Page 218 - Servo Motors and Industrial Control Theory -

216 Appendix C

Diameter of the lead screw = 2 cm
Pitch of lead screw = 2 mm/rve
Material of lead screw = mild steel
The properties of the motor selected for this application are,
Power rating = 1 kW
Rotor inertia = 0.0093 kg·m 2
Rated velocity = 1260 rpm
Maximum torque limit = 113 N m
Arm resistance = 0.58 Ω
Arm inductance = 0.0023 H
Motor voltage constant = 0.83
Motor torque constant = 0.83
You should note that for 100 % efficiency the torque and velocity constants are
the same. Transform the governing differential equations to state space form.
Note that for this you do not need to find the transfer function of the system but
remember that there are two input variables of demand position and external
torque applied to the table.
To study the stability of the system assume maximum gain for the power unit
and adjust the gain of proportional and integral and derivative gains so there is
at least a damping ratio of 0.7 in the fundamental eigenvalues. You should note
that eigenvalues that are not dominant must be stable even though the damping
ratio is low. The response characteristic of higher mode will disappear quickly
from the response.
Repeat the analysis for low value of the gain of power unit and investigate the
effect on the stability. In theory at low gain the response should become over-
damped and slow response characteristics. Solve the state equation with the
numerical integration technique and find the maximum dynamic position drop
when a force of 1000 N is applied to the table.
In the above block diagram the position and velocity were directly fed back to
the position controller. In some applications it might be better to separate the
position controller with that of velocity controller. This is shown diagrammati-
cally below,

To power unit
+ K i +
– K p + s – K 2
Velocity feedback
K d s

Position feedback

The power unit, motor and load mechanism remains as previously shown in
the diagram. Repeat the analysis with this new configuration and discuss the