Page 225 - Servo Motors and Industrial Control Theory -

Appendix C 223

supply continuously. This makes the single phase motor rather expensive and
less reliable because a mechanical device must be used to disconnect the starter
once the motor starts running. In this book, only three phase motors are studied.
Consider a constant speed application where a 0.5 kW of wind power must be
delivered to a cooling system. The fan moment of inertia is 0.02 kg·m and the
2
selected motor has the following specifications,
Power rating = 1 kW
Rotor inertia = 0.0034 kg·m 2
Rated velocity = 1410 rpm
Maximum Torque = 16 N m

Predict the inductance and resistance of the motor from the data presented in
book written by the author. Calculate the time it takes the speed of the motor to
reach to the required speed. Assume that the rated torque is available right from
the time when the motor started. This time must not be too long because the mo-
tor at low speed is very inefficient and considerable heat will generate if the mo-
tor does not reach the required speed very quickly. Repeat the analysis assuming
that only 70 % of the maximum torque is available when the motor is started. For
real application, you should obtain all the required data from the manufacturer.
2. For a variable speed application, it is proposed to use an AC servo motor. The
motor is connected to the load by a gearbox with input output velocity ratio of
2
30. The load inertia is 2 kg·m . Calculate the moment of inertia of the load to the
motor. The motor has the following specifications,
Power rating = 3 kW
Rotor inertia = 0.0115 kg·m 2
Rated velocity = 1420 rpm
Maximum torque = 40 N m
Arm resistance = 22 Ω
Arm inductance = 0.05 H
You should note that the resistance and inductance of the motor are highly non-
linear and it changes with velocity. The above values are just a prediction and
for real application you should obtain these values from the manufacturer. Write
the voltage equation similar to DC servo motors. Determine the voltage constant
of the motor assuming that each phase of the motor a voltage of 220 V produces
the rated velocity. Note that in real situation to change the velocity both the volt-
age and frequency must be changed. For mathematical modeling it is sufficient
to assume that the voltage changes and the frequency variation implicitly is ac-
counted for. Also, assume that the torque is proportional to the current passing
through the motor. It is suggested that a proportional and integral controller must
be used in order to achieve zero steady state error. The block diagram shows the
principle of operation of the system. A velocity feedback must also be added to
increase the damping of the system. When the motor reaches the steady state an
external torque is applied. This must not exceed the maximum torque of the mo-
tor and it should be noted at very low velocity the maximum torque of the motor