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Citation: Li, J.; Wang, L.; Li, G.; Mu, S.
Designing an Accurate Temperature
Control System for Infrared Earth
Simulators Using Semiconductor and
Air Cooling Integration. Sensors 2023,
23, 6908. https://doi.org/10.3390/
s23156908
Academic Editor: Chelakara
S. Subramanian
Received: 8 June 2023
Revised: 12 July 2023
Accepted: 28 July 2023
Published: 3 August 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
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4.0/).
sensors
Article
Designing an Accurate Temperature Control System for
Infrared Earth Simulators Using Semiconductor and Air
Cooling Integration
Jiachong Li, Lingyun Wang *, Guangxi Li and Sida Mu
School of Optoelectronic Engineering, Changchun University of Science and Technology,
Changchun 130022, China; lijiachong126@163.com (J.L.); liguangxi@mails.cust.edu.cn (G.L.);
mstardcl@163.com (S.M.)
*Correspondence: wanglingyun_510@163.com
Abstract:
In a laboratory environment, in order to test the attitude recognition capability and accuracy
of the satellite attitude sensor—the infrared Earth sensor—the infrared Earth simulator is fixed on
a five-axis turntable to enable multi-angle testing. In the past, the temperature control system
of the Earth simulator was water cooled, which not only affected the working accuracy of the
Earth simulator but also affected its size and portability and made it more difficult to use on the
turntable. Therefore, we designed a cooling method for the cold plate based on semiconductor cooling
technology combined with air cooling, and we designed a fuzzy PID control algorithm to accurately
control the temperature according to this cooling method. In this article, we use SOLIWORKS to build
the system model for the system and use the ANAYS Workbench to perform temperature analysis of
the Earth simulator. The results show that the cold plate temperature can be maintained at 20.089
◦
C
when the hot plate temperature is 85
◦
C. The overall temperature uniformity of the hot plate is better
than
±
0.3
◦
C, which meets the index requirements of the Earth simulator. We found that this cooling
method can replace water cooling, giving the simulator the advantage of being miniaturized, and it
can be adaptable to the turntable, which can be widely used in various sizes of Earth simulators and
in various complex environments and operating conditions.
Keywords: Earth simulator; temperature analysis; fuzzy controls; temperature control
1. Introduction
The infrared Earth sensor is an important attitude measurement component for satel-
lites in space [
1
] that takes the Earth as the target source for the satellite attitude’s reference.
Different attitude information of the satellite with respect to the Earth is obtained by means
of infrared optical detection, which enables the measurement of satellite roll and pitch
attitude deviation angles [2].
The infrared Earth simulator is a special piece of ground performance test equipment
for infrared Earth sensors, which is a necessary means of realizing the ground test evalu-
ation of the sensor’s performance index; the simulation accuracy of the Earth simulator
directly affects the performance test of the sensors. The United States first successfully
developed an infrared Earth simulator, followed by Italy, which developed two Earth simu-
lators that can simulate the height of geosynchronous orbit. France and other European
and American countries have also completed the development of Earth simulators. The
China Aerospace Science and Technology Corporation developed an Earth simulator with
an aperture of 250 mm. Changchun University of Science and Technology [
3
] developed
an Earth simulator that can change according to the orbital altitude, and the Shanghai
Institute of Technology Physics [
4
] has also made breakthroughs in the development of
Earth simulators. However, the infrared Earth simulators studied above still have more
problems, and all of their cooling links are constructed with water cooling. Because the
Sensors 2023,23, 6908. https://doi.org/10.3390/s23156908 https://www.mdpi.com/journal/sensors
Sensors 2023,23, 6908 2 of 16
structure of water-cooled radiators is very large, it takes up a lot of space. And, as the
water-cooled structure is complex and costly, there is a risk of damaging system parts if
water leaks. In addition, water cooling also leads to the inability to control the temperature
precisely, which in turn affects the overall working of the Earth simulator.
To improve the testing accuracy of Earth sensors, we propose to use the simulator
on a turntable. And, for the problems of excessive volume, poor working reliability, and
low temperature control accuracy of Earth simulators, semiconductor cooling combined
with air cooling is proposed to replace the traditional water cooling system and to optimize
the temperature control system of Earth simulators. The cold plate temperature of the
simulators is maintained at 20
◦
C, the temperature of the Earth hot plate is continuously
adjustable between 35
◦
C and 85
◦
C, and the temperature uniformity of the hot plate is
guaranteed to be better than ±0.5 ◦C. This opens up the development of Earth simulators
and provides a new idea for it.
The rest of this paper is organized as follows. We will first introduce the infrared
Earth simulator composition and the working principle. In Section 3, we design the
Earth simulator temperature control system. Firstly, the temperature control range of the
Earth hot plate is calculated, and secondly, a fuzzy PID control algorithm is designed and
verified; finally, the specific parts of the Earth simulator are designed. Then, we validate the
overall Earth simulator with experimental simulations in Section 4. Finally, we conclude in
Section 5.
2. Infrared Earth Simulator Composition and Working Principle
The infrared Earth simulator designed in this paper mainly consists of a collimat-
ing lens and its components, a background mirror cylinder, an Earth cold plate and its
components, an Earth hot plate and its components, a temperature control system, a heat
insulation layer, a base and support, etc. The overall structure of the Earth simulator is
shown in Figure 1.
Sensors2023,23,xFORPEERREVIEW2of15
problems,andalloftheircoolinglinksareconstructedwithwatercooling.Becausethe
structureofwater-cooledradiatorsisverylarge,ittakesupalotofspace.And,asthe
water-cooledstructureiscomplexandcostly,thereisariskofdamagingsystempartsif
waterleaks.Inaddition,watercoolingalsoleadstotheinabilitytocontrolthetemperature
precisely,whichinturnaffectstheoverallworkingoftheEarthsimulator.
ToimprovethetestingaccuracyofEarthsensors,weproposetousethesimulatoron
aturntable.And,fortheproblemsofexcessivevolume,poorworkingreliability,andlow
temperaturecontrolaccuracyofEarthsimulators,semiconductorcoolingcombinedwith
aircoolingisproposedtoreplacethetraditionalwatercoolingsystemandtooptimizethe
temperaturecontrolsystemofEarthsimulators.Thecoldplatetemperatureofthesimu-
latorsismaintainedat20°C,thetemperatureoftheEarthhotplateiscontinuouslyad-
justablebetween35°Cand85°C,andthetemperatureuniformityofthehotplateisguar-
anteedtobebeerthan±0.5°C.ThisopensupthedevelopmentofEarthsimulatorsand
providesanewideaforit.
Therestofthispaperisorganizedasfollows.Wewillfirstintroducetheinfrared
Earthsimulatorcompositionandtheworkingprinciple.InSection3,wedesigntheEarth
simulatortemperaturecontrolsystem.Firstly,thetemperaturecontrolrangeoftheEarth
hotplateiscalculated,andsecondly,afuzzyPIDcontrolalgorithmisdesignedandveri-
fied;finally,thespecificpartsoftheEarthsimulatoraredesigned.Then,wevalidatethe
overallEarthsimulatorwithexperimentalsimulationsinSection4.Finally,weconclude
inSection5.
