Thermal Dynamics Modeling of a 3D Wind Sensor Based on Hot Thin FilmAnemometry

Maria-Teresa Atienza,∗, Lukasz Kowalski, Sergi Gorreta, Vicente Jiménez, Manuel Domínguez-PumarMicro and Nano Technologies Group, Electronic Engineering Department. Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034

Barcelona, Spain

Abstract

The objective of this paper is to obtain time-varying models of the thermal dynamics of a 3D hot thin film anemometerfor Mars atmosphere. To this effect, a proof of concept prototype of the REMS (Rover Environmental Monitoring Station)wind sensor on board the Curiosity rover has been used. The self and cross-heating effects of the thermal structures havebeen characterized from open-loop measurements using Diffusive Representation. These models have been proven tobe suitable in the analysis of the thermal dynamics of the sensor under constant temperature operation employing thetools of Sliding Mode Controllers. This analysis allows to understand the long term heat diffusion processes in the wholestructure and how they may affect the raw output signals.

Key words: Diffusive representation, sliding mode controllers, time-varying systems, thermal sensors

1. Introduction

The objective of this paper is to obtain time-varyingthermal dynamics models using recent aplication of Diffu-sive Representation (DR), [1], of a proof of concept pro-totype of the REMS (Rover Environmental Monitoring5

Station) wind sensor. The REMS sensor suite is an instru-ment from the Mars Science Laboratory (MSL) on boardthe Curiosity rover that landed in Mars in 2012. REMSincluded humidity, pressure, temperature, radiation andwind velocity sensors [2, 3, 4]. In this paper, we used a10

prototype of the engineering model developed in 2008 thatled to the flight model which is currently on board of theCuriosity rover. The prototype is very similar in conceptand size to the flight model.

Wind and temperature sensors from the REMS Booms15

Spare Hardware have been refurbished into TWINS Booms,for NASA’s Insight mission, expected to be launched in

∗Corresponding authorEmail addresses: maria.teresa.atienza@upc.edu

(Maria-Teresa Atienza )

Figure 1: Photography of the proof of concept prototype of REMSwind sensor. One of the PCBs with a group of dice can be seen.

2018 [5]. The performance in terms of dynamic range andresolution has been enhanced in these wind and tempera-ture sensors. The same device concept, although including20

many significant changes in structure and number of sen-sors, is scheduled to fly in NASA’s Mars 2020 Rover, aspart of the wind sensor that will include the MEDA (MarsEnvironmental Dynamics Analyzer) instrument [6].

The main novelty of this paper resides in the application25

of diffusive representation to extract the thermal dynamicalmodels of complex space sensor structures such as thoseof the wind sensors in REMS, TWINS or MEDA, which,to the best knowledge of the authors, has never been done.

UPC 2D wind transducer

A B

D CEtemperature

difference ? T

Cold point

Hot point

A B

D CEtemperature

difference ΔT

Cold point

Hot point

PCB

Hot terminals:

dice A, B, C, D

Cold terminal:

die E

Temperaturesensing

airconvection

How it works ?

Because of the dice are thermally coupled with surrounding gas due the

natural and forced convection their thermal conductance is sensible for

wind velocity and wind direction.

GthA,B,C,D=f(Windspeed, Winddirection)

A

BC

D

Figure 2: Photography of a dice set over the PCB. The dice arenamed A, B, C and D.

Preprint submitted to Elsevier February 12, 2018

Rsens

Rheat

Rref

Figure 3: Zoom of one die, where the heating, sensing and referenceresistors are shown. In the experiments of this paper Rheat has beenused for heating and sensing temperature.

This modeling is very important for designing the control30

algorithm at the system level.All these wind sensors are based on thermal anemom-

etry, which is the method that has been used in multipleoccasions for the challenging task of sensing wind in Mars(CO2 atmosphere, low pressure in the range 6-12mBar and35

a large temperature dynamical range from 150K to 300K)[7, 8]. It consists in the detection of the wind velocityby measuring the power dissipated of a heated elementdue to forced convection. The wind velocity and directionin REMS wind sensor, is detected by measuring the tan-40

gential wind components at three points of a cylindricalsupporting structure (boom). This is done by measuringthe convection heat transfer of four silicon dice with plat-inum (Pt) resistors. These resistors are grouped in sets offour in a coplanar plane, to achieve 2D wind sensitivity.45

Full 3D direction is measured placing three of these setsat 120 to each other in the boom. These dice-sets areplaced on three PCBs (Printed Circuit Board). In Figure1, the boom used in the experimental setup with the viewof one of the resistors set on its PCB is shown. In Figure50

2, one of the three silicon dice sets can be seen , while inFigure 3 the resistors’ structure of one die is observed. Thedice are named, A,B,C and D. In this prototype the diceare placed on a supporting structure of Pyrex pillars toincrease thermal isolation to the boom.55

Diffusive Representation is a mathematical tool thatallows the description of a physical phenomena based ondiffusion, using state-space models of arbitrary order in thefrequency domain. It is appropiate for model extraction offractional systems, such as thermal [9, 10, 11] or electrical60

