“HENRI COANDA”
AIR FORCE ACADEMY
ROMANIA
“GENERAL M.R. STEFANIK”
ARMED FORCES ACADEMY
SLOVAK REPUBLIC
INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER
AFASES 2015
Brasov, 28-30 May 2015
EFFECT OF LIGHT DEPENDANT RESISTOR MISMATCHING AND
IMPACT OF NON LINEARITY IN A SMALL SCALE
SOLAR TRACKING SYSTEM
Philippe Dondon*, Ecaterina-Liliana Miron**
*Université de Bordeaux, IPB, Talence, France, **Faculty of Aeronautical Management, “Henri Coandă”
Air Force Academy, Brasov, Romania
Abstract: The design of a didactical small scale “green” house and its power production systems has
been previously presented in [1]. As power generation is one of the challenges in Sustainable
Development, some scaled accessories have been included on house surroundings. In particular, a small
scale simplified solar tracking analogue system based on LDR sensors, has been designed and installed
[2]. A mixed SPICE modelling of the system, including geometrical, optical, electronic linear and
nonlinear aspects has been built. This new paper focuses on effects of Light Dependant Resistor
mismatching, and impact of non-linearity on the solar tracking performances. Firstly, the principle of
tracking and its SPICE modelling are shortly described; Secondly, impacts of each imperfection are
detailed and simulated. Finally, impacts are quantified and discussed before conclusion.
Key words: Sun tracking, Mixed SPICE modelling, Analogue design, Sustainable development
1. INTRODUCTION
1.1 Small scale house project state of art.
Within the framework of an innovative
sustainable development project, the design a
functional realistic small scale house, built in
genuine materials took almost three years. The
building (with true materials) of small scale
house itself is finished. It required more than
1500 hours of work and was detailed in [1].
Figure 1 shows a picture of the finished small
scale model (at 1/20 scale).
The small scale model will be used as:
- Demonstrator (sustainable development
exhibition in town halls or local
sustainable development events)
-
Pedagogical support for practical lessons
and electronic projects, for sensitizing
engineering students to green power
management, power saving and low
power electronic in first and 2nd year
study
1.2 Study background. We designed several
electronic boards and their electronic control
circuits, as indicated hereafter, in order to
make the “green” house model, didactical and
fully functional:
- A small scale home automation including
weather station, low voltage LED lighting for
the terrace, roof solar panel and battery cells
management, “air conditioned” system
powered by an hydrogen fuel stack (i.e. scaled
Canadian well under the house), an electrical
heater circuit house and its temperature
control.
- A solar tower and its performance
measurement system,
- A small scale simplified solar tracking
system for a solar panel…
not, one of the two LDR receives more flux
than the other. This generates an analogue
difference voltage V diff (“left minus right”)
and the feedback loop moves the servo motor
into the right direction until to cancel the
voltage V diff .
A classical hobbyist servo Futaba (or
equivalent) is used to move the panel.
According to standards, the rotation angle α is
proportional to an input control signal V pwm
with the following characteristics: two voltage
level signal 0, +5V, period 20ms, pulse width
variable from 1ms to 2ms for a 0° to 180°
rotation. Thus, a DC to PWM converter is
required between subtraction block and Servo
input (Cf. figure 2).
substractor
Figure 1: View of house and surroundings.
The present paper focuses on intrinsic
imperfection of this last accessory. Modelling
and design has already been detailed [2].
However, effects of mismatching and other
imperfection must be taken in consideration
for a fine analysis of the system’s behavior.
For a better understanding, we bring back to
mind in §2. and §3. some important points.
2. SUN TRACKING CIRCUIT
PRINCIPLE
2.1 Generalities. The didactical designed
circuit is obviously a simplified version of a
true system [3], [4], [5]. Main goals were to
illustrate feedback theory taught in our
electronic engineering school and more
generally to introduce sustainable development
in scientific studies.
2.2 Principles and schematic. The small
scale “green house” is used for in-door
demonstration and applications. Thus, a
halogen spot light is used to “replace” the sun
light.
The system consists of an analogue system
with one rotation axis control (horizontal plan)
[6], [7] to simplify the approach. Figure 2
shows the sun tracking principle.