2.InfraredEarthSimulatorCompositionandWorkingPrinciple
TheinfraredEarthsimulatordesignedinthispapermainlyconsistsofacollimating
lensanditscomponents,abackgroundmirrorcylinder,anEarthcoldplateanditscom-
ponents,anEarthhotplateanditscomponents,atemperaturecontrolsystem,aheatin-
sulationlayer,abaseandsupport,etc.TheoverallstructureoftheEarthsimulatoris
showninFigure1.
Figure1.InfraredEarthsimulatorcompositionstructure.
ThepurposeoftheinfraredEarthsimulatoristocompletethesimulationoftheEarth
onthegroundsoastochecktheperformanceoftheinfraredEarthsensoranddetermine
whetheritstechnicalparametersareuptostandard.TheinfraredEarthsensorisasatellite
aitudedetectioncomponentthatusesinfraredthermalimagingprinciplestoobservethe
Earthinspacetodeterminethesatellite’saitude[5,6].TheEarthsimulatorneedstosim-
ulatetherelevantstates,suchasthesizeofthehorizoncircleandtheradiancedifference
oftheEarthinspace,andsettheturntableparameterstosolveforthedifferencebetween
thesatelliteaitudeparametersoutputbytheEarthsensorandtheaitudeparameters
setbytheturntable.Then,itneedstosettheparametersofthesensorsothatthe
Figure 1. Infrared Earth simulator composition structure.
The purpose of the infrared Earth simulator is to complete the simulation of the Earth
on the ground so as to check the performance of the infrared Earth sensor and determine
whether its technical parameters are up to standard. The infrared Earth sensor is a satellite
attitude detection component that uses infrared thermal imaging principles to observe
the Earth in space to determine the satellite’s attitude [
5
,
6
]. The Earth simulator needs to
simulate the relevant states, such as the size of the horizon circle and the radiance difference
of the Earth in space, and set the turntable parameters to solve for the difference between
the satellite attitude parameters output by the Earth sensor and the attitude parameters set
Sensors 2023,23, 6908 3 of 16
by the turntable. Then, it needs to set the parameters of the sensor so that the measurement
error can be minimized. The working principle of the infrared Earth simulator designed in
this paper is shown in Figure 2.
Sensors2023,23,xFORPEERREVIEW3of15
measurementerrorcanbeminimized.TheworkingprincipleoftheinfraredEarthsimu-
latordesignedinthispaperisshowninFigure2.
Figure2.InfraredEarthsimulatorworkingprinciple.
ThecoreoftheinfraredEarthsimulatordesignisthetemperaturecontrolsystem,
whichaimstosimulatetheintensityoftheEarth’sradiationinspaceinthelaboratory.
Thetemperaturecontrolsystemmakestheradianceoftheblackbodylightsource(i.e.,the
Earthhotplate)reachtheradiancevalueoftheEarthproperthroughtheheatingdevice,
andthenitmakestheradianceoftheEarthcoldplateequaltothecosmicradiancevalue
throughthecoolingdevice[7].Bycontrollingtherelationshipbetweenthepositionofthe
hotplateandcoldplateintheEarthsimulator,theEarthasseenbyasatelliteintheback-
groundofspacecanbesimulatedinthelaboratory.
3.EarthSimulatorTem perat ureControlSystemDesign
3.1.TemperatureDetermination
TheEarth’stemperaturevarieswiththeseason,thelongitude,andthesunlightdi-
rection,andtheEarth’sradiationvaries[8,9].Inthe14µm~16µmband,theEarth’sradi-
ancereachesthemaximum(Arcticsummer)N
max
=6.2W/m
2
·Srandtheminimum(Arctic
winter)N
min
=3.7W/m
2
·Sr,sotheEarthsimulatorshouldmeettheradiationenergyinthis
range.TheradiationenergyofthepartoutsidetheEarthcoldplatesimulatestheradiative
propertiesofthespacebackground,andtheradiativeenergyofthepartinsidethecold
platesimulatestheradiativepropertiesoftheEarth.Thedifferencebetweentheradiation
energyofthesetwopartsshouldbetheradiatedenergyobtainedbytheinfraredEarth
sensorwhenthesatelliteisoperatinginspace,i.e.,Earth’sradiationenergyinrealspace
[10].
AsshowninFigure3,theEarthsimulatorisplacedinalaboratorywithanambient
temperatureof20°C.ThetemperatureoftheEarthcoldplateiscontrolledat20°C.Itis
necessarytodeterminetheinfraredradiationenergyoftheEarthhotplate,i.e.,todeter-
minethetemperatureofthehotplate.
Figure3.StructureoftheEarthsimulator.
TheradiationenergyofablackbodyiscalculatedaccordingtoPlanck’sradiation
equationforitsradiantexitance[11],asshowninEquation(1):
Figure 2. Infrared Earth simulator working principle.
The core of the infrared Earth simulator design is the temperature control system,
which aims to simulate the intensity of the Earth’s radiation in space in the laboratory. The
temperature control system makes the radiance of the blackbody light source (i.e., the Earth
hot plate) reach the radiance value of the Earth proper through the heating device, and then
it makes the radiance of the Earth cold plate equal to the cosmic radiance value through
the cooling device [
7
]. By controlling the relationship between the position of the hot plate
and cold plate in the Earth simulator, the Earth as seen by a satellite in the background of
space can be simulated in the laboratory.
3. Earth Simulator Temperature Control System Design
3.1. Temperature Determination
The Earth’s temperature varies with the season, the longitude, and the sunlight direc-
tion, and the Earth’s radiation varies [
8
,
9
]. In the 14
µ
m~16
µ
m band, the Earth’s radiance
reaches the maximum (Arctic summer) N
max
= 6.2 W/m
2·
Sr and the minimum (Arctic
winter) N
min
= 3.7 W/m
2·
Sr, so the Earth simulator should meet the radiation energy in
this range. The radiation energy of the part outside the Earth cold plate simulates the
radiative properties of the space background, and the radiative energy of the part inside
the cold plate simulates the radiative properties of the Earth. The difference between the
radiation energy of these two parts should be the radiated energy obtained by the infrared
Earth sensor when the satellite is operating in space, i.e., Earth’s radiation energy in real
space [10].
As shown in Figure 3, the Earth simulator is placed in a laboratory with an ambient
temperature of 20
◦
C. The temperature of the Earth cold plate is controlled at 20
◦
C. It is
necessary to determine the infrared radiation energy of the Earth hot plate, i.e., to determine
the temperature of the hot plate.
The radiation energy of a blackbody is calculated according to Planck’s radiation
equation for its radiant exitance [11], as shown in Equation (1):
M=Zλ2
λ1
C1
λ5(eC2/λT−1)dλ(1)
where
λλ
denotes the wavelength,
λ1λ1
and
λ2λ2
denote the lower and upper limits
of the wavelength, respectively, C
1C1
= 3.7418
×
10
−16
W
·
m
2
denotes the first radiation
constant, C
2C2
= 1.4338
×
10
−2
m
·
K denotes the second radiation constant, and T denotes
the temperature (K).
