ELEC 242 Lab
Background
The System
The figure below is a schematic of the position control system.
As a simplification we have omitted the gearbox and absorbed its
effect into the values of
and
.
We have also absorbed the reflected moment of intrtia of the gears
and motor armature into J'
.
This translates into the following block diagram
Ignore for now the effects of the mass m
(i.e. assume there are no weights on the hook and
that the weight of the cord and the hook are negligable).
Then the motor, gearbox, and drum can be modeled by the
first order transfer function
.
Integrating the angular velocity
to give the shaft angle
corresponds to the transfer function
.
Finally the mapping of the shaft angle into the potentiometer
output voltage
is given by
.
Putting it all together, we have the following block diagram for
the closed loop control system:
One thing we have not modeled is the solid friction between the
various mechanical components of the system.
Unlike viscous friction which is proportional to velocity,
solid friction is a threshold force which must be exerted before
any motion can be initiated.
This produces a dead zone in the relation between applied force
and resulting acceleration similar to that in the complimentary
emitter follower.
We have seen this effect before in the speed vs. voltage curve of
the motor.
It will be particularly pronounced in this system because of the
additional friction introduced by the gear train and the potentiometer
and will make it difficult to control the position manually.
As in the case of the motor amplifier where we reduced the
crossover distortion by placing the emitter follower inside the
feedback loop, feedback will reduce this effect in the closed loop
system.
Sensing Angle
Previously we have used another motor as a tachogenerator to
measure speed.
We will be using a type of variable resistor known as a
potentiometer
to measure the angle of the gearbox output.
A
potentiometer
(or
pot
for short)
is a fixed value resistor with a third, movable contact
or
slider
which may be positioned anywhere along the
resistive element.
If we represent the position of the slider by
, where
varies between 0 (fully counterclockwise)
and 1 (fully clockwise), then the resistance between the lower
end of the resistor and the slider will be
and between
the slider and the upper end will be
,
where R
is the total resistance of the potentiometer.
If we connect the two fixed contacts to a voltage source and measure
the output between the movable contact and one fixed contact,
we get a variable voltage divider:
Then the output is
The potentiometer we are using is a
10-turn
pot, which means that ten turns
(
)
of the shaft are required to go from
to
.
We will be using -5 V for
, so