Chapter VIII Results and Discussion
8.4 Results of the “basic tracker control functionality experiments”
8.4.1 Basic sun tracking experiment (A), on the 23/Jun/09.
Figure 97 shows the graphic results of sun tracking, where we compare the set point hour and declination angles with their actual values on the solar time axis.
Figure 97a - Plot of the basic sun tracking experiment 1
Figure 97b - Plot of the basic sun tracking experiment 1 (with further legends) -35
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845.0 850.0 855.0 860.0 865.0 870.0 875.0 880.0 885.0
StPtHourAngle StPtDeclAngle ActualDeclAng ActualHourAng
-35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45
845.0 850.0 855.0 860.0 865.0 870.0 875.0 880.0 885.0
StPtHourAngle StPtDeclAngle ActualDeclAng ActualHourAng
E C G
A
H
M F
N L
K
O J
D
B
I
Solar time (min)
Angle (degrees of arc)
Solar time (min)
Angle (degrees of arc)
For clarity, in the Figure 97b, we add more legends to help discussing the plots and finding the results. In the figures, the various traces are as follows:
(a)ActualDeclAng represents the actual declination angle (green graph).
(b)ActualHourAng represents the actual hour angle (violet graph);
(c)StPtDeclAngle represents the set point declination angle (red graph); and (d)StPtHourAngle represents the set point hour angle (blue graph);
Observing the figure(s) we find the following:
1) The tracking process begins at 850 min (points A, B, C, D) of the solar time axis (which equates to about 14h10 of solar time) and stops at about 878 min (≈14h39). From 850min to 873min (points H, I, J, K) a normal/automatic tracking mode was taking place and from point H (873 min) to the end, a parking process has taken place, as a result of a sudden supervisory command to park immediately and unconditionally (= send the dish assembly to its resting position). These observations apply to all curves;
2) The set point hour angle (blue curve), from points D to H, is a straight line with a slope of about 0.250/min. This is because the set point hour angle is a linear function of solar time (see eq. 2.1.1.11), whilst from points J to N, the set point hour angle is a straight line parallel (also collinear) to the time axis.
This is because the dish’s resting position set point hour angle is fixed (and equal to zero);
3) In turn, the set point declination angle (curve in red) is a straight line parallel to the time axis, at the value of about 23.50. This was the declination angle for 23th June. The value of declination angle does not change in a single day, which is the reason for the parallelism with the time axis. From point K afterwards, the value of set point declination angle remains at -300 which is the set point declination angle for the dish’s resting position;
4) The tracking motion begins from the declination axis. The value of the actual declination angle (green curve) was about -210 at the beginning (point A, 850min). The dish moves northwards at full angular speed until it reaches the set point (on point F, about minute 851 of time axis). From point F to I the actual declination angle remains roughly overlapped with its set point, until this changes to the value of dish resting position from points I/K onwards;
5) From the experimental data we found that the value of the declination axis angular speed between points A and F is 0.940/S (about 56.50/min). This is approximately the maximum mean angular speed developed by the declination axis under normal load conditions (neglecting the variation of tracker assembly load due to the displacement of its centre of gravity during the motion);
6) At minute 851, once the declination angle matched the set point, the tracking process passes to the hour axis. The value of the actual hour angle (violet curve) was about 00 from the beginning (from point B to E). From point E onwards, the dish moves westwards at full speed, until it reaches the set point (on point G, about minute 854 of time axis);
7) From the experimental data, we found that the value of the hour axis angular speed between points E and G is 0.170/S (about 100/min). This is approximately the maximum mean angular speed developed by the hour axis under normal load conditions (neglecting the variation of tracker assembly load due to the displacement of its centre of gravity during the motion);
8) From point G to H we observe a stair case evolution of the actual hour angle (violet curve), following the slope of the set point hour angle. The stair case is due to the step tracking strategy embodied into the FSM controller as discussed in earlier sections;
9) As mentioned above, on points H and J (curve in blue)as well as I and K (curve in red), the set points are changed to their resting position values (00 for the hour angle and -300 for the declination);
10)From point H to L, the hour axis is rotated eastwards (curve in violet) until the resting set point (00) is reached. At this time, from point M to O, the declination axis is rotated southwards (curve in green), until the declination angle matches the resting set point (-300).