When the solar panel is aligned in “sun”
direction, the received left and right lights flux
L1 and L2 are equal (Cf. figure 3). When it is
Vin1
Vcc
Vin2 Vcc lar panel
so
LDRs
sensors
amplifiers
summation
Vsum
PID
corrector
DC voltage
to PWM
converter
Vdiff
Vc
logic

spotlight
Vpwm
servo motor
Figure 2: Sun tracking system block diagram
Two light sensors LDR1 and LDR2 (LDR:
Light Dependant Resistors,), are located on
left and right side of the panel. They receive
the “sun” light.
A summation V sum of the two sensors
voltages is used to distinguish dark and sunny
situation; and power consumption is
minimized during the “night” by turning off
the servo voltage supply.
left photoresistor
LDR2
L2
solar
panel
L1
spot light
(sun simulation)
LDR1
right photoresistor
Figure 3: Solar panel alignment
“HENRI COANDA”
AIR FORCE ACADEMY
ROMANIA
“GENERAL M.R. STEFANIK”
ARMED FORCES ACADEMY
SLOVAK REPUBLIC
INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER
AFASES 2015
Brasov, 28-30 May 2015
3. MODELLING OF TRACKING
SYSTEM
With these conditions, received flux is
given by [2]:
3.1 Generalities. L1, L2 represents the
received light (in Lux) on each LDR, α ref the
“sun” angular position, α e the error angle, α
the angle given by the servo motor (referenced
as indicated in figure 5). Thus, the tracking
system can be modelled as follow:
L 1 = L 0 cos (Θo −α e )
L 2 = L 0 cos (α e + Θo )
(2)
Nominal values in our small scale system
are D=1m and l=10cm and L 0 =1000 lux.
3.2 Tracking system global modelling.
The global equivalent mixed Spice schematic
previously built in [2] is given in figure 6.
received
luminous light
(lux)
control
returned
voltage (V) voltage (V)
Vin1
PID
DC/PWM
electronic circuit
corrector
V
conv. V controller
transfer function in2
PID V
c
out
Vpwm servomotor
transfer
function
PWM
control
signal

e
-
LDR
transfer
function
L1
East
L2
LDR2
L2
e
optical /geometrical

servomotor
(body)
+
transfer function
error angle
motor
angle
ref: reference angle I: source light D: local
(sunlight position)
intensity disturbances
l
L1
ref
Lo
spot light
South
LDR1
West
Figure 4: System identification
is the main input of the feedback
- α ref
system.
- Source light intensity input (I) can be seen as
a parasitic input which represents fluctuation
of source intensity (fog, sky partially cloudy,
etc).
- Local disturbances input (D) represent
disturbances that can occur individually, on
each LDR optical way. (object passing over
the LDR etc).
We set up:
L 0 = I / D2 and α 0 = artg (l/2.D)
(1)
Where, I is the light intensity of the source
(in Candela), D the distance light source/solar
panel, and l the distance between LDR sensors
(in cm).
Figure 5: Reference angles (top view)
modelling
3.3 LDR detailed modelling. LDR sensors
are intrinsically nonlinear. Our commercial
LDRs samples (VT90N) vary over 3 decades
as a non-integer power of the received light
(i.e. from L-0.5 to L-0.7), thus:
LDR(Ω) = k.
1
Ly
(3)
(with 0.5<y<0.7, and L in Lux)
The corresponding Spice modelling is given
in figure 7. LDR, modelled by a Voltage
Controlled Resistor block (“VCR”), is inserted
in a resistor bridge supplied under +5V.
Capacitor C4 represents the average time
constant of the LDR as defined in [2].