The radiation brightness can be calculated by the radiant exitance when, for the surface
radiation, its radiation brightness is:
N=M
π(2)
The correspondence between the temperature of the hot plate and the actual Earth’s
radiance calculated by MATLAB is shown in Figure 4. The radiant exitance is 38.9 W/m
2
,
which corresponds to a radiance of 12.4 W/m
2·
Sr. When the radiance of the cold plate is
Sensors 2023,23, 6908 4 of 16
taken to be 6.2 W/m
2·
Sr, the radiance of the hot plate is 18.6 W/m
2·
Sr, which corresponds
to a radiant exitance of 58.4 W/m
2
, and the temperature of the hot plate is 332.25 K, or
59.1
◦
C. When the radiance of the cold plate is taken to be 3.7 W/m
2·
Sr, the corresponding
hot plate temperature is 316.35 K, i.e., 44.2
◦
C. Considering the blackbody emissivity,
and to ensure that the infrared Earth sensor receives enough Earth radiation energy, the
temperature of the hot plate is designed to be continuously adjustable, the adjustment
range is 35 ◦C~85 ◦C, and the temperature distribution is required to be uniform.
Sensors2023,23,xFORPEERREVIEW3of15
measurementerrorcanbeminimized.TheworkingprincipleoftheinfraredEarthsimu-
latordesignedinthispaperisshowninFigure2.
Figure2.InfraredEarthsimulatorworkingprinciple.
ThecoreoftheinfraredEarthsimulatordesignisthetemperaturecontrolsystem,
whichaimstosimulatetheintensityoftheEarth’sradiationinspaceinthelaboratory.
Thetemperaturecontrolsystemmakestheradianceoftheblackbodylightsource(i.e.,the
Earthhotplate)reachtheradiancevalueoftheEarthproperthroughtheheatingdevice,
andthenitmakestheradianceoftheEarthcoldplateequaltothecosmicradiancevalue
throughthecoolingdevice[7].Bycontrollingtherelationshipbetweenthepositionofthe
hotplateandcoldplateintheEarthsimulator,theEarthasseenbyasatelliteintheback-
groundofspacecanbesimulatedinthelaboratory.
3.EarthSimulatorTemperatureControlSystemDesign
3.1.TemperatureDetermination
TheEarth’stemperaturevarieswiththeseason,thelongitude,andthesunlightdi-
rection,andtheEarth’sradiationvaries[8,9].Inthe14µm~16µmband,theEarth’sradi-
ancereachesthemaximum(Arcticsummer)N
max
=6.2W/m
2
·Srandtheminimum(Arctic
winter)N
min
=3.7W/m
2
·Sr,sotheEarthsimulatorshouldmeettheradiationenergyinthis
range.TheradiationenergyofthepartoutsidetheEarthcoldplatesimulatestheradiative
propertiesofthespacebackground,andtheradiativeenergyofthepartinsidethecold
platesimulatestheradiativepropertiesoftheEarth.Thedifferencebetweentheradiation
energyofthesetwopartsshouldbetheradiatedenergyobtainedbytheinfraredEarth
sensorwhenthesatelliteisoperatinginspace,i.e.,Earth’sradiationenergyinrealspace
[10].
AsshowninFigure3,theEarthsimulatorisplacedinalaboratorywithanambient
temperatureof20°C.ThetemperatureoftheEarthcoldplateiscontrolledat20°C.Itis
necessarytodeterminetheinfraredradiationenergyoftheEarthhotplate,i.e.,todeter-
minethetemperatureofthehotplate.
Figure3.StructureoftheEarthsimulator.
TheradiationenergyofablackbodyiscalculatedaccordingtoPlanck’sradiation
equationforitsradiantexitance[11],asshowninEquation(1):
Figure 3. Structure of the Earth simulator.
Sensors2023,23,xFORPEERREVIEW4of15
2
2
1
1
C/ T
5(e 1)
C
M
d
(1)
whereλ
denotesthewavelength,λ11
andλ22
denotethelowerandupperlimitsof
thewavelength,respectively,C11C=3.7418×10−16W·m2denotesthefirstradiationcon-
stant,C22C=1.4338×10−2m·Kdenotesthesecondradiationconstant,andTdenotesthe
temperature(K).
Theradiationbrightnesscanbecalculatedbytheradiantexitancewhen,forthesur-
faceradiation,itsradiationbrightnessis:
M
N
(2)
ThecorrespondencebetweenthetemperatureofthehotplateandtheactualEarth’s
radiancecalculatedbyMATLABisshowninFigure4.Theradiantexitanceis38.9W/m2,
whichcorrespondstoaradianceof12.4W/m2·Sr.Whentheradianceofthecoldplateis
takentobe6.2W/m2·Sr,theradianceofthehotplateis18.6W/m2·Sr,whichcorresponds
toaradiantexitanceof58.4W/m2,andthetemperatureofthehotplateis332.25K,or59.1
°C.Whentheradianceofthecoldplateistakentobe3.7W/m2·Sr,thecorrespondinghot
platetemperatureis316.35K,i.e.,44.2°C.Consideringtheblackbodyemissivity,andto
ensurethattheinfraredEarthsensorreceivesenoughEarthradiationenergy,thetemper-
atureofthehotplateisdesignedtobecontinuouslyadjustable,theadjustmentrangeis
35°C~85°C,andthetemperaturedistributionisrequiredtobeuniform.
Figure4.Radianceversustemperature.
3.2.TemperatureControlAlgorithm
3.2.1.FuzzyPIDControlAlgorithm
ThroughtheanalysisoftemperaturechangesintheEarthsimulatorafterheating,it
isknownthatthesystemisalargeinertiaandlargehysteresissystem;thedynamicchar-
acteristicsarenoteasytograsp,anditisdifficulttoestablishanaccuratemathematical
model.Therefore,usingonlythetraditionalPIDcontrollercontrolsystemoftenleadsto
disadvantages,suchaslargesystemovershootandalongtransitiontime[12].
Tocompensateforthesedeficiencies,weuseafuzzyPIDcontrolalgorithminthis
paper.Theessenceistoobtainthebestcontrolperformanceofthesystembyautomati-
callyadjustingthePIDparameters[13].Thedeviationamounteandthedeviationchange
ecareusedasinputvariables,andp
K
,i
Kandd
Kareoutputvariables.Bycontin-
uouslydetectingeandec,thevaluesofp
K
,i
K,andd
Kareadjustedaccordingto
thefuzzyrulesandthenoutputtothePIDcontrollertoobtainthreenewparameters.The
Figure 4. Radiance versus temperature.
Sensors 2023,23, 6908 5 of 16
3.2. Temperature Control Algorithm
3.2.1. Fuzzy PID Control Algorithm
Through the analysis of temperature changes in the Earth simulator after heating,
it is known that the system is a large inertia and large hysteresis system; the dynamic
characteristics are not easy to grasp, and it is difficult to establish an accurate mathematical
model. Therefore, using only the traditional PID controller control system often leads to
disadvantages, such as large system overshoot and a long transition time [12].