[12, 13, 14]. A first analysis of heat flow dynamics describedby diffusive representation in a hot thin film anemometerwas described in [1], where thermal models were obtainedfor a spherical 3D wind anemometer for different wind ve-locities. These models provide the temperature dynamics65

of the components of the system under study as a functionof the power delivered to the heat sources. On the otherhand, the time evolution under closed-loop operation (con-stant temperature control) was obtained using the theory ofSliding Mode Controllers (SMC) [15]. The necessary state-70

space models for the sliding mode analysis are providedfrom open-loop measurements at different wind velocitiesusing Diffusive Representation modeling. These state-spacemodels have proven to be very well suited for thermal ap-plications [9]. In [1], each thermal dynamics model was75

extracted from a constant wind speed experiment. In thispaper, however, the method is different, as the thermaldynamics models are extracted from a single experimentwith wind velocity switching due to the working principleof the wind tunnel used. Furthermore, the obtained models80

are more complex, since they include self and cross-heatingeffects across the different subsystems in the sensor.

The REMS wind sensor is operated under constanttemperature anemometry mode. This is achieved using athermal sigma-delta modulator, which places the system85

within the control surface determined by Temperature =constant in finite time, which is followed by a sliding motion.It must be noted that in the case that concern us, theanalysis of the resulting dynamics is performed under theinfinite sampling frequency approximation using the tools90

of equivalent control typical of SMC.The experiments described in this paper, were carried

out at CAB (Center for Astrobiology, INTA-CSIC) facili-ties in Madrid, Spain. For the experimental setup, a fivemeter linear wind tunnel has been used. The wind tunnel95

operation mode is different from the hypobaric chamberused in [1] where a fan set the wind velocities. In this case,the tunnel has a rail inside where the sensor is positioned.The equivalent Mars velocities are achieved by moving thesensor through the rail. The sensor support also has a100

pan and tilt system which provides different pitch and yawpositions for the boom. Figure 4 shows the wind sensoremployed in the experimental setup inside the tunnel atthe start position, and with pitch and yaw angles set to 0.

DR and SMC are used together and are explained in105

Section 2 of this paper. Section 3 describes the sensor andthe experimental setup. Three main experimental resultsare shown in section 4. Firstly, in 4.1 diffusive models ofthe dice have been obtained for different wind conditions.Secondly, the heating of the boom due to the heating of the110

dice has been characterized in paragraph 4.2. The thirdexperiment shown in subsection 4.3, consists in predictingthe closed-loop behaviour from the DR models of the diceobtained previously. Finally, the conclusions of the paperare presented in section 5.115

2. Diffusive Representation and Sliding Mode Con-trollers

This section describes briefly the theoretical groundsand tools of diffusive representation and sliding mode con-trollers used in the sensor thermal dynamics analysis.120

2

2.1. Diffusive RepresentationDiffusive Representation theory allows obtaining ex-

act and approximate state realizations of a wide classof integral operators of rational or non-rational nature.Given a non-rational transfer function, H(p), associated125

with a convolution causal operator denoted by H(∂t), thediffusive realization of this operator is expressed by thefollowing input (u) – output (y) state space realization ofu 7−→ y = H(∂t)u = h ∗ u of the form [13]:

∂ψ(ξ,t)∂t = −ξψ(ξ, t) + u(t), ψ(ξ, 0) = 0

y(t) =∫∞

0 η(ξ, t)ψ(ξ, t)dξ (1)

where ξ ∈ R is frequency, η(ξ, t) is the diffusive symbol ofH(∂t) that represents the system behaviour, i.e., how thesystem evolves as a function of the input signal, u(t). Thestate-variable ψ(ξ, t) is a time-frequency representationof the input, called the diffusive representation of u(t) .The diffusive symbol is a solution of the following integralequation directly obtained from Laplace transform (withrespect to t) [13]:

H(jω) =∫ ∞

0

η(ξ)jω + ξ

dξ, ω ∈ R∗ (2)

When modeling thermally a device, two distinguisableeffects can be considered: the self-heating effect, due to theinjection of power into the heaters of the own device, andthe cross-heating effect, consequence of injecting power intoheat sources in parts of the structure different from the onein which temperature is sensed. If we consider four similardevices thermally coupled, the temperature of each devicewhen the four of them are working simultaneously will bethe result of the superposition of the self and cross-heatingeffects. The modeling of the four coupled devices of Figure2, A, B, C and D, will consider four inputs (PA(t), PB(t),PC(t) and PD(t)) and four outputs (TA(t), TB(t), TC(t) andTD(t)). Besides, to be able to handle experimental data, adiscrete approximation of H(∂t) can be built discretizingthe continuous variable ξ into ξk1≤k≤K , where K is theorder of the discretized model. Now equation (2) remainslike this:

H(jω) =K∑k

ηkjω + ξk

dξk, ω ∈ R∗ (3)

from which the bandwidth of the model can be extracted130

from the diffusive symbol. The diffusive representationequations are the followings:

• Self-Heating. Power only in device X, the rest of thestructure is passive

dψXk (t)dt = −ξkψXk (t) + PX(t), ψXk (0) = 0 (4)

where X = A,B,C or D is the corresponding device.135

• Cross-Heating. Power only in device Y, the rest ofthe structure is passive

dφYj (t)dt = −υjφYj (t) + PY (t), φYj (0) = 0 (5)

for j = 1 . . . J , and Y = A,B,C or D. J is the modelorder and υj is the discretized frequency mesh forthe cross-heating models.140

The frequency discretization for the self-heating effect,ξk, may be different to the frequency mesh of the cross-heating effect, υj . Their model orders can also be different:K for the self-heating case and J for the cross-heating.In general, self and cross responses may be very different.145

As the frequency mesh is chosen with respect to the timeresponse characteristics of the devices, they will be differentwhen considering the self or the cross effects. The frequencymesh of the diffusive symbols, ξk and υj , is set accordingto the spectral contents of the dynamic characteristics of150

the system. The frequency sets are usually geometricallyspaced. The minimum frequency is set to fmin = U/T ,where T is the total duration of the experiment and U is thenumber of wind velocities applied during the experiment.The maximum frequency, on the other hand, is chosen155

accordingly with the sampling period, fmax = 12Ts

, whereTs is the sampling period [9].

The output at each device when the four devices areworking simultaneously is:

TA(t) =∑Kk η

AAk (t)ψAk (t) +

∑Jj η

BAj (t)φBj (t)

+∑Jj η

CAj (t)φCj (t) +

∑Jj η

DAj (t)φDj (t)

(6a)

TB(t) =∑Jj η

ABj (t)φAj (t) +

∑Kk η

BBk (t)ψBk (t)

+∑Jj η

CBj (t)φCj (t) +

∑Jj η

DBj (t)φDj (t)

(6b)

TC(t) =∑Jj η

ACj (t)φAj (t) +

∑Jj η

BCj (t)φBj (t)

+∑Kk η

CCk (t)ψCk (t) +

∑Jj η

DCj (t)φDj (t)

(6c)

TD(t) =∑Jj η

ADj (t)φAj (t) +

∑Jj η

BDj (t)φBj (t)

+∑Jj η

CDj (t)φCj (t) +

∑Kk η

DDk (t)ψDk (t)

(6d)

where ηXXk ∈ RK is the self-heating diffusive symbol160

for device X (represents the thermal behaviour of device Xas a function of power injected into itself) and ηXYj ∈ RJ isthe cross-heating diffusive symbol for device Y when poweris being injected into device X (represents the thermalbehaviour of device X as a function of the power injected165

into device Y ).If ηXXk is time-varying (i.e. varies with different wind

velocities) the dynamical system for the self-heating caseof device X is described by:

ψX(n)k (t) = 0 t ∈ [t0, tn]

ψX(n)k (t) = −ξkψX(n)

k + u(t) t ∈ [tn, tn+1]ψX(n)k (t) = −ξkψX(n)

k t > tn+1

(7)

3

170

TX(t) =∑n,k η

XX(n)k ψ

X(n)k (t) +

∑Kk cke

−ξk(t−t0)

where ηXX(n)k ∈ RK is the self-heating diffusive symbol of

device X associated to the system’s conditions in the n-thinterval in t ∈ [tn, tn+1]. ck ∈ RK represents the initialconditions of the system at the beginning of the measure-ments, at t = t0. In these discretized time intervals, the175

diffusive symbols can be considered constant in a windexperiment. With this approach, the thermal models fordifferent wind situations can be extracted from a singleopen-loop experiment, with t ∈ [t0, tF ], in which windspeed is continuously switched between several wind veloc-180

ities. The sensor will be characterized for U wind speeds,w1, . . . wU. Each wind speed is applied in an intervalt ∈ [tn, tn+1]n=0,...,N , where N is the number of wind events,such that, N U . All the wind velocities are applied fora short time ∆tn = (tn+1 − tn), where ∆tn tF , for all185

n. In the meantime, a Pseudo Random Binary Sequence(PRBS) current is applied to the heat sources in open-loopmode with a period TPRBS ∆tn tF . This type ofinput signal has a wide frequency spectrum which improvesthe quality of the fittings in presence of noise [16].190

The self, ηXXk , and cross-heating, ηXYj diffusive symbols,together with the initial condition constants, ck, are inferredby solving the finite dimensional least-squares problemformulated as in [17].