LDR1 BEHAVIOUR
Received Flux L1 et L2
function of alphae
SUM
R22 3k
U5
PWR
-0.7
IN
OUT
1
OUT
COS
IN
OUT
346
8
R=V*RES
C8
+
-
V
IN2
IN1
atténuation
optique
R
1u
R23 3k
3
OUT
2
VC_RES
RES = 1K
R4
1k
L1
346
DIFFERENCE LDR1-LDR2
R=V*RES
C9
OUT
IN2
IN1
+
V
R
-
1u
R11
9k
8
3
+
V+
U8A
2
R12
-
4
1k
R25
30k
1
OUT
VC_RES
RES = 1K
V16
R13
V11
2.5Vdc
8
V-
3
+
3k
OUT
IN2
IN2
IN1
IN1
OUT
 
Lo flux=
I/D2; ech
1V=1LUX
8
0
5
distance inter LDR 10cm
distance lampe 1m soit
thetazero=2.8° -> 0.05 rd
4
R15
V30k
0
OUT
0.6
IN
OUT
-0.6
consigne position
OUT 1 IN
OUT
saturation vitesse

1+0.01*s
filtre 10Hz
(anti-neon 100Hz)
R17
0.62
IN2
IN1
alpha (radians)
alpha:V angle par
rapport au sud
 ref
7
V+
+
5
OUT
IN 1 OUT
0.1*s
vitesse->position
4
R19
V-
6
1k
LMC6482A/NS
entrée DC 0-5V
sortie -Pi/2 à +Pi/2
V
SUN
gain pur
8
U9B
20k
alpha ref= position du soleil
angle en radian par rapport au sud
V1 = 0
V2 = 3
TD = 0
TR = 1
TF = 200m
PW = 1m
PER = 3
V8
2.5Vdc
alphae
V
0.62
balayage Est Ouest
1
V-
LMC6482A/NS
7
IN1
+ IC= 0
4
Vc:tension de commande
0.62rd/ V, soit 36°/V
IN2
COMPARATOR
αe
-
3k
LMC6482A/NS
0
écart angle du soleil-axe du system
-
2
V+
U10B
OUT
V13
-1
+
V+
U11A
OUT
R14
0
6
0.05Vdc
LMC6482A/NS
R20
LMC6482A/NS
theta zéro
(radians)
1
V-
3k
U7
PWR -0.7
IN
OUT
4
0
L2
V20
-
R24
18K
LDR2 BEHAVIOUR
V1 = 0
V2 = 0
TD = 10m
TR = 0.1m
TF = 0.1m
PW = 1m
PER = 10m
1000Vdc
V+
U10A
+
R21 3k
remarque: fonction cos :
entrée en rd
COS
IN
OUT
R3
9k
V19
V12 de 0V a 5V pour -90° a +90°
sud=>2.5V
DC/PWM converter
+SERVOMOTOR
fcBfermée=1.58Hz
R18
C7
0.1u
50k
0
CORRECTOR P. I. D.
V15
attention cste
detemps a revoir
2Vdc
0
POSITION
Alpharef
Figure 6: Global SPICE modelling
3.4 LDR detailed modelling. LDR sensors
are intrinsically nonlinear. Our commercial
LDRs samples (VT90N) vary over 3 decades
as a non-integer power of the received light
(i.e. from L-0.5 to L-0.7), thus:
LDR(Ω) = k.
1
Ly
(3)
(with 0.5<y<0.7, and L in Lux)
The corresponding Spice modelling is given
in figure 7. LDR, modelled by a Voltage
Controlled Resistor block (“VCR”), is inserted
in a resistor bridge supplied under +5V.
Capacitor C4 represents the average time
constant of the LDR as defined in [2].
4. IDENTIFICATION OF
IMPERFECTIONS
Since the tracking system is basically a
feedback circuit, imperfections of active
blocks are obviously greatly reduced.
However, quality of sensors (which belong to
the return loop) can impact directly the
performances of the system (accuracy, stability
etc.).
Received PWR0.7
346
IN OUT
light (Lux) k
Non integer power U5 R=V*RES
+
V
-
R
+5V
C4
100u
VC_RES RES = 1K
R3 9k
Vin (V)
R4 1k
0 Figure 7: LDR generic modelling
In order to reduce this impact, the two LDR
sensors were obviously sorted and a selection
of two “similar” LDR was done. However, we
estimate the residual global mismatching up to
10%.
Thus, it is important first to identify the
different imperfections sources and to predict
their effects and finally to suggest some
possible compensations.
“HENRI COANDA”
AIR FORCE ACADEMY
ROMANIA
“GENERAL M.R. STEFANIK”
ARMED FORCES ACADEMY
SLOVAK REPUBLIC
INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER
AFASES 2015
Brasov, 28-30 May 2015
The main imperfections identified are as
follow.