To compensate for these deficiencies, we use a fuzzy PID control algorithm in this
paper. The essence is to obtain the best control performance of the system by automatically
adjusting the PID parameters [
13
]. The deviation amount e and the deviation change ec
are used as input variables, and
∆Kp
,
∆Ki
and
∆Kd
are output variables. By continuously
detecting e and ec, the values of
∆Kp
,
∆Ki
, and
∆Kd
are adjusted according to the fuzzy
rules and then output to the PID controller to obtain three new parameters. The output
quantity of the controller is continuously updated to finally find the best combination of
Kp,Ki, and Kd[14,15]. The principle of fuzzy PID control is shown in Figure 5.
Sensors2023,23,xFORPEERREVIEW5of15
outputquantityofthecontrolleriscontinuouslyupdatedtofinallyfindthebestcombina-
tionofp
K
,
i
K
,and
d
K
[14,15].TheprincipleoffuzzyPIDcontrolisshowninFigure5.
Figure5.FuzzyPIDcontrolprinciplediagram.
Accordingtotheinputrandtheoutputyofthetemperaturecontrolsystem,selecte,
ecwithp
K
,
i
K
,and
d
K
,whosefuzzylanguagevariablesareall[−6,6]andwhosefuzzy
subsetsareall{NB,NM,NS,ZO,PS,PM,PB},andestablishafuzzycontrolruletable
basedonthecontrolexperience.Forexample,iftheinputquantityeisPBandthedevia-
tionchangeecisNBatthesamemoment,thismeansthatthedifferencebetweentheactual
temperatureandthesettargetisgreat,buttheerrorisrapidlydecreasingandisnotad-
justedp
K
.IfeisPBandecisNS,itmeansthatthedifferencebetweentheactualtemper-
atureandthesettargetisverylarge,andthechangeoferrorreductionisnotobvious.
Then,theheatingpoweroftheheatingfilmneedstobereducedinordertoreducethe
processofincreasingtemperatureerror,sop
K
needstobereducedappropriately.
Inothercases,thefuzzyrulesfor p
K
,
i
K
,and
d
K
aredeterminedalongthe
samelines.Accordingtothefuzzyruletable,dynamicrectificationisperformedforp
K
,
i
K
,and
d
K
.Letp
K
,
i
K
,and
d
K
bethepre-tunedvaluesofp
K
,
i
K
,and
d
K
obtainedby
usingconventionalmethods[16].Selectappropriatefuzzificationanddefuzzification
methods,andthenthefuzzyPIDparametersare:
pp p
ii i
dd d
KK K
KK K
KK K
(3)
TheaffiliationfunctioncurvesareshowninFigure6.
Figure6.Affiliationfunctioncurve.
Figure 5. Fuzzy PID control principle diagram.
According to the input r and the output y of the temperature control system, select e, ec
with
Kp
,
Ki
, and
Kd
, whose fuzzy language variables are all [
−
6, 6] and whose fuzzy subsets
are all {NB, NM, NS, ZO, PS, PM, PB}, and establish a fuzzy control rule table based on the
control experience. For example, if the input quantity e is PB and the deviation change ec
is NB at the same moment, this means that the difference between the actual temperature
and the set target is great, but the error is rapidly decreasing and is not adjusted
Kp
. If e is
PB and ec is NS, it means that the difference between the actual temperature and the set
target is very large, and the change of error reduction is not obvious. Then, the heating
power of the heating film needs to be reduced in order to reduce the process of increasing
temperature error, so Kpneeds to be reduced appropriately.
In other cases, the fuzzy rules for
∆Kp
,
∆Ki
, and
∆Kd
are determined along the same
lines. According to the fuzzy rule table, dynamic rectification is performed for
Kp
,
Ki
,
and
Kd
. Let
K0p
,
K0
i
, and
K0
d
be the pre-tuned values of
Kp
,
Ki
, and
Kd
obtained by using
conventional methods [
16
]. Select appropriate fuzzification and defuzzification methods,
and then the fuzzy PID parameters are:
Kp=K0p+∆K0p
Ki=K0
i+∆K0
i
Kd=K0
d+∆K0
d
(3)
The affiliation function curves are shown in Figure 6.
Sensors 2023,23, 6908 6 of 16
Sensors2023,23,xFORPEERREVIEW5of15
outputquantityofthecontrolleriscontinuouslyupdatedtofinallyfindthebestcombina-
tionofp
K
,
i
K
,and
d
K
[14,15].TheprincipleoffuzzyPIDcontrolisshowninFigure5.
Figure5.FuzzyPIDcontrolprinciplediagram.
Accordingtotheinputrandtheoutputyofthetemperaturecontrolsystem,selecte,
ecwithp
K
,
i
K
,and
d
K
,whosefuzzylanguagevariablesareall[−6,6]andwhosefuzzy
subsetsareall{NB,NM,NS,ZO,PS,PM,PB},andestablishafuzzycontrolruletable
basedonthecontrolexperience.Forexample,iftheinputquantityeisPBandthedevia-
tionchangeecisNBatthesamemoment,thismeansthatthedifferencebetweentheactual
temperatureandthesettargetisgreat,buttheerrorisrapidlydecreasingandisnotad-
justedp
K
.IfeisPBandecisNS,itmeansthatthedifferencebetweentheactualtemper-
atureandthesettargetisverylarge,andthechangeoferrorreductionisnotobvious.
Then,theheatingpoweroftheheatingfilmneedstobereducedinordertoreducethe
processofincreasingtemperatureerror,sop
K
needstobereducedappropriately.
Inothercases,thefuzzyrulesfor p
K
,
i
K
,and
d
K
aredeterminedalongthe
samelines.Accordingtothefuzzyruletable,dynamicrectificationisperformedforp
K
,
i
K
,and
d
K
.Letp
K
,
i
K
,and
d
K
bethepre-tunedvaluesofp
K
,
i
K
,and
d
K
obtainedby
usingconventionalmethods[16].Selectappropriatefuzzificationanddefuzzification
methods,andthenthefuzzyPIDparametersare:
pp p
ii i
dd d
KK K
KK K
KK K
(3)
TheaffiliationfunctioncurvesareshowninFigure6.
Figure6.Affiliationfunctioncurve.
Figure 6. Affiliation function curve.
According to the characteristics of the Earth simulator temperature control system,
the first-order inertial pure hysteresis model is chosen to identify the system [
17
], and its
mathematical model is:
G(s) = Ke−τs
Ts +1(4)
The design uses an incremental PID control algorithm, whose output quantity u(t)
u(t)
is only related to the current cycle and the value of the first two cycles of the deviation
quantity e(t) e(t), which is a simple algorithm that can achieve good control effects [18].
The digital PID incremental type control formula is:
∆u(k) = Kp[e(k)−e(k−1)] + Kie(k) + Kd[e(k)−2e(k−1) + e(e−2)] (5)
That is:
∆u(k) = Kp∆e(k) + Kie(k) + Kd[∆e(k)−∆e(k−1)] (6)
3.2.2. MATLAB Simulation
To test whether the algorithm can effectively control the temperature variation of
the Earth simulator, simulation tests are conducted using the Simulink part of MATLAB.
According to the temperature control system, to establish a mathematical model, input the
step signal, ignore other signal interference, compare the traditional PID controller and
the fuzzy PID controller, respectively, input the signal processing, and observe the signal
change at the output; the overall structure is shown in Figure 7.