2.2. Sliding Mode Controllers195

It is is known that constant temperature operationmode in anemometers (CTA mode) is better in terms oftime response [2]. In this operation mode, the temperaturein the heating elements is forced to be constant and thepower required at every element to keep constant the tem-200

perature is the output signal of the sensor. To this effect,thermal sigma-delta modulators have been used, whichapply a modulated power to maintain the temperatureconstant in the structure, [15]. In this control, at eachsampling period, Ts, the temperature of the hot element,205

Tn = T (nTs), is compared with the desired target temper-ature, ∆T . If Tn ≥ ∆T , Poff is injected into the systemduring the following sampling period. On the contrary, ifTn < ∆T , Pon is injected. In the literature other controlmethods can be encountered to maintain the temperature210

constant in a thermal sensor, as in [18] and [19]. In thispaper, the analysis of the closed-loop dynamics has beenundertaken using the tools of equivalent control, typical ofsliding mode controllers for the infinite sampling frequencyapproximation. These types of controllers alter the dy-215

namics of the system by applying a discontinuous controlsignal so that under some conditions the system ’slides’ ona certain control surface [1, 15]. For the general case offinite order thermal systems, the following control surfaceis defined:220

σ(ψ(t)) = ∆T − TX(t) = ∆T −∑n,k η

XX(n)k ψ

X(n)k (t)(8)

where TX(t) is the temperature in device X. If the reacha-bility conditions from [1] are accomplished, the system willbe placed within the control surface σ(ψ(t)) = 0 in finitetime.

The equivalent control under a sliding motion that main-225

tains the temperature of the thermal structure constant isgiven by the condition σ(ψ(t)) = 0. For a system describedby diffusive representation the equivalent control is [1]:

ueq(t) = Γ(n)−1 ∑m,k η

XX(m)k ξkψ

X(m)k (t) t ∈ [tn, tn+1](9)

where Γ(n) =∑k η

XX(n)k . In [1] and [17], a more complete

development of SMC theroy can be found.230

The time evolution of the power requiered to maintainthe temperature constant can be predicted by the SMCanalysis, even in the case of wind speed changes. Theequivalent control is predicted from the diffusive symbolsfor each specific wind velocity inferred in the open-loop235

characterization. In the closed-loop experiment, the wind iskept constant within the time intervals ∆tn = (tn+1 − tn),for n = 0, . . . N , where N is the number of wind intervalssuch as N ≥ U , in this case.

3. Experimental Setup Description240

In this section, a detailed description of the sensor andof the wind tunnel used in the experiments is given. Asit has been mentioned above, for the experimental mea-surements the wind sensor was enclosed in a five meterlinear wind tunnel. The air pressure inside the tunnel was245

set to 240 mBar and the experiments were made at roomtemperature. Air temperature and pressure information

Figure 4: Photography of the prototype of REMS wind sensor insidethe tunnel used in the experiments. In this photo, the sensor ispositioned at the start position (0m) with pitch and yaw angles setto 0.

4

is provided by four temperature and four pressure sensorsplaced along the tunnel. The operating method of thetunnel consists of a car on a rail that moves at a certain250

velocity. The range of velocities the car can take goes from6m/min to 30m/min. At the given pressure and tempera-ture conditions, the equivalent Mars wind velocities thatprovide the same Reynolds numbers range approximatelyfrom 2m/s to 10m/s. The tunnel has a pan and tilt system255

that allows the boom to move in yaw direction ±165 andin pitch direction +33 and −43. Depending on the pitchand yaw position of the boom, the signal observed at agiven velocity will be different in forward movements (from0m to 5m position) than in reverse movements (from 5m to260

0m position). The time the car lasts in travelling from thestart to the finish position points ranges from 50s to 10s(for 6m/min and 30m/min respectively), which is a veryshort time taking into account the expected values of sometime constants in the system.265

The prototype of the REMS wind sensor is composed ofthree PCBs placed on a cilyndrical boom of 152mm lenghtand 20mm diameter. Inside the boom, a Pt100 resistormeasures its temperature. The three PCBs are 120 fromeach other with four silicon dice set in each one. The dice of270

each set have a dimension of 1.5x1.5 mm and are named: A,B, C andD, and they are positioned as a grid (see Figure 2).Each die contains three platinum resistors, one for heating,another for temperature sensing and a third one used asa temperature reference within the closed loop (see [2]).275

These resistors can be observed in Figure 3. The electricalconexion between the PCB and the resistors is made bya wire bonding process. The resistors were fabricated inclean room facilities using a silicon wafer. Silicon oxide(SiO2) was grown thermally for electrical isolation. On top280

of the SiO2, the platinum resistors were patterned with aphotolitography process. The platinum, thanks to its hightemperature coefficient of resistance, is the most suitablematerial for these devices [20]. In our case, only the heatingresistor has been used, both for heating and measuring the285

temperature. The dice’s heating resistors are named RA,RB, RC and RD, and their nominal resistance values at0C are: R0A = 1767Ω, R0B = 1753Ω, R0C = 1755, and ΩR0D = 1760Ω. The resistors of the PCB on the top of theboom, when this is placed parallel respect the longitudinal290

axis of the tunnel, have been used in the measurements.For the measurements, a National Instruments’ FPGA

connected to a PC and located outside the tunnel is used.Both the open and closed-loop operation modes of theexperiments are implemented in the FPGA.295

4. Experimental Results

In this section the experimental results obtained fromthe application of the theory described in section 2 areexplained. Three main experimental results have beenobtained. Firstly, in experiments A.1 to A.4, the ther-300

mal dynamics models of self-heating and cross-heating of

the silicon dice, at different wind velocities, have been ob-tained. From the obtained models, the prediction of thetemperature of each dice when all the resistors are workingtogether has been made. Secondly, from experiment B.1,305

a DR model has been obtained describing the temperatureevolution in the boom as a result of the total power injectedin the four dice of one PCB. Finally, the prediction of theoutput power of the sigma-delta modulator of a die workingin closed-loop under constant temperature mode has been310

made in experiment C.1.