- Intrinsic non linearity of the LDR
- Mismatching between LDRs:
 Variation in k factor
 Dispersion of the y exponent from -0.5 to
-0.7
 Dispersion of time response
 Optical attenuation on LDR protection
layer due to the dirt.
- LDRs ambient temperature variations
5. ANALYSIS OF LDR SENSOR’S NON
LINEARITY
5.1. Impact of non-linearity. Non linearity
leads to several consequences:
- A non-constant sensitivity over the full
luminous flux range,
- A higher difficulty to match the two sensors
response
- A possible instability depending on light
level L 0 .
5.2. Non linearity SPICE simulations.
Due to non-linearity, open loop gain depends
on L 0 value. And the frequency response of
the closed loop, with a parametric sweep for
L 0 = 10, 100, 1000 and 10000 Lux is like
indicated in figure 8. Gain in bandwidth is
obviously close to 1, and a resonant frequency
appears at high source intensity level.
6. ANALYSIS OF LDR SENSOR’S
MISMATCHING
6.1 Impact of mismatching. Mismatching
leads to several consequences:
- A possible permanent position angle error,
- Local instability.
Gain
10
Lo=10000Lux
1.0
100m
Lo=10Lux
10m
1m
100u
10u
10mHz
100mHz
1.0Hz V(LAPLACE1:OUT)/ V(GAIN9:OUT) 10Hz 100Hz
1.0KHz
Frequency
Figure 8: Closed loop gain
6.2 Impact of “k” factor
6.2.1 Analysis method
In a Log/log representation of LDR
characteristic, varying k corresponds to a
change of vertical offset (Cf. figure 9). A
parametric sweep corresponding to a 10%
variation on the LDR1sensor is performed.
6.2.2 SPICE simulations
For these simulations, the system is initially
pointed to south direction. A preliminary
simulation is done as indicated hereafter:
- Tracking system in open loop. DC sweep
from L 0 = 10 to 10000 Lux (full luminous
range) with a parametric sweep of k value
from 306 to 386 on LDR1 (Symmetric
compared to the nominal value) to produces a
voluntary mismatching.
Figure 9 shows the corresponding simulated
behaviour of the LDR. Once LDR behavior
checked, another simulation is run:
- a DC sweep from L0 = 10 to 10000 Lux in
closed loop with the same parametric sweep of
k.
Using the «Spice performance analysis»
option, once can extract the average error
angle α e vs. k (Cf. figure 10).
A variation of ±11% of k value around the
nominal value leads to a huge error α e of ±1rd
(i.e. ±57 °).
6.3 Impact of y exponent
6.3.1 Analysis method
We perform a parametric sweep of
exponent number y, in the “power block”
ABM spice element. In Log/log representation
of LDR characteristic, variation of power
order y corresponds to a change in curve slope
(cf. figure 11).
α e around L 0 = 300 Lux. (as α e depends on
absolute value Lo).
LDR (in ohm)
1.0M
100K
y=-0.65 10K
LDR( in ohm)
y=-0.75
1.0K
100K
100
10K 10
30
100
(V(U11A:V+)-V(U8A:+))/I(U5:D)
300
1.0K
3.0K
10K
L O (in Lux)
Figure 11: LDR(Ω) = f (L 0 ) Lux (parameter y)
1.0K
Error angle  e (in rd) 2.0
100 10
30
100 300
(V(U11A:V+)-V(U8A:+))/I(U5:D) 1.0K 3.0K
Lo (in Lux)
10K
Figure 9: LDR(Ω) = f(L 0 ) Lux parametric
analysis k
0
Error angle  e (in rd) 1.0
-2.0
-720m
-700m
-680m
-660m-650m
Figure 12: Error angle α e = f(y) vs. y exponent
0
-0.5
-1.0
-750m -740m
exponent y
0.5
300
320
340
360
380 k factor 400
Figure 10: Error angle α e = f(k)
6.3.2 SPICE simulations
A first simulation is done as indicated
hereafter:
- Tracking system in open loop. DC sweep
from L 0 = 10 to 10000 Lux with a parametric
sweep of exponent y of LDR1 from -0.65 to 0.75 (symmetric compared to the nominal
value -0.7). Figure 11 shows the corresponding
simulated behavior of the LDR.
Once LDR behavior checked, a second
simulation is run:
- DC sweep from L 0 = 10 to 10000 Lux in
closed loop with the same parametric sweep of
y.
