Methods to operate and evaluate the performance of a cold ...

IN DEGREE PROJECT MECHANICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2020

Methods to operate and evaluate the performance of a cold-gas CubeSat propulsion system on a magnetically stabilised satellite

VICTOR ALBERTO GONZALEZ MARIN

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES

DEGREE PROJECT IN SPACE TECHNOLOGY 1

Methods to operate and evaluate the performance ofa cold-gas CubeSat propulsion system on a

magnetically stabilised satelliteVictor Alberto Gonzalez Marin, MSc Student

KTH Royal Institute of Technology, Stockholm, Sweden24 August 2020

Abstract—Propulsion systems allow satellites to perform manyfunctionalities in space, such as orbital station keeping, re-entry control, attitude control, orbital transferring, rendezvousoperation, and even more thrilling, interplanetary travel. Indeed,propulsion systems in satellites have fostered a new favorableera of space exploration and application, therefore, detailedprocesses to operate propulsion systems need to be developedso that space missions, carrying this valuable system, arecompleted successfully. The aim of this study is to describe themost relevant operating procedures for the cold gas propulsionsystem NanoProp 3U, developed by GomSpace, on-board the3U CubeSat MIST satellite developed by KTH. Procedures,such as power levels, telemetry considerations, propellantmass determination, Fault Detection Isolation and Recoveryanalysis, and decommissioning plan allow proper operation ofNanoProp according to the mission requirements determined forMIST mission. Moreover, this study describes detailed missionexperiments to be performed with NanoProp with the objectiveof assessing the performance delivered by the propulsion systemitself, and other on-board subsystems which are required formonitoring and controlling the spacecraft according to theeffects generated by the propulsion system. The planning andoperation of a propulsion system should be outlined on-ground,during the mission design, so a clear understanding of thecharacteristics and limitations of the system are highlightedtowards the development of a secure and solid space mission.

Sammanfattning - Framdrivningssystem tillater satelliter attutfora manga funktioner i rymden, som t.ex. att halla kon-stant avstand till en annan rymdfarkost, utlosa aterintrade iatmosfaren, attitydstyrning, manovrera mellan olika omlopps-banor, och, till och med, interplanetara uppdrag. Framdrivn-ingssystem i satelliter har framjat en ny lovande era av rymd-forskning och praktisk tillampning av rymden, och darforbehover detaljerade, men praktiskt hanterbara, metoder foratt operativt anvanda framdrivningssystem utvecklas. Basen fordetta arbete ar att beskriva de mest relevanta driftsrutinerna forframdrivningssystemet NanoProp 3U, utvecklat av GomSpace,for anvandning ombord pa MIST-satelliten (en 3U Cubesat) somutvecklats av KTH. Aspekter pa NanoProps anvandning i MISTsom forbrukning av elektrisk energi, telemetribehov, drivmedels-massa, hantering av felfunktioner (upptackt och avhjalpande) ochavveckling av satelliten vid drifttidens slut analyseras i detalj.Dessutom analyserar detta arbete hur detaljerade driftprovkan utforas med NanoProp i syfte att bedoma de prestandasom framdrivningssystemet tillhandahaller och hur dessa provpaverkar och stods av driften av satellitens ovriga delsystem. Detovergripande syftet med detta arbete ar att saledes att utvecklaen metod for att planera driften av ett framdrivningssystemunder ett satellitprojekts definitions- och utvecklingsfaser sa atten tydlig forstaelse av systemets egenskaper och begransningarleder till ett sakert och stabilt rymduppdrag.

Index Terms—propulsion system, CubeSat, performance, op-erating procedure, mission experiment.

List of Symbols

a Semi-major axisa0 Initial semi-major axisaf Final semi-major axisacc AccelerationA Cross-sectional areaB Magnetic field9B Derivative of magnetic fieldc BDOT gainCD Drag coefficientCr Reflectivity coefficientd Distancee Eccentricitye0 Initial eccentricityef Final eccentricity

fsampling Sampling frequencyF Thrustg0 Gravitational acceleration (9.81 m/s2)hp Perigee altitudeha Apogee altitudei InclinationI Moment of inertiaItot Total impulseIsp Specific impulseL External torquem Mass of MIST satellitemd Magnetic dipolem0 Initial massmf Final massmp Mass of propellant

9m Mass flow rateM Mean anomalyn Mean motion

R0 Radius of Earth (6 378.15 km)rp Perigee radiusra Apogee radiust Time

tburn Burn timeT0 Initial temperatureTf Final temperature


Tp Orbital periodv True anomalyve Effective exhaust velocityβ Quaternion

∆V Total velocity change∆Vmax Maximum total velocity change

∆a Semi-major axis change∆e Eccentricity change∆h Altitude change∆Tp Orbital period change