Sensors2023,23,xFORPEERREVIEW6of15
AccordingtothecharacteristicsoftheEarthsimulatortemperaturecontrolsystem,
thefirst-orderinertialpurehysteresismodelischosentoidentifythesystem[17],andits
mathematicalmodelis:
(s) 1
s
Ke
GTs
(4)
ThedesignusesanincrementalPIDcontrolalgorithm,whoseoutputquantityu(t)
(t)u
isonlyrelatedtothecurrentcycleandthevalueofthefirsttwocyclesofthedeviation
quantitye(t)
(t)e
,whichisasimplealgorithmthatcanachievegoodcontroleffects[18].
ThedigitalPIDincrementaltypecontrolformulais:
(k) [ ( ) (k 1)] ( ) [ ( ) 2 ( 1) ( 2)]
pid
u K ek e Kek K ek ek ee
(5)
Thatis:
(k) ( ) ( ) [ ( ) ( 1)]
pid
u K ek Kek K ek ek
(6)
3.2.2.MATLABSimulation
Totestwhetherthealgorithmcaneffectivelycontrolthetemperaturevariationofthe
Earthsimulator,simulationtestsareconductedusingtheSimulinkpartofMATLAB.Ac-
cordingtothetemperaturecontrolsystem,toestablishamathematicalmodel,inputthe
stepsignal,ignoreothersignalinterference,comparethetraditionalPIDcontrollerand
thefuzzyPIDcontroller,respectively,inputthesignalprocessing,andobservethesignal
changeattheoutput;theoverallstructureisshowninFigure7.
Figure7.Systemmodelbuilding.
WhentheinitialEarthhotplatetemperaturevalueissetto20°Candthetargettem-
peratureis85°C(thetemperatureoutputcurveoftheScopemoduleinSimulinkisshown
inFigure8),thebluelineisthetraditionalPIDcontrolcurve,andtheredlineisthefuzzy
PIDcontroleffectcurve.AccordingtotheEarthsimulatortemperaturecontrolsystemin-
dicators,thetraditionalPIDhasalargeamountofovershoot,amaximumtemperatureof
morethan95°C,andafuzzycontrolofthemaximumtemperatureofabout90°C,andthe
amountofovershootisreducedby5°C.ThetraditionalPIDtemperaturecontrolisaround
86°C,andthefuzzyPIDcontrolisaround85°C,whichimprovestheaccuracybyabout
1°Cincomparison.And,theresponsetimeisabout0.5minfaster.Thisconfirmsthefea-
sibilityandeffectivenessofapplyingthealgorithmtothetemperaturecontroloftheEarth
simulator.
Figure 7. System model building.
When the initial Earth hot plate temperature value is set to 20
◦
C and the target
temperature is 85
◦
C (the temperature output curve of the Scope module in Simulink is
Sensors 2023,23, 6908 7 of 16
shown in Figure 8), the blue line is the traditional PID control curve, and the red line is the
fuzzy PID control effect curve. According to the Earth simulator temperature control system
indicators, the traditional PID has a large amount of overshoot, a maximum temperature
of more than 95 ◦C, and a fuzzy control of the maximum temperature of about 90 ◦C, and
the amount of overshoot is reduced by 5
◦
C. The traditional PID temperature control is
around 86
◦
C, and the fuzzy PID control is around 85
◦
C, which improves the accuracy by
about 1
◦
C in comparison. And, the response time is about 0.5 min faster. This confirms
the feasibility and effectiveness of applying the algorithm to the temperature control of the
Earth simulator.
Sensors2023,23,xFORPEERREVIEW7of15
Figure8.FuzzyPIDandtraditionalPIDcontrolresponsecurve.
3.3.TemperatureControlModuleDesign
3.3.1.ElectricHeatFilmHeatingModule
ThemainbodyoftheEarthhotplateisdesignedwithanaluminumdiscbecauseof
itslowdensityandbecauseitiseasytouseontheturntableandhasgoodheattransfer
performance;itisalsoeasytoensureuniformtemperaturewhenheating.Thefrontsur-
faceofthehotplateistreatedwithablackanodicoxidecoatingtoimprovetheemissivity,
andtherearsurfaceisanelectricheatingfilm.
Toensurethetemperatureuniformityofthehotplate,theelectricheatingfilmisdi-
videdintotwoparts:themainheatingfilmandauxiliaryheatingfilms.Themainheating
filmisheatedextensivelytomakeitstemperaturereachtherequiredtemperatureandto
provideaconstanttemperature,whiletheauxiliaryheatingfilmsensurethatthehotplate
isheatedevenly.Inordertoensuretheaccuracyofthetemperaturecontrolofthehot
plate,multiplethermostatsareadoptedtoachieveclosed-loopcontroloftheblackbody.
Thatis,theheatingfilmisdividedintoseveraluniformindependentunits,andthetem-
peratureofeachunitistestedandsetseparatelytomakethehotplatewarmupsothatits
temperatureremainsconstantatacertainsetvalueintherangeof35°C~85°C.
Thismethodcanmanipulatethetemperatureofeachpartindividually,whichfacili-
tatesthecompletionofthehotplatetemperatureuniformitybeerthan±0.5°Cindex.
Whentheelectricheatingfilmstopsheating,thehotplateiscooleddownbytheambient
temperatureandthefansinfrontofthecoldplate.And,duetothecontinuousdetection
ofthetemperaturesensor,whenthetemperaturedoesnotmeettheconditions,thehot
plateisheatedsoastoachievethepurposeofcontrollingthetemperatureofthehotplate.
Accordingtothetheoryofconvectiveheatexchangeinasmallspace,theheatex-
changeonthesurfaceofthehotplateisdeterminedbythefollowingequation:
()
mhc
k
qtt
b
(7)
TheRayleighcoefficient
a
R
associatedwith
m
q
is:
3
()
hc
a
gt t L
Rva
(8)
where
a
isthethermalconductivityofthehotplate,
istheexpansioncoeffi-
cientofthehotplate,
L
isthecharacteristiclength,
v
isthematerialviscositycoeffi-
cient,
h
t
isthetemperatureofthehotplateforradiationheattransfer,and
c
t
isthera-
diationambienttemperature.
Iftheheattransfercoefficientis
k
and
k
=0.035413W/m·°C,theheatexchange
Q
is:
Figure 8. Fuzzy PID and traditional PID control response curve.
3.3. Temperature Control Module Design
3.3.1. Electric Heat Film Heating Module
The main body of the Earth hot plate is designed with an aluminum disc because of
its low density and because it is easy to use on the turntable and has good heat transfer
performance; it is also easy to ensure uniform temperature when heating. The front surface
of the hot plate is treated with a black anodic oxide coating to improve the emissivity, and
the rear surface is an electric heating film.
To ensure the temperature uniformity of the hot plate, the electric heating film is
divided into two parts: the main heating film and auxiliary heating films. The main heating
film is heated extensively to make its temperature reach the required temperature and to
provide a constant temperature, while the auxiliary heating films ensure that the hot plate
is heated evenly. In order to ensure the accuracy of the temperature control of the hot plate,
multiple thermostats are adopted to achieve closed-loop control of the black body. That is,
the heating film is divided into several uniform independent units, and the temperature of
each unit is tested and set separately to make the hot plate warm up so that its temperature
remains constant at a certain set value in the range of 35 ◦C~85 ◦C.
