Modelling and design of a two axis small scale solar tracking system for an ecological small scale house model

Abstract

Nowadays power generation is one of the greatest challenges of humanity in the framework of Sustainable Development. For example, as it is globally accepted sun tracking systems allows improvement of solar panel power ratio. In order to illustrate this concept, this paper presents the design and a behaviour modelling of a two axis small scale system for future didactical applications. The principle of tracking is described. Mathematical description is done and a mixed SPICE modelling of the system, including geometrical, optical, electronic linear and non-linear aspects is built. Simulations results are analysed. Practical mechanical and electronic designs are detailed, before conclusion. This small scale solar tracking system is now installed in a eco-friendly small scale house model.

Full text

MATEC Web of Conferences 210, 02001 (2018) https://doi.org/10.1051/matecconf/201821002001
CSCC 2018
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution
License 4.0 (http://creativecommons.org/licenses/by/4.0/).
* Corresponding author: philippe.dondon@enseirb-matmeca.fr
Modelling and design of a two axis small scale solar tracking
system for an ecological small scale house model
Philippe Dondon1,*,Pascal Gauterie2,Renaud Charlet3,
1ENSEIRB MATMECA – Bordeaux INP, Domaine Universitaire 33405 TALENCE, France
2 Lycée Alfred Kastler, 14 av. de l'Université 33402 Talence, France
3IMS, UMR 5218, EPHE, 351 cours de la Libération 33405 Talence Cedex
Abstract. Nowadays power generation is one of the greatest challenges of humanity in the framework of
Sustainable Development. For example, as it is globally accepted sun tracking systems allows improvement
of solar panel power ratio. In order to illustrate this concept, this paper presents the design and a behaviour
modelling of a two axis small scale system for future didactical applications. The principle of tracking is
described. Mathematical description is done and a mixed SPICE modelling of the system, including
geometrical, optical, electronic linear and non-linear aspects is built. Simulations results are analysed.
Practical mechanical and electronic designs are detailed, before conclusion. This small scale solar tracking
system is now installed in a eco-friendly small scale house model.
1 Introduction
1.1 Small scale house project
Three years were necessary to design a functional
realistic eco-friendly small scale house, built in genuine
materials. It was completed successfully within the
framework of an innovative sustainable development
project. The building (with real materials) of small scale
house itself is finished [1]. The model is now used as:
-Demonstrator (sustainable development
exhibition in town halls or local sustainable
development events)
-Didactical support for practical lessons and
electronic projects, for sensitizing engineering
students to power saving and low power
electronic design in first and 2nd year study.
To make the house model more realistic, didactical and
functional, various accessories and their electronic
control circuits were designed, for example:
- Low power LED lighting for the terrace and house
supplied by a roof solar panel and battery cells.
- Hydrogen fuel stack to power “air conditioned” system
(i.e. scaled Canadian well under the house),
- A solar dish with temperature measurement,
- A solar tower and its performance measurement
system,
- An electrical heater circuit for the house and its
temperature control
- Solar tracking system for small solar panel (9cm x
5cm) …
Figure 1 shows a picture of the finished modular scale
model (1/20 scale, i.e. house is 50cm x 50cm, garden
100cm x120cm).
Fig. 1. View of small scale house and surroundings.
The present paper focuses on the modelling and design
of the small scale 2 axis solar tracking system installed
in the “house garden”. This new system is an improved
version of a first previous design which was working
only on one axis tracking [2].
1.2 Solar tracking interest
Professional and industrial true systems are generally
based on processor board; the position of the sun is
generally tabulated (from astronomical data), all over the
year. Position of the solar panel follows the programmed
law on two axes, taking into account the sun ray optical
diffraction or refraction into atmosphere. From
experiments and available data [3, 4], a real solar
tracking system can improve the electricity production of