4.1. Thermal dynamics model of self-heating and cross-heating of the silicon dice at different wind velocities

The self-heating models have been obtained for twocases, for wind velocity zero (no movement of the car) and315

for Mars equivalent wind velocity ±2.5m/s.For the zero wind velocity case (experiment A.1), four

identical experiments have been carried out. Each experi-ment consisted in exciting only one of the Pt resistors of thedice set (RA, RB , RC or RD) with a 10Hz PRBS of current,320

between 1mA and 4mA, while the rest of the resistors of

10-3 10-2 10-1 100 101

Frequency [Hz]

-200

0

200

400

600

Diff

usiv

e sy

mbo

l [K/J]

AA

BB

CC

DD

Figure 5: 8-th order self-heating diffusive symbols of each die (A, B,C and D) at zero wind velocity, obtained from experiment A.1. Thefour diffusive symbols are very similar among them.

0 100 200 300 400 500 600 700 800 900

time [s]

0

10

20

30

T [K

]

measuresfitting500 505 510

[s]

14

24

Figure 6: Fitting of time evolution of the temperature of die B atzero wind velocity from the open-loop experiment A.1. There is agood agreement between the experimental data (in blue) and thefitting data (in red). The inset figure shows a 10s zoom.

5

Figure 7: Top view of the boom inside the tunnel. Boom is positionedat pitch 0, yaw −45 to ensure good sensitivity in die B both inforward and reverse movements.

the sensor system are switched off. Each experiment lasted15 minutes and it was sampled with a period Ts = 0.05s.Taking these parameters into account the frequency meshfor the diffusive model is set in the range 1.1x10−3, 10Hz325

while the model order chosen is set to K = 8. In Fig-ure 5 the diffusive symbols obtained for the four dice (A,B,C and D) are shown. The four diffusive symbols foreach die are almost indistinguishable among them. This issomething to be expected since the four components have330

the same thermal characteristics. A frequency peak canbe encountered around 0.2Hz. As the fitting is done withan arbitrary discretization of the frequency, the frequencyset with significant values of the diffusive symbols give anapproximate value of the time constants of the thermal335

filters of the system. To avoid repetition, only the fitting ofthe experimental measurement of die B is shown in Figure6. As it can be observed in the zoom of the Figure 6, thematching between experimental and fitting data is good.

In the case of Mars equivalent wind velocities ±2.5m/s340

(experiment A.2), only die B has been analyzed. For thisexperiment, the pan and tilt system is set to pitch angle0 and yaw angle −45. This choice in the boom positionis made based on the best wind incidence in die B whenthe car is moving. At this position, a good wind sensitivity,345

both in forward and reverse movements, is ensured in die B(see Figure 7). The experiment consisted in a continuoussequence of forward and reverse movements of the car,therefore, good sensitivity in both directions was neededto obtain the models for the two velocities given:350

- for v = +2.5m/s from 0m to 5m.- for v = −2.5m/s from 5m to 0m.

It must be noted that, although die B has good sensitivity

to both movements, the response is higher in the forwarddirection. If we look at the top view of the boom of Figure355

7, it can be observed that in forward movements dice Aand B are the two most sensitive to the wind. However, inreverse movements, die B is left behind respect dice C andD and therefore its response is not as high.

During experiment A.2, a 20Hz PRBS sequence of cur-360

rent, between 1mA and 4mA, was injected in the heaterof die B, while the rest of the resistors remained off. Theexperiment lasted 1700s, and the sampling frequency wasset to 40Hz. The geometrically distributed frequency meshis set in the range 1.7x10−3, 20Hz and the model order365

0 250 500 750 1000 1250 1500 1750

time [s]

10

15

20

25

30

T [K

]

measuresfitting

500 505 510

[s]

15

20

0 250 500 750 1000 1250 1500 1750

time [s]

-2.5

0

2.5

velo

city

[m/s

]

Figure 8: Top: Fitting of the time evolution of the temperature ofdie B with velocities ±2.5m/s, from open-loop experiment A.2. Inblue, the experimental data, and in red the fitting data is shown.The inner figure shows a 10s zoom. Bottom: Wind velocity sequenceapplied to the die along experiment A.2.

10-3 10-2 10-1 100 101 102

Frequency [Hz]

-100

0

100

200

300

400

500

600

Diff

usiv

e sy

mbo

l [K

/J]

(w1) = +2.5m/s

(w2) = -2.5m/s

Figure 9: 8-th order self-heating diffusive symbols for die B forvelocities ±2.5m/s, obtained from experiment A.2. There is a fre-quency peak at approximately 0.3Hz, where diffusive symbols aredistinguisable between each other.