Using the «Spice performance analysis»
option, once can obtain an average error angle
A +/-5% variation of y around -0.7,
produces a huge deviation of angle error +/- 1
rd (i.e. 57°). The relative impact of y is greater
than the one of k.
6.4 Impact of response time
6.4.1 Analysis method
A parametric sweep of 10% on capacitor
value C4 is performed.
6.4.2 SPICE simulations
A mismatching on capacitor value does not
have any impact in DC mode. But it may have
an impact. Thus, the following transient
analyses are performed:
- Response to a α ref step pulse. The pulse
characteristics are rise time 10ms, pulse width
4s, step of +/-1/2 rd around 0 (south position).
L 0 = 1000Lux, Figure 13 shows the response in
closed loop, when capacitors are equal to
100μF and perfectly matched.
A 10% variation on capacitor value does
not have significant effect. So, an extreme
capacitor mismatching is simulated (100μF for
“HENRI COANDA”
AIR FORCE ACADEMY
ROMANIA
“GENERAL M.R. STEFANIK”
ARMED FORCES ACADEMY
SLOVAK REPUBLIC
INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER
AFASES 2015
Brasov, 28-30 May 2015
LDR2 and 1μF LDR1) to check asymptotic
behavior.
Angle (in rd)
Error angle  e
2
0 -2
1.5
angle  ref
0
angle 
-1.5
0s
1.0s
2.0s
3.0s
4.0s
5.0s
6.0s
Time Figure 13: Transient simulations (C matched)
Figure 14 shows the response curve. The
transient shape changes a little bit but the
global behavior remains correct.
Angle (in rd)
Error angle  e 2
0
-2 1.5
angle  ref
0
angle 
-1.5
0s
1.0s
2.0s
3.0s
4.0s
5.0s
Time
6.0s
Figure 14: Transient simulations (C huge
mismatch)
- Response to a 100Hz squared stimuli on L 0 :
It represents the parasitic 100Hz flicker noise
coming from fluorescent neon tubes in the
room, during in door experimentation. The
simulation conditions are rise time 0.1ms,
pulse width 1ms, period 10ms, nominal value
L 0 =1000 Lux, μ ref =0.
A 10% variation on capacitor value does
not have significant effect. Like previously,
the same extreme capacitor mismatching is
simulated to check asymptotic behaviour.
Figure 15 shows the response curve. A
permanent small error angle α e (less than 4.5°)
is observed.
Thus, the system is almost insensitive to
this noise since mismatching between LDR
time response remains small (less than 10%).
In fact, the previous simulations do not
represent realistic phenomenon and should not
be necessary for a real system, because all
natural phenomenon are extremely slow: sun
goes always in the same direction; there is no
sudden movement of the sun or sudden change
of light intensity in the Nature.
However, simulations were required to
check reaction of the system since it works
with “in door” conditions, which are different
from reality.
6.5 Impact of optical attenuation
6.5.1 Modelling of optical attenuation.
A 0.9 attenuator SPICE element is placed in
series on LDR1 received light input to produce
voluntarily a difference in optical ways
between LDR1 and LDR2.
Light flux (Lux)
Light flux (Lux) 1.0K
1.0K
0.9K
L 1 L 2 0.5K
0.8K Error angle  in (rd) e
-72m
0
Error angle  e
-74m
-76m
5.0s
5.2s
5.4s
5.6s
5.8s
6.0s
Time Figure 15: Transient simulations
6.5.2 SPICE simulations
Theses simulations investigate the static
behavior in open loop, when submitting the
system to a DC sweep of α angle from -90° to
+90° (i.e. full rotation from East to West). The
spot light is locked in south position (α ref =
0°), D=1m and L 0 =1000 Lux.
As the distance between sensors is an
important parameter, two cases have been
tested:
- Distance between LDR sensors
l=10cm
(i.e Θ 0 2.8°) (Cf. figure 16).
- Distance between LDR sensors
l=60cm
(i.e. Θ 0 18°) (Cf. figure 17).