This method can manipulate the temperature of each part individually, which facil-
itates the completion of the hot plate temperature uniformity better than
±
0.5
◦
C index.
When the electric heating film stops heating, the hot plate is cooled down by the ambient
temperature and the fans in front of the cold plate. And, due to the continuous detection of
the temperature sensor, when the temperature does not meet the conditions, the hot plate
is heated so as to achieve the purpose of controlling the temperature of the hot plate.
According to the theory of convective heat exchange in a small space, the heat exchange
on the surface of the hot plate is determined by the following equation:
qm=kε
b(th−tc)(7)
Sensors 2023,23, 6908 8 of 16
The Rayleigh coefficient Raassociated with qmis:
Ra=βg(th−tc)L3
va (8)
where
a
is the thermal conductivity of the hot plate,
β
is the expansion coefficient of the
hot plate,
L
is the characteristic length,
v
is the material viscosity coefficient,
th
is the
temperature of the hot plate for radiation heat transfer, and
tc
is the radiation ambient
temperature.
If the heat transfer coefficient is
kε
and
kε
= 0.035413 W/m
·◦
C, the heat exchange
Q
is:
Q=Akε(th−tc)
D(9)
where
A
is the area of the cold plate aperture (effective radiation area),
A=πD2
4
, and
D
is
the effective radiation diameter of the hot plate (determined by the cold plate).
The heating power required is:
P=Akε(th−tc)mhotdt
Ddτ(10)
where
mhot
is the mass of the hot plate,
dt
is the adjustable range of the hot plate temperature,
and dτis the heating time.
According to the heating requirements, the heating film heating power can be calcu-
lated to be about 70 W, and the appropriate heating film can be selected.
3.3.2. Semiconductor Cooling Module
A TEC semiconductor cooling chip is a device based on the thermoelectric effect,
which has the advantages of easy control, low thermal inertia, a fast cooling rate, and high
power [
19
]. Its basic element is a thermocouple; the formation of multiple P–N junctions
in series forms a thermocouple. Furthermore, an insulating ceramic sheet is connected to
both ends of the thermocouple to form the most basic semiconductor cooling sheet. In the
semiconductor cold junction, the current flows from the N to the P, where the temperature
drops and heat is absorbed from the environment; in the hot junction, the current flows
from the P to the N, and the temperature rises, releasing heat.
The cold end of the cooling chip is attached to the Earth cold plate to cool it down.
The installation of cooling fins and fans for forced cooling at the hot end can ensure heat
dissipation at the hot end with the aim of improving the efficiency of the cooling chip, as
shown in Figure 9[
20
]. The hot-end fins are made of aluminum, which has good heat
transfer and is made into a dense tooth design to increase the contact area with the air.
Then, by setting a fan to speed up the air flow, this helps a lot with heat dissipation.
Sensors2023,23,xFORPEERREVIEW8of15
()
hc
Ak t t
QD
(9)
where
A
istheareaofthecoldplateaperture(effectiveradiationarea),
2
4
D
A
,and
D
istheeffectiveradiationdiameterofthehotplate(determinedbythecoldplate).
Theheatingpowerrequiredis:
()
h c hot
Ak t t m dt
PDd
(10)
where
hot
m
isthemassofthehotplate,
dt
istheadjustablerangeofthehotplatetem-
perature,and
d
istheheatingtime.
Accordingtotheheatingrequirements,theheatingfilmheatingpowercanbecalcu-
latedtobeabout70W,andtheappropriateheatingfilmcanbeselected.
3.3.2.SemiconductorCoolingModule
ATECsemiconductorcoolingchipisadevicebasedonthethermoelectriceffect,
whichhastheadvantagesofeasycontrol,lowthermalinertia,afastcoolingrate,andhigh
power[19].Itsbasicelementisathermocouple;theformationofmultipleP–Njunctions
inseriesformsathermocouple.Furthermore,aninsulatingceramicsheetisconnectedto
bothendsofthethermocoupletoformthemostbasicsemiconductorcoolingsheet.Inthe
semiconductorcoldjunction,thecurrentflowsfromtheNtotheP,wherethetemperature
dropsandheatisabsorbedfromtheenvironment;inthehotjunction,thecurrentflows
fromthePtotheN,andthetemperaturerises,releasingheat.
ThecoldendofthecoolingchipisaachedtotheEarthcoldplatetocoolitdown.
Theinstallationofcoolingfinsandfansforforcedcoolingatthehotendcanensureheat
dissipationatthehotendwiththeaimofimprovingtheefficiencyofthecoolingchip,as
showninFigure9[20].Thehot-endfinsaremadeofaluminum,whichhasgoodheat
transferandismadeintoadensetoothdesigntoincreasethecontactareawiththeair.
Then,byseingafantospeeduptheairflow,thishelpsalotwithheatdissipation.
Figure9.Hot-endaircoolingdiagram.
ThetemperaturecontrolsystemoftheEarthsimulatorcontrolsthetemperatureof
boththehotandcoldplatessothatthetemperaturedifferencebetweenthetwoissimilar
tothedifferenceinradiancebetweentheEarthandspaceduringtheoperationofthesat-
ellite.Thebackofthecoldplatehasaheatsourceprovidedbythehotplate,sothereisno
needtoconsiderheating,onlycooling.Furthermore,addingheatinsulationfilmtothe
backoftheEarthcoldplatereducestheimpactofthehotplatetemperature.Forcooling,
weusetheTECsemiconductorcoolingringmethod,asshowninFigure10.Byconstantly
checkingthetemperatureofthecoldplate,thepowerofeachcoolingplateiscontrolled
Figure 9. Hot-end air cooling diagram.
Sensors 2023,23, 6908 9 of 16
The temperature control system of the Earth simulator controls the temperature of
both the hot and cold plates so that the temperature difference between the two is similar to
the difference in radiance between the Earth and space during the operation of the satellite.
The back of the cold plate has a heat source provided by the hot plate, so there is no need to
consider heating, only cooling. Furthermore, adding heat insulation film to the back of the
Earth cold plate reduces the impact of the hot plate temperature. For cooling, we use the
TEC semiconductor cooling ring method, as shown in Figure 10. By constantly checking
the temperature of the cold plate, the power of each cooling plate is controlled to obtain
the desired temperature. And, it is well integrated with the Earth simulator by using the
embedded precise control method.
Sensors2023,23,xFORPEERREVIEW9of15
toobtainthedesiredtemperature.And,itiswellintegratedwiththeEarthsimulatorby
usingtheembeddedprecisecontrolmethod.
Figure10.Semiconductorchipposition.