µ Standard gravitational parameter(398 600.8 km3/s2)

ω Angular velocityωARW Angle random walk noiseωbias Static errorωBi

Bias instability noiseωg Angular velocity from gyroscopeωp Argument of perigeeωRRW Rate random walk noise

Ω Right ascension of the ascending node

I. INTRODUCTION

S INCE 1957, when the first artificial satellite, Sputnik I,was launched into orbit, space technology has been devel-

oped for different applications such as Earth observation, spaceexploration and science, communications, and more. However,it was not until the development of small, standardised, andaffordable satellites in the late 1990s that the opportunity toprovide hands-on experience in space technology and accessto space to everyone became a reality.

These breakthrough satellites, called CubeSats, are 10 cmsquare-shaped satellites that are nowadays developed mainlyfor technology demonstration, scientific experiments, commer-cial interest, and most importantly, educational projects. Inrecent years, as a result of the miniaturisation and affordabilityof technologies, there has been an increasing trend in thenumber of CubeSats being deployed into orbit every year. Overthe next 6 years, over 2 500 are scheduled to launch, [1].

Few of these CubeSats, however, contain a propulsionsystem limiting the functionalities they can provide to the enduser. Without a propulsion system, CubeSats are orbiting inthe same orbit they are deployed, increasing their likelihoodof colliding with space debris and limiting their lifetimes dueto being deployed at low altitudes. Therefore, a propulsionsystem allows CubeSats to manoeuvre their way into a desiredorbit, or even just regulate their current orbit for a longertime. It also allows them to be deorbited to prevent them fromcontributing to the space debris problem.

A. Purpose and motivation

CubeSat propulsion will definitely drive in a new era ofaffordable space exploration. This will mean propulsion willbecome a standard component on the majority of CubeSatswhich clearly requires the development of structured operatingprocedures so the satellite can complete its mission objectivesas planned.

Therefore, the purpose of the present study is to identifyand characterise the operating procedures needed to run acold gas CubeSat propulsion system, NanoProp 3U developedby GomSpace, on a magnetically stabilised CubeSat, KTH’sMIniature Student saTellite (MIST). The study also aims toidentify and describe the mission experiments that could beperformed with this propulsion module with the objectivesof evaluating the performance delivered by the system itself,and determining the capability of other subsystems such asthe on-board Magnetorquer/Magnetometer board (iMTQ) ofISISpace or the new incorporated Inertial Measurement Unitboard (IMU) to operate according to the outcomes induced bythe propulsion system.

B. Scope of the study

The present study aimed at identifying and defining theoperating procedures and mission experiments of NanoPropby considering the latest operating and design analyses of theMIST mission, and the required internal system operations ofthe propulsion module and the other interested subsystems.

Moreover, the overall approach of this study followed someof the space project and application standards developed bythe European Cooperation for Space Standardisation initiative(ECSS), principally in the development of the Fault DetectionIsolation and Recovery (FDIR) analysis and decommissioningplan:

‚ ECSS-Q-ST-30C - Dependability‚ ECSS-Q-ST-30-02C - Failure modes, effects (and criti-

cality) analysis (FMEA/FMECA)‚ ECSS-U-AS-10C - Space Sustainability - Adoption No-

tice of ISO 24113: Space Systems - Space Debris Miti-gation Requirements

‚ ESSB-HB-U-002 - ESA Space Debris Mitigation Com-pliance Verification Guidelines

This thesis does not, however, cover the identification andcharacterisation of system engineering general requirements ofeither NanoProp or MIST mission.

Proposed mission experiments and an analytical model ofNanoProp operation were developed assuming the variationof thrust between thrusters as the main cause of thrust mis-alignment in NanoProp with a maximum difference of 10%.Moreover, the torques derived from thruster firings are theonly ones influencing the spacecraft dynamics model, thus thisstudy assumed an unperturbed environment for MIST. Addi-tionally, the study was developed considering the applicationof iMTQ and IMU subsystems for monitoring and controllingthe outcomes of NanoProp experiments instead of using theADCS system on MIST.

Finally, thruster firing control was not included in thisstudy mainly because NanoProp does not include throttledevices to regulate the thrust levels. Thrusters in principle onlyprovide a particular thrust level based on thermal and pressurespecifications as explained further on, leading to the need of arobust feedback firing control design which could be coveredin a subsequent study.


