8.4.1 Step Response after Implementation of Controller
The step response of the system was tested after the controller was implemented to verify the controller design. The PC oscilloscope (Cleverscope) was used once again to obtain the data.
The probe was attached to the shaft potentiometer on one of the servos, and the step was initialised as had been done to acquire the initial data.
Figure 71 Step response after implementation of digital controller
Although the oscilloscope picks up noise on the probe, it is clear that the controller has reduced the response of the system to an approximate first order curve. The noise is due mainly to the potentiometer as its wiper moves across the windings.
8.4.2 Mechanical (Positioning)
Accuracy is the degree of conformity of a measured or calculated quantity to its actual or true value. Accuracy is closely related to precision, the degree to which further measurements or calculations will show the same or similar results. Accuracy is defined as the maximum deviation from the theoretical, calculated or intended value, whereas precision is the maximum deviation from the mean value. The accuracy also gives an indication of repeatability which is the extent to which a similar result is attained. Due to the unavailability of a 3D metrology system, a method was devised to estimate the accuracy of the PKM. This method, although rudimentary, does provide some indication of the errors in positioning.
Method
To get the accuracy or repeatability of the positioning systems, the electronic screens were removed and replaced with cardboard backings sporting a printout of the screens. These indicated exactly the positions of the sensors and facilitated tracking of the laser from above as well as the marking of positions and measuring of distances. The position offset was taken to be the distance from the centre of the laser point to the centre of the OP521 footprint. 15 Readings were taken for each of 3 coordinate sets (different X, Y and Z coordinates). Taking more measurements wouldn't offer much value based on the accuracy of the method. The measurements are made to the nearest mm. The coordinate sets chosen were (0, 0, — 20);
( - 7 , - 7 , - 1 8 ) and (5, - 5 , - 1 6 ) . The tables of results are located in Appendix D. The results are shown graphically in Figure 72 (a, b and c).
Figure 72 Positional accuracy results a. Error in X Coordinates
b. Error in Y Coordinates c. Error in Z Coordinates
3 _ Error irt X coordinates
b.
Error in Y coordinates3 2
— 1
E
£ o
> •
a -1
• Q „
1 | 2 j 3
'
[ 4>
5 l1 '
[m
lm
]' f \
1 0\
1 1/
1 2/
13 i 14 / l 5A- y3
Attempt
c.
Error in Z coordinatesE E
•—<
N
* -1 Q
-2 -3
: $
/ i
13...
H i - A.J ( $
^.
6
A.
8 9 W^ 1 1 / 12\
M \-wk&t"
...13./..1.4.. 15
Attempt
The axial accuracy of the positioning is 2 mm, 3 mm and 3 mm for the X, Y and Z axes. This is the maximum measured deviation along the axis. The spatial accuracy is about 4 mm, this is the magnitude of the vector from the intended position to the actual position (occurs at data set 14, for coordinate set 3). The axial mean of the absolute values of the errors are 1.3 mm, 1.3 mm and 1.5 mm (X, Y and Z respectively). The spatial mean is therefore 2.4 mm. From the definition the precision (beginning of this section) is 1.6 mm (4 - 2.4). These values were obtained from mathematical functions. As the smallest measurement discemable has mm resolution these values are applied to a ceiling function yielding 2mm for each of the axial mean errors, 3 mm for the spatial mean and 2 mm for the precision.
The major factors involved in the positioning inaccuracy are due to hysteresis as well as backlash in the servo gearing system, and the ball socket joints.
Hysteresis is the difference in reading or positioning when the physical quantity being investigated is approached from different directions. It is due to mechanical friction, elastic deformation and thermal effects. It is a property of systems (usually physical systems) that do not instantly follow the forces applied to them, but react slowly, or do not return completely to their original state.
Backlash is the play or loose motion in an instrument due to the clearance existing between mechanically contacting parts. In gearing systems, it is the clearance between two gears, the amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the pitch circles. It also occurs in lead screws, and is the amount of free movement between a screw and nut. Backlash cannot be eliminated completely as it is required to allow for lubrication, manufacturing errors, deflection under load and differential expansion between the gears and the housing.
Other errors due to inaccurate machining of parts and their placement also factor into the problem, but they are not nearly as significant as those from hysteresis and backlash.
Most manufacturers of geared motors do provide some indication of these errors in their datasheets. The hysteresis and backlash due to the ball and socket joints which were actually modified from ball in socket bearings are not quantifiable. In general this problem exists for all delta type mechanisms that use ball in socket joints. The problem can be alleviated with the use of compliant joints which was mentioned in section 2.2. Compliant joints are difficult to manufacture and are expensive. It was not possible to make them on this scale.
8.4.3 Electronic (Sensing) Repeatability
The repeatability measurement for the detector screen was done within the positioning capabilities of the rig. The PKM was commanded to sensor coordinate positions at Z displacements of 14 cm, 17 cm and 20 cm, and 25 attempts were made for each of 16 sensors.
The repeatability for each distance is taken as the average of all the readings in the group measurement, and expressed as a percentage of the 25 attempts. They are 99.25%, 98.75%
and 98% respectively. The repeatability decreases mainly due to the fact that the further away the laser, the more difficult it is to stabilize and hold a position. A stiffer machine with vibration damping should have no such problem.
Sensor System Repeatability 25.5
At 14 cm At 17 cm
—4—At 20 cm
-i 1 1 1 1 1 1 1 1 1 1-
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Sensor Number
Figure 73 Electronic sensor system repeatability