6

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

AB

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

AC

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

AD

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

BA

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

BC

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

BD

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

CA

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]CB

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

CD

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

DA

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

DB

10-4 10-3 10-2 10-1 100 101

[Hz]

-1000

100200

[K/J

]

DC

Figure 10: Cross-Heating diffusive symbols for dice A, B, C and D, inferred from experiment A.3. The active die in the first row (all in blue)is A. In the second row (all in red) the active die is B. In the third row (all in pink) the active die is C. And finally, in the fourth row (all ingreen) the active die is D. The nine cross-heating diffusive symbols have an order J = 7, and their frequency peak is around 0.1Hz.

chosen is set again to K = 8. Figure 8 shows the fitting ofthe temperature measurement together with the wind veloc-ities applied inside the tunnel. There is a good agreementbetween experimental and fitting data. Besides, Figure 9shows the obtained diffusive symbols for v = ±2.5m/s. As370

observed, the diffusive symbols are distinguishable fromeach other, depending on their wind velocity, in the uniquefrequency peak at approximately 0.3Hz. The wind depen-dence can be parameterized as a variable amplitude of thepole at that frequency. At higher wind speeds, the temper-375

ature in the die is lower which means that the amplitudein the corresponding diffusive symbol is lower too. In [17],the relationship between different wind velocities and am-plitudes can be observed better for a spherical wind sensorusing the same sensing principles.380

On the other hand, the DR cross-heating models havebeen obtained (experiment A.3). In this case, the tempera-ture evolution of a die is obtained from the heat dissipatedin another die where power is being injected. It has beenobserved empirically that in presence of different wind385

velocities, no sustainable differences are observed in thecross-heating diffusive symbols, therefore, only the zerowind velocity case is presented.

In experiment A.3, four identical measurements havebeen carried out to obtain each die’s cross-heating diffu-390

sive symbols. The die where the PRBS current sequenceis injected is considered the active die. In each measure-ment, a 1.25Hz PRBS current between 1mA and 4mA isinjected in the active die of a PCB, while the remaining

dice of the PCB are measured with a low current to avoid395

self-heating. The four experiments lasted 1 hour and weresampled at a 2.5Hz frequency. The frequency mesh forall is approximately in the range 2.7x10−4, 0.2Hz, andthe order chosen for the cross models is J = 7. As thecross-heating effect is expected to have a slower respone,400

the excitation PRBS current is of a lower frequency thanthe used when obtaining the self-heating models. Figure10 shows the cross-heating diffusive symbols obtained fromthe experiments. At each row, the diffusive symbol foreach die respect to the active die is observed. For exam-405

ple, the first row represents the diffusive symbols of diceB, C and D when the active die is A. The models aresymmetric with respect to the active die. The thermalinfluence of the adjacent dice to the active die is alwayssimilar, whereas the die in diagonal respect to the active410

one is heated differently and with much smaller amplitude.For example, if we look at the first row of Figure 10 thediffusive symbols, ηAB and ηAD are very similar betweenthem, as dice B and D are adjacent to the the active dieA. Similarly, in the second row we can see the similitude415

between diffusive symbols ηBA and ηBC , because A and Care adjacent to active die B in this case. At the same time,the four mentioned diffusive symbols take the same shape.In the same way, this concordance also happens with thediagonally positioned die. The most significant frequency420

peak in the cross-heating models is around 0.1 Hz. Inthese models a displacement of the frequency peak to lowerfrequencies can be observed, due to the slow dynamics of

7

the cross-heating if comparing with the self-heating models.This cross-heating is due to thermal transport within the425

boundary layer and thermal conduction through the setpillars–PCB.

From the models of Figures 5 and 10, from experimentsA.1 and A.3, it is possible to predict the temperature ateach die when all the dice are working simultaneously,430

applying superposition as in equation (6). The DR modelshave been validitaded in the four dice at zero wind speed.Results from die B are only presented due to the similarityamong the other dice’s predictions. In this experiment, A.4,of 1h of duration, a 10Hz PRBS sequence between 1mA435

and 4mA is injected in the four dice, while the temperatureat each die is registered with a sampling period of 0.05s.The input signal is fed into the self and cross-heatingmodels and by superposition the temperature prediction isobtained. Figure 11 shows the experimental temperature440

evolution of die B and the predicted temperature from themodels. In Figure 12 the self-heating and cross-heatingindependent temperature contributions, together with dieB’s temperature measurement is shown. As it can beobserved, the total temperature of the die, depends on how445

much the die has been heated by its own injection of power(self-heating) and by the heating produced by the rest ofthe dice (cross-heating).