Undergeneraloperatingconditions,letthetemperatureofthecoldendofthecooling
chipbe
c
T
,andthemagnitudeofitscoolingcoefficientdoesnotchangeduetothechange
intemperature[21].IftheheatgeneratedbytheThomsoneffectisneglected,thenaccord-
ingtothefirstlawofthermodynamics,wecanobtain:
hc
QQP
(11)
ThePeltierheatgeneratedatthecoldendofthesemiconductor,i.e.,theidealcooling
capacity,canbeexpressedas:
,
()
pc P N C PN C
Q I IT IT
(12)
DuetotheexistenceofirreversibleJouleheatinthecircuit,someheatwillflowtothe
coldendofthecoolingchipintheclosedcircuit,sotheheatgeneratedbyJouleheatcon-
ductionshouldberemovedfromtheidealcoolingcapacity,i.e.,theactualcoolingcapacity
is:
2
,
11
22
cpc JPNC
QQ Q IT IR
(13)
where
J
Q
istheirreversibleJouleheat.
Then,theactualheatdissipationofthecoolingchipis:
2
,
11
22
hph JPNC
QQ Q IT IR
(14)
Takingintoaccountthecoolingcapacityandtherequireddriverequirements,the
maximumtemperaturedifferencebetweenthehotandcoldends,theinstallationsize,and
otherfactors,weselectedtheTEC1-19908model,anditsspecificparametersareshownin
Table1.
Table1.TECcoolingfilmtypeandeachparameter.
TECModel
Max.Temperature
<break>Difference
Current(A)
Max.Temperature
<break>Difference
Voltage(V)
Max.Temperature
Difference(°C)
Max.Cooling
Power(W)
Dimension
(mm)
TemperatureUse
Range(°C)
TEC1-199088.024.66811140×40−60~200
4.TemperatureControlSystemSimulationResults
Toimplementthesimulatortemperaturecontrolsystem,thispaperusesANSYS
WorkbenchsoftwarefortemperatureanalysisoftheEarthcoldplateandshowstheeffect
oftheEarthhotplatetemperatureonthetemperatureofthecoldplatethroughthe
Figure 10. Semiconductor chip position.
Under general operating conditions, let the temperature of the cold end of the cooling
chip be
Tc
, and the magnitude of its cooling coefficient does not change due to the change in
temperature [
21
]. If the heat generated by the Thomson effect is neglected, then according
to the first law of thermodynamics, we can obtain:
Qh=Qc+P(11)
The Peltier heat generated at the cold end of the semiconductor, i.e., the ideal cooling
capacity, can be expressed as:
Qp,c=πI= (αP−αNITC) = αPN ITC(12)
Due to the existence of irreversible Joule heat in the circuit, some heat will flow to
the cold end of the cooling chip in the closed circuit, so the heat generated by Joule heat
conduction should be removed from the ideal cooling capacity, i.e., the actual cooling
capacity is:
Qc=Qp,c−1
2QJ=αPN ITC−1
2I2R(13)
where QJis the irreversible Joule heat.
Then, the actual heat dissipation of the cooling chip is:
Qh=Qp,h+1
2QJ=αPN ITC+1
2I2R(14)
Taking into account the cooling capacity and the required drive requirements, the
maximum temperature difference between the hot and cold ends, the installation size, and
other factors, we selected the TEC1-19908 model, and its specific parameters are shown in
Table 1.
Sensors 2023,23, 6908 10 of 16
Table 1. TEC cooling film type and each parameter.
TEC Model
Max.
Temperature
Difference
Current (A)
Max.
Temperature
Difference
Voltage (V)
Max.
Temperature
Difference (◦C)
Max. Cooling
Power (W)
Dimension
(mm)
Temperature
Use Range (◦C)
TEC1-19908 8.0 24.6 68 111 40 ×40 −60~200
4. Temperature Control System Simulation Results
To implement the simulator temperature control system, this paper uses ANSYS Work-
bench software for temperature analysis of the Earth cold plate and shows the effect of the
Earth hot plate temperature on the temperature of the cold plate through the temperature
map. For better temperature analysis, we built a simulation model based on the actual
Earth simulator, as shown in Figure 11.
Sensors2023,23,xFORPEERREVIEW10of15
temperaturemap.Forbeertemperatureanalysis,webuiltasimulationmodelbasedon
theactualEarthsimulator,asshowninFigure11.
Figure11.ActualEarthsimulator.
DuringthemodelingprocessusingSOLIDWORKS(2017),themodelwasappropri-
atelysimplifiedinordertoreducecomputerworkloadandtoimprovecomputingeffi-
ciency,andthefinalresultisshowninFigure12.
Figure12.Earthsimulatormodel.
ImportthemodelmadewithSOLIDWORKSintoANSYSWorkbenchanddefinethe
materialpropertiesofthemodel.Themodelasawholeismadeofaluminumalloy,and
thesurfaceofthemetaldiscisblackanodizedtoimprovethesurfaceemissivityandto
makeitahotplatewithuniformheatdissipation.Themeshingofthemodelisshownin
Figure13.Themeshdivisionhasadecisiveinfluenceonthefinalstructuralanalysis,soit
isimportanttoensurethequalityofthedividedmeshcells.Therefore,weensurethatthe
qualityofthedividedgridcellsis>0.3.
Figure13.Earthsimulatormeshing.
Figure 11. Actual Earth simulator.
During the modeling process using SOLIDWORKS (2017), the model was appropri-
ately simplified in order to reduce computer workload and to improve computing efficiency,
and the final result is shown in Figure 12.
Sensors2023,23,xFORPEERREVIEW10of15
temperaturemap.Forbeertemperatureanalysis,webuiltasimulationmodelbasedon
theactualEarthsimulator,asshowninFigure11.
Figure11.ActualEarthsimulator.
DuringthemodelingprocessusingSOLIDWORKS(2017),themodelwasappropri-
atelysimplifiedinordertoreducecomputerworkloadandtoimprovecomputingeffi-
ciency,andthefinalresultisshowninFigure12.
Figure12.Earthsimulatormodel.
ImportthemodelmadewithSOLIDWORKSintoANSYSWorkbenchanddefinethe
materialpropertiesofthemodel.Themodelasawholeismadeofaluminumalloy,and
thesurfaceofthemetaldiscisblackanodizedtoimprovethesurfaceemissivityandto
makeitahotplatewithuniformheatdissipation.Themeshingofthemodelisshownin
Figure13.Themeshdivisionhasadecisiveinfluenceonthefinalstructuralanalysis,soit
isimportanttoensurethequalityofthedividedmeshcells.Therefore,weensurethatthe
qualityofthedividedgridcellsis>0.3.
Figure13.Earthsimulatormeshing.
Figure 12. Earth simulator model.
Sensors 2023,23, 6908 11 of 16
Import the model made with SOLIDWORKS into ANSYS Workbench and define the
material properties of the model. The model as a whole is made of aluminum alloy, and the
surface of the metal disc is black anodized to improve the surface emissivity and to make it
a hot plate with uniform heat dissipation. The meshing of the model is shown in Figure 13.
The mesh division has a decisive influence on the final structural analysis, so it is important
to ensure the quality of the divided mesh cells. Therefore, we ensure that the quality of the
divided grid cells is >0.3.
Sensors2023,23,xFORPEERREVIEW10of15
temperaturemap.Forbeertemperatureanalysis,webuiltasimulationmodelbasedon
theactualEarthsimulator,asshowninFigure11.
Figure11.ActualEarthsimulator.
