Page 114 - Servo Motors and Industrial Control Theory -

108 6 AC Servo Motors

Where s is the Laplace operator, and the resistance and inductance are highly non-
linear. At different supply voltage and frequency both resistance and inductance
change. At small variation from the operating point the resistance and inductance
can be assumed to be constant. The remaining governing differential equation for
the rotor and load can be written similar to the equations derived for DC servo mo-
tors. Various operating conditions must be considered in order to study the stability
and accuracy for velocity and position control applications.
The second method is to write the voltage equation similar to DC motors, as

V : RI LsI C · = + + m ω m (6.7)

In Eq. (6.7) C is the voltage constant and accounts for the fact that as the speed
m
of the motor increases the current reduces. In this case the average resistance and
capacitance may be considered.
It should be stressed that the voltage equation is only an approximation and various
values of the constants may be used to study the stability and accuracy of the complete
servo system. AC motors for position and speed control applications is the subject of
intensive research. The reader must keep an eye on the new development in this field.

6.4 Frequency Converter

As it was discussed earlier, in order to achieve a variable speed AC motors both the fre-
quency and the amplitude of the supplied voltage must be changed. The purpose of this
section is not to give detailed circuit diagrams but to briefly explain the basic methods.
The idea of using a variable frequency supply to control the speed of AC motors
is not new and rotating frequency converters have been employed for many years.
These are used principally in multi-motor mill drives and in special applications
where a high operating frequency is chosen in order to permit the use of compact
AC motors. Nowadays the rotating machine variable frequency AC power genera-
tions are being largely supplanted by static conversion methods.
The performance and reliability of variable speed AC systems is improved if the
rotating frequency converter is replaced by static methods of variable frequency
power generation. The renewed interest in static frequency conversion is due to
the improved characteristics of the thyristor and transistors as compared with other
switching devices. The thyristor is a more efficient switching since the voltage drop
in the on condition is only about one volt.
In steady state the motor frequency (rad/sec) for most frequency inverter is pro-
portional to the error voltage. Although the frequency of motor changes when the
error signal is received, there is dynamical behavior that should be considered. In
most frequency converter, the relation between the motor speed and apply voltage
and input error signal may be shown to be the same as the case discussed for DC
motors. An equation similar to Eqs. (6.6) and (6.7).