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MATEC Web of Conferences 210, 02001 (2018) https://doi.org/10.1051/matecconf/201821002001
CSCC 2018
a solar panel up to 23 % for a single axis tracker and
27 % for a double axis tracker.
2Solar tracking circuit
2.1. Generalities
The designed circuit, mostly based on analogue
electronic components, is obviously a simplified version
compared to a true tracking system [4, 5]. However, it is
a complex looped system which requires a full modelling
to predict behaviour, accuracy and stability, before
electronic design.
2.2 Tracking system principles and schematic
As the “eco-friendly house” is used for in-door
demonstration, a halogen spot light will “replace” the
sun light.
The design is based on a simple system with two rotation
axis control. Figure 2 shows the sun tracking block
diagram.
electronic
circuit
servomotor
firstaxis
PID
corrector
Vdiff
Vcc
Vcc
Vpwm
DCvoltage
toPWM
converter

Vin1
Vin2
spotlight
Vc
solar
panel
Vin3
Vin4
LDR1
LDR2
LDR3
LDR4

DCvoltage
toPWM
converter
PID
corrector
servo
motor 2ndaxis
Fig. 2. Sun tracking system block diagram
The same principle is used on the two axis (elevation
and azimuth ) for the feedback control loop; this
explanation is given only for the azimuth control.
It works as follows: two light sensors LDR1 and LDR2
(LDR: Light Dependant Resistors), located on left and
right side of the panel receive the “sun” light.
When the solar panel is well align in “sun” direction, the
received left and right lights flux L1 and L2 are equal.
When it is not, one of the two LDR receives more flux
than the other, and feedback loop moves the servo motor
into the right direction to cancel the voltage difference
Vdiff “left minus right” signals (Cf. figure 3). Vdiff being a
DC voltage, a DC to PWM converter is lastly required:
indeed, the servomotor is a classical hobbyist servo. The
rotation angle of such servomotor is proportional to a
control signal pulse width Vpwm (1ms to 2ms for a 180°
range) according to hobbyist standards.
receiverlobe
receiverlobe
emissionlobe
leftphotoresistor
rightphotoresistor
solarpanel spotlight
(sunsimulation)
L2
L1
LDR1
LDR2
l
o
Fig. 3. Solar panel alignment
2.3 Modelling interest
The principle explained in §2.2 is well known by
electronic designers. Similar applications using infrared
diodes or ultrasonic sensors instead of LDR are
described in [6-9]. Thus, an “intuitive” electronic design
can be directly done without a preliminary high level
theoretical approach.
However, for a fine understanding of parameters impact
(i.e. spotlight distance, matching and non-linearity of
LDR sensors, mechanical behaviour of servomotor etc.),
a global modelling is required as described in § 3.
3 Tracking system modelling
3.1 One axis feedback loop modelling
One could note that modelling is not easy because the
whole system consists of several heterogeneous parts.
That requires a global approach.
Among several possibilities, (analytic calculus,
MATLAB software, SPICE simulator…) we propose
hereafter, the building of a mixed SPICE modelling
adapted to our electronic initial culture.
It must take into account the electronic behaviour
(Electronic circuits, non-linear sensors (LDR1 and
LDR2), the mechanical behaviour (servomotor), and also
the optical and geometrical aspects, due to the rotation of
the spot light (simulating the sun).
Preliminary step is to establish a block diagram
representing the global feedback system.
In order to simplify the approach, the range of rotation
angle -i.e. 180° for a classical servomotor- is supposed
covering a sweep from East to West.
Figure 4 shows the identified blocks of the whole system
and figure 5 gives the corresponding geometrical angles
for one rotation axis  (azimuth).
- L1, L2 represents the received light (in Lux) on each
LDR,
-ref is the main input and represents the sun azimuth
position (0° to 180°),
- the angle given by the servo motor,
-e the error angle,
- Source light intensity input (I) can be seen as a
parasitic input in the loop which represents fluctuation of
source intensity (fog, sky partially cloudy, etc),
-0 is the angle defined as 0 = arctg(l/2D), where l is
the distance between sensors and D the distance to
spotlight as shown on figure 3,

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- Local disturbances input (D) represent disturbances
that can occur individually, on each LDR optical way.
(LDR partially hidden by an object passing over, etc).
servomotor
transfer
function
V
in1
motor
angle
control
voltage (V)
returned
voltage (V)
received
luminous light
(lux)