All the above observations fit the expected behaviour of the sun tracking process, under the control performed by the ST-RTOP program, particularly the FSM tracker controller software component.
There are some aspects however that deserve remarking:
(a)The plot lines where the tracking assembly is rotating freely, towards a given set point, e.g. segments AF (green), EG (violet), HL (violet), MO (green), etc., show that the rotating motion is not smooth. This lack of smoothness is more noticeable on the hour axis (violet curve). As discussed in section 4.3.1.5.3(b), this may have to do with the variation and non-linearity of the mechanical load, caused mainly by:
(i) mechanical imperfections (lack of cleanliness, unevenness and severe rusting) of the motion transmission system, as well as;
(ii) sudden and unpredictable changes of the environment conditions (like the wind) and also;
(iii)The displacement and variation of the concentrator’s centre of gravity with respect to the supporting structure;
(iv)The limited resolution of the MCU’s internal ADC (10 bits) for reading the AVC potentiometers (with a scale of 2900 of arc). In this case, the 10 bits
ADC can only yield a mere 0.280/LSB as opposed to the required minimum resolution of 0.250. Also, the limited accuracy of the AVC potentiometers may be contributing to this issue.
It is worth noting that the problems mentioned in (i) several times caused the tracking assembly to get stuck and needed human intervention for releasing it and restarting the automatic tracking;
(b)Although respecting the step tracking strategy, the value of the actual hour angle (violet) in the interval GH is always below the set point. That results in a non null mean error. This equates to: “the dish is almost all the time slightly defocused”. The desired behaviour would be: “the dish is almost all the time focused (and only defocused in short whiles)”. This unwanted behaviour can be well observed on the plots of Figure 98 as well.
(c)To address the shortcoming discussed in (b) we have taken measures in time, to improve the tracking behaviour accordingly. Such improvements can be observed in the plots of Figure 99 and Figure 100.
8.4.2 Basic sun tracking experiment (B), on the 24/Jun/09.
In Figure 98, the curves represent a section of the sun tracking experiment carried out on the 24th June. The various traces are as follows:
(a)ActualDeclAng represents the actual declination angle (green curve).
(b)ActualHourAng represents the actual hour angle (violet curve);
(c)StPtDeclAngle represents the set point declination angle (red curve); and (d)StPtHourAngle represents the set point hour angle (blue curve);
Figure 98 - Plots showing a section of the basic tracking experiment of 24/Jun/09
As mentioned in previous section, the staircase (actual hour angle, violet trace) in
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700 710 720 730 740 750 760 770 780 790 800
StPtHourAngle StPtDeclAngle ActualDeclAng ActualHourAng
Solar time (min)
Angle (degrees of arc)
the plot of Figure 98, is always below the set point. We now present (in Figure 99) a section of the results of the 25th June experiment and compare their characteristics. The various traces are named and coloured as in Figure 98.
In the Figure 99 above, we can see that, the actual hour angle staircase plot walks around (above and below) the set point straight line, which now yields a mean error that, is closer to zero (see table 8.1). In fact the calculated errors for the plot in Figure 99 show evident improvement as compared to those of Figure 98. The maximum error should be neglected because it may be a result of a sporadic disturbance, not a persistent error.
Date of experiment / Variable Maximum Error Mean Error RSM Error
24th June (Figure 98) Hour angle 2.75 1.22 1.32
25th June (Figure 99) Hour angle 3.73 0.23 0.97
Table 8.1 – Actual hour angle errors relative to its set point in normal tracking (automatic mode tracking, parking mode excluded).
On the other hand, in Figure 99, we see that although the tracking step was set to 0.50 and the accuracy to 0.250, in some sections of the hour angle plot noticeable deviations or lack of uniformity can be observed. These have to do with the shortcomings discussed in section 8.4.1 (a) above, which can be overcome by improving the system (plant) condition and/or the control strategy to the ones suggested in chapter IV.
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640 660 680 700 720 740 760 780 800 820 840
StPtHourAngle StPtDeclAngle ActualDeclAng ActualHourAng
Figure 99 - Plots showing a section of the integrated sun tracking experiment, on the 25/Jun/09.
Solar time (min)
Angle (degrees of arc)
8.5 Results of the integrated tracker control with temperature logging