Page 108 - Servo Motors and Industrial Control Theory -

102 6 AC Servo Motors

a versatile and robust variable speed machine which has an advantage over con-
ventional variable speed drives, of better reliability and reduced maintenance. The
main objection to the static AC drive has been on economic grounds and its lower
starting torque compared with DC servo motors. However, power semi-conductor
prices are steadily decreasing as production volume grows and manufacturing tech-
niques improve. In a static frequency converter, the power supply is first rectified
using diodes and then thyristors or transistors are used to convert the DC voltage to
a variable frequency output which is then connected to the motor. The most appro-
priate method of changing the speed of AC motors is to change the frequency of the
power supply. At low frequency, the amplitude of the voltage must also be reduced;
otherwise, large current will flow in the stator windings which is not desirable.
The speed of rotation of the motor is given by
f
: 2· ·ω= π (6.1)
f
p
where

ω is the synchronous rotating speed (rad/sec)
f
f is the supplied frequency (Hz)
p is the number of stator pole-pairs. The minimum value is one which gives a speed
of 3000 rpm.

6.3 Mathematical Model

For constant speed control applications, the supply voltage and frequency are both
constants. When the motor is at rest, the synchronous rotating field induces e.m.f.s
at supply frequency in the stationary rotor. The rotor conductors are short circuited
at each end and if the circuit is purely resistive, the current and e.m.f. distributions
are identical. The torque contribution of each rotor conductor is proportional to the
product of the conductor current and the local flux density. This is the optimum
condition for the production of electromagnetic torque. If the rotor circuit is purely
inductive, the resultant torque is zero. In practice, the rotor power factor is always
greater than zero, and hence a motor torque is developed which causes the machine
to run-up from the standstill in the same direction as the air-gap field.
At the synchronous speed, the torque becomes zero. Because of the mechanical
and windage friction, the rotor always rotates at a speed smaller than the synchro-
nous speed. If the motor is running at a speed n less than the synchronous speed n ,
1
the difference, n − n, is called the slip speed of the machine and usually expressed
1
as a fraction of the synchronous speed to give the fractional slip s ℓ as
(n − n)
s := 1 (6.2)
1
n
1