V
c
L
1
L
2
V
in2

ref
: reference angle
(spotlight position)
electronic
circuit
transfer
function
+
-

e
error angle
corrector
PID
LDR sensors
transfer function
V
out
DC/PWM
conv.
I: source light
intensity
optical /geometrical
transfer function
D: local
disturbances
V
pwm
PWM
control
signal
Fig. 4. System identification
LDR2
spot light
(sun simulation)
South
East
West

e

ref
(azimuth)
servomotor
(body)
L
2
L
1
LDR1
L
o
D
l
Fig. 5. 2D reference angles (top view)
Feedback loop for the second rotation axis is similar.
And the two axis movements are obviously coupled to
track the spot light. Thus, coupling equation between
elevation and Azimuth must be known (cf. §3.2).
3.2 Sun position modelling
Fig. 6. 3 D azimuth and elevation diagram
In figure 6, it is depicted a 3 D representation of two
angles and 
From the web site “sunearthtools.com” [10] and Google
maps, one can obtain the sun position everywhere on
planet in real time. For example, figure 7 gives the
situation for Bordeaux Talence University, the 21 of
June 2017 (summer solstice).
Fig. 7. Sun path over Bordeaux city (hours and direction).
Figure 8 shows the corresponding sun elevation angle
vs. azimuth angle Lower curve corresponds
to winter solstice, and upper curve to summer solstice.
Fig. 8. Sun elevation vs. azimuth (in °) in Bordeaux
Horizontal scale: azimuth 0° to 360° (south <=>180°)
Vertical scale: elevation -90° to +90°
From figure 8, we can extract a mathematical 2nd degree
function (figure 9) to approximate theses curves on the
interesting segment (i.e. during the day, East to West).
Fig. 9. Elevation modelling in Bordeaux (in rd)
y = -0,4118x2
+ 1,2937x - 0,614
y = -0,2289x2
+ 0,7192x + 0,6521
-1
0
1
1,5
0 0.5 1 2 2.5 3 3.,5
winter
summe
r
4
Elevation (in rd)
South Azimuth (in rd)
Eas
t
1.5
winte
r
summe
r
day
night SWestEast
Wes
t
0,5
-0,5