C. Structure of the study

A more detailed account of the MIST mission and thefundamental internal system operations and specifications ofNanoProp and all other subsystems are provided throughSection II.

Section III of this study first describes the analytical modelto evaluate the performance of NanoProp (thrust, thrust mis-alignment and Isp), followed by the description of a Mat-lab/Simulink model designed to study the behaviour of MISTand subsystems throughout a NanoProp operation. After that,the study assesses the feasibility to operate NanoProp eitherautomatically or manually by analysing the latest thermaland ground station accessibility analyses developed for MISTmission as well as power budgets for particular operating sce-narios. Finally, the study describes the fundamental operatingprocedures for NanoProp such as power levels, telemetry con-siderations, propellant mass determination procedure, FDIRanalysis and decommissioning plan.

In Section IV, NanoProp mission experiments are sum-marised, including a description of the Standard OperatingProcedure (SOP) for NanoProp and a dynamic simulation ofthe entire process expected to be observed when operatingNanoProp.

II. BACKGROUND

In order to characterise the operation of NanoProp, it isimportant to know the requirements of the space missionwhere this propulsion system will be working on, and theessential internal operations and specifications of each sub-system used throughout the firing operation. Therefore, thissection describes the most relevant features of the MISTmission as well as significant internal system operations andspecifications of NanoProp, iMTQ, and IMU.

A. MIST

The MIST mission aims at demonstrating new scientificinstruments and electronic technologies in space. MIST is a3U CubeSat whose payload consists of six experiments foreducational or industry purposes as illustrated in Fig. 1.

1) Reference orbits: In the MIST project, analyses are per-formed using two reference orbits to cover the possible rangeof orbits corresponding to the available launch opportunities,[2]. The reference orbits are described in Two-Line Elementsets (TLE), Fig. 2 shows the TLE description of one of theMIST reference orbits.

The other reference orbit for MIST only differs by itslongitude of the ascending node, thus the altitude range andperiod are the same for both reference orbits. The orbitalelements for MIST are defined for 0000:00 UT on 21 June2017, [2].

Table I outlines the orbital parameters determined by MISTreference orbits and other resultant parameters such as orbitalperiod and perigee and apogee radii.

The orbital period was calculated by using (1) where t isthe quantity of time in a day.

Fig. 1. MIST satellite with experiments. NanoProp is placed at the top stackof the satellite

Fig. 2. TLE set of a MIST reference orbit, [2].

Tp “t

n(1)

Using (2), the semi-major axis of MIST reference orbit wascalculated where µ is the standard gravitational parameter, [3].

a “

«

µˆ

Tp2π

˙2ff13

(2)

Consequently, the perigee and apogee radii were calculatedby using (3), and (4), [3].

rp “ a p1´ eq (3)

ra “ a p1` eq (4)

2) Communication access opportunities: In order to havean overview of the communication access to MIST’s groundstation, the reference orbits are modelled using the AGI’sSystems Tool Kit (STK). The model indicates the averageorbital period is approximately 98 min during which 33 minare spent in eclipse and 65 min in sunlight, [2].

Considering that the ground station will be located atKTH, Stockholm, Sweden, a 98-min orbital period yieldsapproximately to 15 revolutions around Earth per day,however, there are only a few good passes over KTH eachlasting 10–12 min, [2].


TABLE IORBITAL PARAMETERS FOR MIST MISSION

Parameter Valuei 97.943˝

Ω 250.6332˝

e 0.001ωp 0˝

M 0˝

n 14.75896 rev/daya 7020.45 kmTp 97.57 minrp 7 013.43 kmra 7 027.47 km

3) Coordinate systems and flight attitude: MIST uses twomain coordinate systems. The body frame (X,Y,Z) and theorbital frame (U,V,W) which are related as shown in Fig. 3.The relation between coordinate systems is then expressed byusing (5), [2].

pU,V,Wq ” pZ,´Y,Xq (5)

Fig. 3. Relation between spacecraft body frame and orbital frame.

In the orbital frame, U is along the radius vector from theEarth’s centre to the satellite, V lies in the orbital plane andpoints in the direction of orbital motion, and W is perpendic-ular to the orbital and completes the coordinate system.

There are three reference attitudes for MIST which areshown in Fig. 4. The primary flight attitude of MIST in orbitwill be a tower configuration, [2].

Fig. 4. Different possible reference attitudes for MIST, [2].

B. NanoProp 3U

NanoProp 3U is a cold gas propulsion module suitablefor 3U CubeSats. A schematic of the NanoProp system isillustrated in Fig. 5. It contains one main electronic boardwhich controls 4 open-loop thrusters, valves, heaters, andtemperature and pressure sensors of the entire system, [4].