Figure 16 shows the received light L1 and
L2 vs. angle α. It can be read as follow:
L 1 , L 2 reach their maximum values L 0 (here
=1000 lux) when the spotlight is exactly in
front of them (Respectively α e =Θ o and α e =Θ o ). And they tend toward 0 when α reaches ±
90° (Sunset or sunrise situation). When
feedback loop operates normally, the system
tends to make the two received lights flux,
equal. This happens on figure 16 (resp. 17) at
the intersection between the two curves L 1 and
L 2 . Thus, the corresponding error angle can
be deduced.
Here, we obtain α e  45°.
Vertical scale: received light in Lux
Green curve: L1 (after optical attenuation
x0.9)
Blue curve: L2 (no attenuation)
-Pi/2
0
angle (in rd) PI/2
Figure 16: DC Sweep Simulations
Figure 17 shows also the received light L1
and L2 vs. angle α. Distance between sensors
is 6 times greater than in figure 16 (i.e. 60cm).
In this situation, error angle α e is reduced to
around 15°; the more sensors are spaced, the
less is the static angle error due to optical
mismatching.
Vertical scale: received light in Lux
 Red curve: L1 (before attenuation)
 Green curve:
L1 (after optical
attenuation x0.9)
 Blue curve: L2
6.6 Temperature impact
The ambient temperature changes from
morning to afternoon. Unfortunately, LDRs
are sensitive to temperature [8]: the LDR
resistance value decreases as the temperature
rises.
The relationship between temperature and
resistance was not completely investigated but
it appears that the resistance of an LDR is a
function of both light flux and temperature.
For our “in door” application with a spot
light of 75 to 100W, 1meter far, and distance
between sensor 10cm, this is not really a
problem. However, for outdoor uses, when the
component is oriented towards the sun, the
LDR resistance becomes very low, and the
effects of temperature variation could appear
more significant.
“HENRI COANDA”
AIR FORCE ACADEMY
ROMANIA
“GENERAL M.R. STEFANIK”
ARMED FORCES ACADEMY
SLOVAK REPUBLIC
INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER
AFASES 2015
Brasov, 28-30 May 2015
important factor: the more they are spaced, the
less is the static angle error.
Light flux (Lux) 1.0K L2
L 1 0.5K Error angle  e Spot light
0 LDRs
-PI/2 0
PI/2
 angle (in rd) Figure 17: DC sweep Simulations
Small scale Solar tracking Figure 18: Practical test
7. EXPERIMENTS
It is difficult, from experimental point of
view, to reproduce exactly the simulated
mismatching because it could require a lot of
mismatched LDR and many repetitive tests.
We only performed some tests with a few
“no sorted” LDRs. Due to the test bench, a
fine measurement of accuracy is difficult to
obtain. However, when LDR are mismatched,
the main tendencies and order of magnitude of
error angle αe predicted by simulation are
experimentally checked.
When the two LDR are matched, the
system tracks correctly the light source with
accuracy better than 5°, which is enough for
demonstrating the theoretical principle of
tracking and for public exhibition purposes.
8. DISCUSSION AND COMMENTS
Angle accuracy of the system is affected by
all the imperfections. Among the four
parameters, non-integer power exponent y is
the most influent. Instability risk comes from
the nonlinear intrinsic behavior of LDR.
Distance l between LDR sensors is an
The small scale solar tracking system will
operates whatever the situation, but with a
more or less important static permanent error.
From simulations, a maximum error of 5°
requires a global matching better than 1%
between LDR sensors.
As perfect matching between sensors is
never possible, some improvements can help
to reduce the error. Two kind of improvement
can be investigated. Whatever the strategy, a
preliminary strong sorting of LDR sensors is
required. Then, a linearization circuit can be
added, if necessary. It can be done in two
ways:
- by using a micro controller with a tabulated
conversion table (a new design is already
planned)
- by using analogue circuits with voltage
dependant gain circuit (diode or multiplier)
and OP amps for offset and gain adjustments.
9. CONCLUSION
A small scale solar tracking system was
designed and an equivalent mixed modelling
was presented. Effects and impacts of major
imperfections were studied and quantified.
Possible improvements to compensate
imperfections have been suggested. However,
the presented system is not mass produced; it
is only a unique experimental device. Thus,
there was no need to include such
improvements in the present design till now.
The tracking system is now installed in on our
small scale greenhouse modelling. And some
exhibitions have been planned for general
public sensitizing in the near future.
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