West
East
Atlantic France
Spain
Bordeaux
0°

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Between these two curves, we can extrapolate an
average annual behaviour.
We can write:
# -0.32+0.945+0.1 (angles in rd) (1)
3.3 Electronic modelling
The main parts of electronics feedback loop circuits
(LDR sensors nonlinear transfer function, analogue
subtraction circuit…) have been previously modelled.
Details can be found in [2].
3.4 Optical/ Geometrical modelling
The mathematical function “received light L1 and L2 (in
lux) on each LDR sensors versus incidence angle of the
spotlight” is also required. Fluxes vary roughly as the
cosines of incidence angle. They depend on the spot light
distance and also on the distance between LDR sensors.
Details are also given in [2].
3.5 Modelling of servomotor
Classical Hobbyist servo Hitec or equivalent, medium
sizes are used. Supply voltage is +5V. The control signal
Vpwm is a PWM periodic signal: period 20ms, pulse
width 1ms to 2ms for an angle range of 180°. Maximum
rotation speed is 60°/0.15s. Modelling includes internal
feedback loop and rotation speed saturation. Details can
also be found in [2].
3.6 One axis tracking system modelling
All the blocks were assembled to build a basic one axis
equivalent Spice schematic. It has been previously
detailed in [2]. After some adaptations, it is usable for
the two axis system. The schematic includes all sub
blocks discussed in §3.3, 3.4, 3.5 and is displayed in
figure 10. Since SPICE stimuli are obviously in Volt and
Amp, correspondence scales have been defined as
follows:
1Vdc <=>1 Lux for light flux
1Vdc <=> 1 rd for angles
69.58mV
0
-19.58mV
0V
distance inter LDR 10cm
distance lampe 1m soit
thetazero=2.8° -> 0.05 rd
1.606V
Lo flux=
I/D2; ech
1V=1LUX
LDR2 BEHAVIOUR
R=V*RES
RV
-
+
RES = 1K
U7
VC_RES
2.762V
IN OUT
-0.7PW R
theta zéro
(radians)
R11
9k
R12
1k
346
CORRECTOR P. I. D.
COMPARATOR
Received Flux L1 et L2
function of alphae
filtre 10Hz
(anti-neon 100Hz) gain pur
1.692V
U9B
LMC6482A/NS
+5
-6
V+
8
V-
4
OUT
7
alpha: angle par
rapport au sud
119.6mV
0V
2.501V
1
2.549V
DIFFERENCE LDR1-LDR2
entrée DC 0-5V
sortie -Pi/2 à +Pi/2
écart angle du soleil-axe du system alphae
R18
50k
0
112.2mV
V8
2.5Vdc
0.62
V11
2.5Vdc
R19
1k
0
992.9V
IN OUT
COS 1.610V
0V
7.944mV
7.983mV
695.8fV
-1
69.58mV
2.500V
LDR1 BEHAVIOUR
-69.58mV
R=V*RES
RV
-
+
RES = 1K
U5
VC_RES
50.00mV
0V
695.8fV
2.749V
IN OUT
-0.7
PWR
R3
9k
346
R4
1k R24
18K
1.485V
U10A
LMC6482A/NS
+
3
-
2
V+
8
V-
4
OUT 1
R20
3k
1.486V
2.971
V
R213k
R223k
R233k
5.000V
SUM
IN1
IN2
OUT
Vc:tension de commande
0.62rd/ V, soit 36°/V
U8A
LMC6482A/NS
+
3
-
2
V+
8
V-
4
OUT 1
U11B
LMC6482A/NS
+
5
-
6
V+
8
V-
4
OUT 7
remarque: fonction cos :
entrée en rd
U12A
LMC6482A/NS
+
3
-
2
V+
8
V-
4
OUT 1
0V
1.000KV
alpha (radians)
R13
3k
R14
3k
IN1
OUT IN2
DC/PWM converter
+SERVOMOTOR
fcBfermée=1.58Hz
1.611V
R17
20k
1.000KV
R15
30k
1.692V
IN1
OUT
IN2
0
IN1
OUT IN2
IN1
IN2
OUT
atténuation
optique
IN OUT
COS
992.9mV
V13
0.05Vdc
0
IN1
OUT
IN2
1.607V
IN
OUT
0.6
-0.6
sunangle
saturation vitesse
INOUT
1
1+0.01*s
vitesse->position
R25
30k
69.58mV 112.2m V
sourceintensity
C8
10u
consigne position
IN OUT
1
0.1*s
C9
10u
servoangle
1.607V
IC=0
+
IC=0
+
Fig. 10. One axis tracking modelling
3.7 Two axis modelling
As the two axis works in the same principle, the previous
schematic given in figure 10, is transformed into a
SPICE sub circuit. Then, we can duplicate this sub-
circuit and associate them: The first one will represent
the azimuth movement and the second, the elevation
movement. Finally, two axis modelling is given in figure
11.
Fig. 11. Two axis solar tracking SPICE modelling
The two sub-circuits are connected together and linked
by equation (1) which is represented by an ABM SPICE
library block (cf. §3.2). Main inputs are the spotlight
azimuth ref, (represented by a ramp voltage source V3
from 0 to 3.14 V), and the spot light intensity L
(represented by a DC voltage source V1). (1000Vdc 
1000 Lux).
Mains available modelling outputs are azimuth and
elevation angles ( and given by the two servomotors
and error angles to check accuracy of the system e and
e.
4 Spice simulations
Among numerous simulations, we give hereafter the
most significant ones.
As SPICE works obviously in Volt and Amp, horizontal
and vertical scales of the simulated response curves are
converted (if necessary) in radians angles and Lux before
display, for better understanding.
4.1 Open loop one axis simulations
Figure 12 represents a DC sweep on azimuth axis under
the following conditions: the spot light is locked in south
position and a rotation of azimuth servomotor from East
to West (0° to 180°), is performed.
2axes_1
azimut tracking sub circuit
sunangle
sourceintensity servoangle
V1
1000Vdc
0spotlight
intensity
V2
0Vdc
V3
TD = 1
TF = 1
PW = 1
PER = 15
V1 = 0
TR = 10
V2 = 3.14
0V
OUT
I
N(V(%IN)*V(%IN)*-0.3+ V(%IN)*0.945+0.1)
2axes_2
elevation tracking sub circui
t
sunangle
sourceintensity servoangle
elevation
vs.azimut
function
V
V
servo
azimuth
a
ngle
servo
e
levation
sun azimuth
angle
a
ngle
L1
L2
ref