4.2. Boom heating DR modelThe objective of this subsection is to model the heating450

of the boom as a result of the power injected in the dice. Tothis effect, a diffusive representation thermal model of theboom has been obtained. For this task, one of the sensor’sPCB is made to work under constant temperature mode.The sum of the necessary power to maintain constant the455

temperature in all the dice is going to be the input ofthe DR system. Therefore, to provide variability to theinput signal, as no wind velocity was applied, the targettemperature set on the dice was changed randomly every 5minutes among three different constant values: 315K, 320K460

and 325K. Experiment B.1 lasted 20h and was sampledevery 0.1s. The sigma-delta current in the four dice wasset to Ilow = 1mA and Ihigh = 4mA. As mentioned before,the input of the DR system is the sum of the dissipatedpower of all the dice, while the output of the model is the465

difference between the temperature of the boom and theair temperature. Specifically we have:

u(t) = PA(t) + PB(t) + PC(t) + PD(t)y(t) = ∆T = Tboom(t)− Tamb(t)

(10)

where Tamb(t) is the air temperature inside the tunnel andTboom is the boom temperature. Air temperature is ob-tained from the sensors along the tunnel. The model order470

chosen in this case is J = 6. In Figure 13, the evolution ofthe changing temperature of the four dice along the wholeexperiment is shown. On the other hand, on top of Figure14, the fitting of the difference between the boom and theair temperature is observed, where there is a reasonable475

0 5 10 15 20 25 30 35 40 45 50 55 60

time [min]

25

30

35

40

45

T [K

]

measurementprediction10 10.5 11

[min]

28

38

Figure 11: Prediction of the open-loop temperature evolution of dieB when all the dice are working simultaneously, in experiment A.4.There is good matching between the experimental measurement (inblue) and the superposition of the models output (in red) as shownin the zoom of 1min of the inner figure.

0 5 10 15 20 25 30 35 40 45 50 55 60

time [min]

5

15

25

35

45

55

T [K

]

measurementprediction (self-heating)prediction (cross-heating)

Figure 12: In blue the experimental measurement of the temperatureof die B, when all the dice are working simultaneously in experimentA.4 is shown. The contribution of the self-heating effect (in red) andof the cross-heating effect (in yellow) are shown independently.

matching between the experimental measurements and thefitted data. Below, the inferred 6-th order diffusive symbolis presented. It has a maximum between f = 2x10−4Hzand f = 2x10−3Hz. These low values make sense since theheating of the boom was expected to be slow. Furthermore,480

it follows that the boom structure is thermally coupledto the dice and therefore the heating of the boom maygenerate drifts in the sigma-delta power dissipated on thedice when the sensor is under regular operation. This willbe further disccused in subsection 4.4.485

4.3. Prediction of the closed loop output from self-heatingmodel

Finally, the prediction of the closed-loop dynamics isgoing to be obtained using SMC theory when differentwind velocities are being applied. Again, the boom is490

positioned at pitch 0 yaw −45 angles and die B is chosenfor this experiment, numbered C.1. The wind velocities forthe experiment are the ones characterized in section 4.1,

8

0 2 4 6 8 10 12 14 16 18 20

time [h]

315

320

325

Tem

p [K]

Figure 13: Temperature evolution of dice A, B, C and D alongexperiment B.1. The target temperature changed every 5min amongthree values: 315K, 320K and 325K.

0 2 4 6 8 10 12 14 16 18 20

Time [h]

0.2

0.4

0.6

0.8

1

T [

K]

measurementFitting

10-5 10-4 10-3 10-2 10-1 100 101

Frequency [Hz]

-1

0

1

2

3

4

diffu

siv

e s

ym

bo

l [K

/J]

10 10.5 11[h]

0.6

0.9

Figure 14: Experimental data (in blue) Vs fitting data (in red) alongthe 20h of experiment B.1, where the temperature of the dice hasbeen changing randomly every 5min. Bottom: 6-th order diffusivesymbol of the boom.

v = ±2.5m/s (A.2) and v = 0m/s (A.1). In C.1 experiment,die B was maintaned at a constant target temperature495

∆T = 17.2K while the rest of the dice were switched offand the wind sequence of Figure 15 (below) was applied forapproximately 290s. From the DR models for each windvelocity (those of Figures 5 and 9), the prediction of thenecessary power to maintain the temperature constant has500

been done. In the top of Figure 15, the predicted equivalentcontrol together with the experimental control waveformcan be observed, with a good agreement between both.As it is observed, the diffusive approach presented in thispaper, allows to predict the thermal dynamics of a wind505

sensor under wind switching conditions.

4.4. DiscussionAs it has been seen in sections 4.1 and 4.2, cross-heating

effects are present in the sensor structure, both in the diceand in the boom. These effects, specially the heating ofthe boom, can introduce drifts in the average power ofthe dice under normal operation. In order to avoid theseundiserable effects in the REMS wind sensor, differential

0 25 50 75 100 125 150 175 200 225 250 275 300

time[s]

16.5

17.5

18.5

19.5

Pow

er [m

W]

ueq

ueq

(SMA)

0 25 50 75 100 125 150 175 200 225 250 275 300

time[s]

-2.5

0

2.5

velo

city

[m/s

]

Figure 15: Top: Experimental average power injected into the heaterof die B under closed loop control (in blue) and the the result ofapplying the sliding mode analysis using the diffusive symbols ofFigures 5 and 9 (in red). Bottom: Sequence of the wind velocitiesalong the experiment C.1.

