Page 89 - Servo Motors and Industrial Control Theory -

82 4 Electrical DC Servo Motors

In this section, the matching of the coefficients of desired and actual character-
istic is used to calculate the gains. There are other methods, which are beyond the
scope of this book. For servo motors applications, the author finds that the above
method is very useful. The method can also be used for simpler applications.
After calculating the gains, it is useful to investigate the steady state values of the
state variables to study the accuracy of the closed loop system. The calculations for
unit step input of θ and external torque of zero is as follows:
i
0
0
B1:= 0 (4.32)
0
K
L

 −  (Α. C) 1 − ⋅ B1

0.185
0 (4.33)
x = 1.852
0
0

The above analysis shows that the two output positions move to a position different
from the required unit one. This is no problem as input can be calibrated in terms of
output position. It is also noted that the motor rotates ten times the output position.
This was expected. The current also becomes zero at steady state since the motor
has moved to the correct position, there is no need for current.
It is also important to study the effect of external torque by using the principle of
superposition. For this the input is set to zero and for unit input of external torque
the method of calculation is as in Eqs. (4.32) and (4.33). First, the input vector of
the external torque is calculated.
The same procedure for calculation of unit step input is used. The results become

0
− (.
12 82)
B2 := 0 (4.34)
0
0