Page 212 - Servo Motors and Industrial Control Theory -

210 Appendix C

Find the steady state error for both the demand input and step input of external
torque of 50 N m. Of course they should be zero because of the integrator in the
system. From the optimized gains find the dynamic position drop when the ex-
ternal torque is suddenly applied. You should solve the state space model using
numerical integration technique.
4. Many servo motors are used in machine tools and CNC applications where it is
required to control various axes of the machine. One particular case is when the
position of the table must be controlled in three axes of X, Y, and Z directions.
The figure below shows the application of one servo motor in X direction. The
position of the table is usually measured by a variable linear potentiometer and
the signal is fed back to the controller for proper control. Alternatively a posi-
tion encoder may be attached to the motor to get a position signal for control.
This can only be used if the transmission mechanism is very stiff. Otherwise the
position must be measured directly from the table. To convert the rotary motion
a lead screw with properly chosen pitch is used. The lead screw must be backlash
free otherwise it poses difficulty in accurate position control.

X 0
Table
X i
Controller Power Motor
Unit
Lead Screw

1+K d s

Position and velocity
feedback

The lead screw has the following specifications;
Maximum length = 1 m
Diameter = 2 cm
Material = mild steel
Pitch = 1.5 mm/rev
Determine the stiffness of the lead screw and for this refer to a book in a subject
area of solid mechanics or strength of material. Calculate the input output speed
ratio of the lead screw. Remember that in all calculations you should use proper
units for parameters. Define parameters and variables and if any parameter is not
given below assume an engineering value for them.
Assume that the power unit is made of transistors controlled DC converter or a
PWM system with negligible time delay. Assume that the gain of the power unit
is ten which means that a low control voltage of ten volts gives a high voltage
of large current of a hundred volts. It should be noted that in the power unit a