(lux)
fcb

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CSCC 2018
Servomotor Azimuth angle (in rd)
01.0 2.0 3.0
0V
2.5V
5.0V
0
1.1K
Received light (in Lux))
/2
Voltage difference V
dif
f
L2 L1

0
Fig. 12. Open loop simulation (DC sweep)
Upper curves shows L1 (green) and L2 (red) received
lights flux on LDR1 and LDR2. L1, L2 reach their
maximum values L0(here =1000 lux) when the spotlight
is exactly in front of each (Respectively for =o
and =o). Lower curve shows the difference
signal Vdiff (as defined in figure 2), centered on
Vsupply/2 (i.e. Vcc/2= 2.5V). It is a classical “S” curve:
when the spotlight is perfectly aligned, Vdiff is centered
on Vcc/2. When the source light is shifted above LDR2,
Vdiff becomes greater than Vcc/2. When the source light is
shifted above LDR1, Vdiff becomes smaller than Vcc/2.
Vdiff is thus well suitable for a feed-back control. When
 reaches 0 or 180° (Sunset or sunrise situation), L1 and
L2 tend together toward zero (tangent light to the LDR
surface), thus Vdiff return to Vcc/2.
Other open and closed loop simulations and
experimental characterisation for checking the stability
and frequency behaviour of the system were already
detailed in [2]. So, they are not given here.
4.2 Closed loop two axis simulations
4.2.1 Response to a full spot light rotation
A DC sweep is applied on spot light azimuth angle input
ref, to simulate a full rotation from East to West. Figure
13 shows the corresponding azimuth and elevation
servomotors angle response.
A
zimuth angle (in rd)
00.5 1.0 1.5 2.0 2.5 3.0
0
2.0
4.0
0
0.5
1.0
an
g
le
(
in rd
)
Sun elevation
an
g
le
Elevation
motor an
g
le
Azimuth
motor an
g
le
Sun azimuth
an
g
le
Fig.13. Closed loop, DC sweep response
Upper plot: sun and servomotor elevation angles e and
 vs. Azimuth angleref.
Lower plot: sun and servomotor azimuth angles ref and
 vs. azimuth angleref
Error angles correspond to the difference between green
and red curves. Tracking is correct since both error
azimuth angle e and elevation angle remain close to
zero (less than ±2.5°C) during all the simulated rotation.
However, it must be mentioned that there is no integral
correction in the feed-back loop circuits for stability
reasons: thus, error angle is proportional to reference
angle and slightly increases from East to West as it can
be seen on the left side of figure 13.
4.2.2 Response to light source intensity fluctuations
The light source is located quite far (around 50 cm) from
the LDR sensors, compared to the size of tracking
system. Thus, fluctuations of source intensity (I input)
should affect identically the four LDRs. They can be
considered as a kind of parasitic common mode for the
loop. This last simulation (figure 14) is done to check
possible effects that can occur due to “in door” uses of
the small scale demonstrator (i.e. flicker noise coming
from artificial light (fluorescent neon tubes in the room
at 100Hz). It shows the transient response when system
is submitted to a 20% fluctuations of the source (200
Lux around de 1000 Lux, square waveform, 10ms
period) with spotlight oriented to south.
Time
5.00s 5.02s 5.04s 5.06s 5.08s 5.10s
868.75m
868.87m
869.00m
1.49105
1.49107
1.49110
1.49112
0.75
K
0.87
K
1
K
L (in Lux)
Elevation motor an
g
le
(
rd
)
Azimuth motor an
g
le
(
rd
)
Fig. 14. Closed loop response to fluctuation of source intensity
(I input).
Variations around the bias position of azimuth and
elevation angles  and  are less than 0.1mrd. These
parasitic variations are well rejected. Thus simulation
confirms an almost total insensitivity of the system while
LDR sensors are perfectly matched.
At this opposite, mismatching between the LDR sensors
could seriously affect the loop behaviour. Fine impacts
and effects have been previously studied in [11].
5 Practice and measurements
5.1 Mechanical assembly