DuringthemodelingprocessusingSOLIDWORKS(2017),themodelwasappropri-
atelysimplifiedinordertoreducecomputerworkloadandtoimprovecomputingeffi-
ciency,andthefinalresultisshowninFigure12.
Figure12.Earthsimulatormodel.
ImportthemodelmadewithSOLIDWORKSintoANSYSWorkbenchanddefinethe
materialpropertiesofthemodel.Themodelasawholeismadeofaluminumalloy,and
thesurfaceofthemetaldiscisblackanodizedtoimprovethesurfaceemissivityandto
makeitahotplatewithuniformheatdissipation.Themeshingofthemodelisshownin
Figure13.Themeshdivisionhasadecisiveinfluenceonthefinalstructuralanalysis,soit
isimportanttoensurethequalityofthedividedmeshcells.Therefore,weensurethatthe
qualityofthedividedgridcellsis>0.3.
Figure13.Earthsimulatormeshing.
Figure 13. Earth simulator meshing.
The temperature field using the transient heat transfer model is shown in Figure 14;
set the ambient temperature (initial temperature) to 20
◦
C for the back of the hot plate
(heating film location) to add the temperature required for the experiment (85
◦
C added
in the experiment). And, add heat flow to the backside of the cold plate by the above
calculation to mimic the gas heat transfer between the hot plate and the cold plate. The
time of the experiment was stretched to observe the effect of heating the hot plate from the
ambient temperature to the maximum temperature and the temperature of the hot plate
stabilized at 85 ◦C on the cold plate, respectively.
Sensors2023,23,xFORPEERREVIEW11of15
Th
et
emperaturefieldusingthetransientheattransfermodelisshowninFigure14;
settheambienttemperature(initialtemperature)to20°Cforthebackofthehotplate
(heatingfilmlocation)toaddthetemperaturerequiredfortheexperiment(85°Cadded
intheexperiment).And,addheatflowtothebacksideofthecoldplatebytheabovecal-
culationtomimicthegasheattransferbetweenthehotplateandthecoldplate.Thetime
oftheexperimentwasstretchedtoobservetheeffectofheatingthehotplatefromthe
ambienttemperaturetothemaximumtemperatureandthetemperatureofthehotplate
stabilizedat85°Conthecoldplate,respectively.
Figure14.ANSYStransientheattransfermodel.
First,whenthesemiconductorcoolingchipisnotworking,determinetherefrigera-
tionchipworkingenvironmenttemperature(onlyaircooling).Convectionwasaddedto
thelocationofthecoolingchipinANSYSWorkbenchtosimulatetheforcedaircooling
devicedescribedabove.Theconvectioncoefficientisabout100W/m
2
·°C.
Aftertheheatingprocesshasgraduallystabilizedandtheheatingandcoolinglinks
intheEarthsimulatorhavestabilized(about5min),wecanviewthetemperaturegraph,
asshowninFigure15.Thetemperatureofthecoldplateismaintainedroughlyat62.632
°C.Accordingtotheuniversalworkingtemperatureofthesemiconductorcoolingchip,
whichis70°Cmaximum,itisknownthatthecoolingchipcanworknormallyintheen-
vironmentoftheEarthsimulator.
Figure15.Aircoolingtemperatureimpact.
Figure 14. ANSYS transient heat transfer model.
First, when the semiconductor cooling chip is not working, determine the refrigeration
chip working environment temperature (only air cooling). Convection was added to the
location of the cooling chip in ANSYS Workbench to simulate the forced air cooling device
described above. The convection coefficient is about 100 W/m2·◦C.
Sensors 2023,23, 6908 12 of 16
After the heating process has gradually stabilized and the heating and cooling links in
the Earth simulator have stabilized (about 5 min), we can view the temperature graph, as
shown in Figure 15. The temperature of the cold plate is maintained roughly at 62.632
◦
C.
According to the universal working temperature of the semiconductor cooling chip, which
is 70
◦
C maximum, it is known that the cooling chip can work normally in the environment
of the Earth simulator.
Sensors 2023, 23, x. hps://doi.org/10.3390/xxxxx www.mdpi.com/journal/sensors
15
16
Figure 15. Air cooling temperature impact.
Finally, the cooling capacity of the semiconductor cooling chip is calculated and added
to the cooling chip. The air cooling device and the cooling chip were made to work
simultaneously, and the results obtained are shown in Figure 16. The results show that the
semiconductor cooling inside the Earth simulator controls the temperature of the cold plate
at about 20.089 ◦C to meet the temperature control requirements.
Sensors 2023,23, 6908 13 of 16
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17
Figure 16. Overall temperature impact.
In order to make the image received by the Earth sensor clear and to reduce the
measurement error [
22
], the Earth needs to be observed as a uniformly heated disk so that
the temperature uniformity at the edge of the disk is better than
±
0.5
◦
C. The temperature
analysis shown in Figure 17 shows that the overall temperature uniformity of the hot
plate is better than ±0.3 ◦C when the heating film is heated on the back of the hot plate to
keep its temperature at 85
◦
C. It is higher than the index requirement and satisfies the test
conditions of the Earth sensors.
Sensors 2023,23, 6908 14 of 16
Sensors 2023, 23, x FOR PEER REVIEW 3 of 3
Figure 17. Earth hot plate temperature uniformity.
5. Conclusions
In this paper, a temperature control system based on semiconductor cooling technology
combined with air cooling is designed for the infrared Earth simulators for a turntable.
The temperature range of the Earth hot plate to be controlled is calculated by the Earth
radiation; a fuzzy PID-based control algorithm is adopted to improve the accuracy of the
Earth simulator. The feasibility of the design results for the temperature control system
is confirmed by software simulation, and the technical index requirements can be met.
Finally, the overall structure of the Earth simulator is designed to achieve miniaturization
and portability of the Earth simulator with guaranteed accuracy. New technologies are
provided for the development of Earth simulators.
This system also has some limitations, such as the higher noise of the air cooling,
higher power consumption, and the need for regular testing or replacement of the cooling
chip sheet. In the future, we will explore new cooling methods to minimize noise and
combine advanced sensing technologies and feedback algorithms to conserve resources.
In addition, we will conduct more extensive testing and optimization of semiconductor
cooling combined with air-cooling technology for a wide range of applications in different
types and sizes of infrared Earth simulators. The Earth simulator will be placed on a
five-axis turntable to calibrate and test specific data on the increased accuracy of the Earth
Sensors 2023,23, 6908 15 of 16
sensors. As aerospace technology continues to evolve, satellites will place increasing
demands on the Earth sensors they carry.
Author Contributions:
Conceptualization, J.L., L.W. and G.L.; methodology, J.L. and L.W.; software,
J.L.; validation, J.L., L.W. and S.M.; formal analysis, J.L.; investigation, J.L. and L.W.; resources,
J.L.; data curation, J.L.; writing—original draft preparation, J.L.; writing—review and editing, J.L.,
L.W., G.L. and S.M.; visualization, J.L.; supervision, L.W. and G.L.; project administration, J.L. and
L.W.; funding acquisition, L.W. All authors have read and agreed to the published version of the
manuscript.
Funding:
This research was funded by the Science and Technology Development Plan of Jilin Province
of China under Grant 20220201089GX.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
References
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