Page 219 - Servo Motors and Industrial Control Theory

Appendix C 217

differences. Note that this time there are four gains to be optimized. Similar to
the previous case, plot the eigenvalues of the system matrix and observe the
movement of the eigenvalues as gains are changed.
8. This problem shows the principle procedures for selecting a DC servo motor for
a particular application. The problem may not be with data for a realistic applica-
tion but it shows the principle calculations that must be carried out for a real case.
The figure below shows a case where the wing of an aircraft must be controlled
with high position accuracy. In order to control the angle of the aircraft wing
the motor must be located vertically as shown below. A lead screw connects
the motor to the wing with a gearbox with input output velocity ratio of 20. The
weight of the wing can be superimposed on the wind force.

Pivots

Lead screw
Gearbox

Motor

The motor must be free to rotate slightly as the angle of the wing changes. The
nut of lead screw is connected to the wing and it is free to slide in order to be
able to control the angular position of the wing. This system is just an imaginary
case and may not be a practical case. The mechanical part of the system has the
following properties,
Length of lead screw = 0.7 m
Pitch of lead screw = 2.5 mm/rev
Gearbox speed ratio = 20
The weight and wind force applied to the wing = 5000 N
The mass of moving parts = 200 kg
First assume that the transmission mechanism is rigid, the torque and load inertia
referred to the motor. From the list of DC servo motors given below select one
noting that the motor must at least overcome the external torque and the load
inertia must not be much greater than the rotor inertia. The motor must also pro-
vide additional torque to accelerate the wing. The angular movement of the wing
might be from zero to maximum of ± 180°. It is not required to move the wing
very fast but also it must not be too slow. From this reasoning you should have
some ideas about the maximum speed of the motor.
Usually when you buy a DC servo motor the power unit which matches the mo-
tor is also given by manufacturer. The motor may also be brushless to maximize