estimators in the wind retrieval algorithm were designed.The four dice A, B, C and D were grouped according to aNorth-South and East-West convection, D and A belongingto the North of the PCB and with C and B belonging tothe South. Similarly, D and C belong to East, and A and Bbelong to the West. (See [2] for more details). The outputpower of each dice was computed with two differentialmagnitudes, cancelling any drift produced, as:

North− South = (PA + PD)− (PB + PC)East−West = (PC + PD)− (PA + PB)

Thus, it is to be expected that the influence of the longterm temperature drifts will be cancelled when using theseestimators. The corroboration of this cancellation may be510

an interesting future work for this type of sensors.

5. Conclusions

A proof of concept prototype of the REMS wind sensor,based on anemometry, has been thermally characterizedin this paper. From open-loop measurements, DR ther-515

mal models of different parts of the sensor structure havebeen obtained for different wind velocities, differentiatingbetween the self-heating and the cross-heating effects. Fur-thermore, the diffusive state-space models obtained havebeen proven to be well suited for predicting the close-loop520

behaviour of the sensor under constant temperature opera-tion mode using the theory of SMC. The obtained modelshelp to understand the long term effects in the temperaturedue to the thermal coupling of the sensor’s components.

9

Acknowledgments525

The authors wish to thank to the Instrumentation De-partment of Center for Astrobiology their support duringthis work, specially to J. Torres, S. Carretero, S. Navarro,M. Marín and J. Gómez-Elvira.

Funding530

This work was supported in part by the Spanish Min-istry MINECO under Projects ESP2016-79612-C3-2-R andFPI grant BES-2012-057618.

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Biographies

Maria-Teresa Atienza receivedthe B.Sc. degree in Electronic En-gineering and the M. Sc. degree inPhysics Engineering from the Basque640

Country University, Spain, in 2012and 2013 respectively. She joined Mi-cro and Nano Technologies ResearchGroup of the Universitat Politécnicade Catalunya (UPC), Spain, as a Ph.D.645

degree student where she is workingon the identification of thermal systems applied to windsensors for space applications.

10

Lukasz Kowalski obtained MSc650

degree in Electronics and Telecommu-nications from the Technical Univer-sity of Lodz, Poland in 2005. He ob-tained PhD from Universitat Politéc-nica de Catalunya, Spain in 2016655

for thesis ’Contribution to advancedhot wire wind sensing’. He hasjoined MNT group in September 2005.He has participated in space explo-

ration projects: REMS(MSL), MEIGA (MetNet), MEDA660

(Mars2020). His work is aimed to the development ofthermal anemometers for the atmosphere of Mars. Hisresearch areas include dimensionless analysis, FEM/CFDsimulations, thermal modeling, inverse algorithm optimiza-tion for wind speed and incidence angle retrieval. He has665

co-authored two patents and several scientific papers.

Sergi Gorreta received the M.Sc.degree in Telecomunication Engineer-ing and the M.Sc. degree in Elec-670

tronic Engineering from the Univer-sitat Politècnica de Catalunya (UPC),Spain, in 2010 and 2011 respectively.He is currently with the Micro andNano Technologies Research Group of675

the UPC as a Ph.D degree student.His working areas are sensors for space

applications, integrated circuit design, non linear circuitsfor MEMS and control of dielectric charging in MEMSswitches.680

Vicente Jiménez received theM.Sc. degree in 1992 and the Ph,degree in 1997 from the Universi-685

tat Politécnica de Catalunya (UPC),Barcelona, Spain. He has been withthe Electronic Engineering Depart-ment, UPC, since 1992, when he be-came Associate Professor. His re-690

search areas include digital BiCMOS design, development ofmicrosystem circuit interfaces, and microsystem modelling.He has participated in industry and space projects relatedto liquid and gas thermal flowmeters. He has coauthoredmore than 20 scientific papers in international journals and695

conferences.

Manuel Domínguez-Pumar re-ceived the M.Sc. and Ph.D. degreesin electronic engineering from the700

Universitat Politécnica de Catalunya(UPC), Barcelona, Spain, and theM.Sc. (Hons.) degree in mathemat-ics from the Universidad Nacional deEducación a Distancia, Madrid, Spain,705

in 1994, 1997, and 2005, respectively. Since 1994, he hasbeen with the Department of Electronic Engineering, UPC,where he is currently an Associate Professor. From Septem-ber 2006 to August 2007, he was a Visiting Scholar at theCourant Institute of Mathematical Sciences, New York,710

NY, USA.He is participating in the design of the MEDAwind sensor for NASA Rover2020. His research interestsinclude control theory, chemical sensors, MEMS/NEMSsensors and actuators, dielectric charge control, sensors forspace applications, sigma-delta modulation, and dynamical715

systems in general. Dr. Domínguez-Pumar received the2013 NASA Group Achievement Award as a member of theMars Science Laboratory REMS Instrument DevelopmentTeam.

11