find the correct roots location to have fast response with sufficient damping in the
system. It is also possible to add zeros and poles to improve the system response.