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CSCC 2018
Figure 15 and 16 shows the installation in the small scale
house surroundings. Size of the small solar panel is 9cm
x 5cm and electronic board 10cm x10cm.
Fig. 15. Small scale solar tracking system (front side view)
5.2 Electronic design
The design uses only COTS components. The four
matched LDR sensors (VT90N2 series or equivalent) are
placed in a Wheatstone bridge. Output signals are
subtracted using rail to rail OP amps LMC6482 to have
the widest dynamic range. Difference Vdiff is applied to
the simple PID corrector (adjustable gain + low pass RC
filter). The resulting DC voltage value is processed by a
microcontroller MC9S12C128 module to generate PWM
signals for controlling the servos Hitec 322-HD.
Actually, this module was not necessary: a simple
analogue to PWM voltage converter should be greatly
enough. But we used it because it also processes various
data that could be transmitted by CAN bus to a distant
computer. Supply voltage comes through a LM7805
regulator +5V.
Fig.16. Small scale solar tracking system (back side)
5.3 Static open loop measurement
A preliminary open loop characterisation was performed
on azimuth axis mainly to check the servomotor transfer
function (no manufacturer data). First cut-off frequency
occurs at 1.58 Hz which is quite common for this kind of
servo.
Secondly, the spotlight was located to south with zero
degrees elevation. The voltage difference LDR1, LDR2
Vdiff vs. azimuth angle was plotted using a simple DC
voltmeter. This experimental curve (figure 17) can be
easily and successfully compared to the simulated
response in figure 12.
Fig. 17. Vdiff vs. azimuth angle 
5.4 Visual test
Once the system looped, we checked by visual tests that
tracking feedback loop worked correctly separately on
each axis and then simultaneously on the two axes.
Validation of the system behaviour was done under
various conditions (light source distance and intensity).
A correct matching between global SPICE modelling,
predicting simulations and experimental behaviour
design is observed.
Finally, a small video clip was recorded to show the
system behaviour.
5.5 Disturbance effects
A shutter (simulating an object passing over) was placed
above one of the LDRs to simulate a “local disturbance
on D input” as define in figure 4. Servomotor first
deviates, and then comes back to the initial position
when the shutter is removed.
A second “non-realistic” test, which can be seen as a
“step response”, was done: moving very suddenly the
spot light out of the visual field of the LDR sensors.
System goes to the mechanical stop (limited by the servo
internal stop) and stays in this position until the spotlight
comes again in the visual field of sensors. Then, the
tracking starts again.
6 Discussions
The current Spice modelling gives satisfaction for
predicting and analysing the main performances of the
small scale solar tracking system. Main tendencies and
order of magnitude obtained by simulation are confirmed
by experimental test on the small scale system. However,
it is not so easy to get extremely precise angles data from
the practical tests: some accessories must be added on
4 LDR
sensors
Azimuth
servo
Elevation
servo
0
0.5
1.5
2.5
3.5
4.5
0 30 60 90 120 150 180
Azimuth angle  ( in degrees)
Vdif
f
(V)
Spot light
centered

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CSCC 2018
the test bench to improve accuracy of measurements (in
particular, needles to point more finely the azimuth and
elevation directions).
Main advantages of the modelling are:
- Quick understanding of the tracking system general
behaviour,
- Electrical modelling suitable for those who do not have
specific knowledge out of the electronic field,
- Fast Spice simulations,
- Enough but not too much complex for didactical uses.
However, there are obviously some limits:
- Approximations have been done to build the modelling:
we cannot be specialists of electronic components, optic
and astronomy at the same time. In particular, optical
modelling blocks might be refined.
- This is not a parametric modelling. Each parameter
(geometrical data, servo motor specifications, light
intensity etc.) must be adjusted or changed manually if
necessary.
7 Conclusions
An equivalent modelling of a small scale two axis solar
tracking system was presented. Mixed Spice modelling
and electronic analogue designs were successfully
validated by experimental tests.
This tracking system is now installed in our small scale
house modelling. Lastly, from a didactical point of view,
this modelling is now used for training the students
during the electronic feed-back projects and practical
lessons as “a case of study”.
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