Fig. 5. Schematic of NanoProp 3U system, [4].

NanoProp also contains a tank where the propellant,butane, is stored. It has a total internal volume of 100.78cm3, however, the maximum amount of propellant allowed inthe tank is 50 g. Overfilling the tank leads to over-pressuresand possible break-up of the system when the tank is heated,[5].

1) Thermal and pressure considerations: The propellantis stored at a two-phase condition where liquid and gas areat equilibrium. The pressure inside the tank corresponds tothe vapour pressure of butane given at a particular tanktemperature, thus the storage tank temperature sets the feedpressure for the rest of the system, [5]. As a result, attention tothermal and pressure influences are crucial for an appropriateoperation of NanoProp.

For instance, there is a risk of propellant condensation indownstream parts such as manifolds, piping or thrusters ifthose parts are set at a colder temperature than the propellant.A positive temperature gradient, however, decreases the riskof propellant condensation. The strategy is to gradually exposethe propellant to warm temperatures as it goes down from tankto thrusters; this can be easily achieved by keeping the storagetank at “spacecraft equilibrium” temperature, i.e. not heatingthe propellant in the tank so the propellant is at its lowesttemperature there, then manifold heaters are switched on forabout 2 min to set manifolds at a warmer temperature than thetank, and thrusters are finally heated to a temperature warmerthan manifolds, [5].


However, since energy is consumed when propellant under-goes a phase transition from liquid to gas, a gradual reductionin temperature, and consequently in feed pressure, usuallyhappens during a firing operation. Therefore, it is also advisedto keep heating the propellant during firing, primarily whenperforming long burns (i.e. more than 5 min), thus it is advisedto permanently use the manifold heaters when performing longmanoeuvres; it was initially suggested to use the tank heaterfor this operation, as suggested in the User Manual, but thishas been modified since the tank actually receives significantradiated heat from thruster and manifold heaters when theyare operating, [5].

Finally, in order to attain efficient thruster performance,pressure and mass flow should be high enough for thepropellant to reach supersonic speed at nozzle throats,thus a minimum operating pressure is characterised to fireNanoProp. For NanoProp 3U this minimum pressure meansthat one has to consider 0 ˝C as the minimum operating tanktemperature, [5].

2) Thrust and specific impulse: Fig. 6 shows that the thrustproduced by NanoProp is proportional to the feed pressure,and consequently proportional to the storage tank temperatureas well.

Fig. 6. Tank pressure and thruster thrust versus tank temperature, [5].

On the other hand, the feed pressure does not affect the Ispof the system. Thrusters can, however, become more efficientby heating the propellant before it enters the nozzle, yet thevariation in Isp is minimal since the change is proportional tothe square root of absolute temperature, [5].

Finally, Table II outlines the most relevant characteristicsand nominal operating features assuming a 3-kg MISTsatellite and all four thrusters of NanoProp firing. Theseparameters were used as reference points further on in thedevelopment of experiments for NanoProp.

3) Thruster states: Thrusters in NanoProp have the follow-ing operating states, [5]:‚ Off: The thruster is inactive and no telemetry is collected.

The thruster has to be Enabled in order to start the thrusteroperation.

‚ Enabled: The thruster is still inactive, but telemetry iscollected. The thruster can now be commanded to enter

TABLE IINANOPROP 3U PARAMETERS

Parameter Valuem 3 kgmp 50 gF 4 mNIsp 50 s

∆Vmax 8.2 m/sve 490 m/sItot 25 Ns

the Arming state.‚ Arming: The thruster is heated to arming temperature

whose nominal value is 40 ˝C. When this temperatureis reached, the thruster automatically goes to the Readystate.

‚ Ready: The thruster can be commanded to Firing stateonly if the thruster is in the Ready state.

‚ Firing: When entering Firing state, valves are openedand propellant is expelled through the nozzle, producingthrust. When the firing is complete, the thruster comesback to the Arming state.

A thruster can fire in two different modes: the indefinitefiring mode and the impulse firing mode. In the former,the thruster fires as long as it is required, thus one definesand controls the duration of the firing. In the latter, on theother hand, the firing is automatically finished when thetotal impulse counter of the thruster reaches a specified totalimpulse set point, [5].

4) General operating procedure: Following operatingprocedures are shown to provide a basic understanding ofhow the system should be operated, [5]:

‚ Satellite commissioning, in-orbit checkout and initial use1) Power on propulsion system2) Set tank heater duty cycle to maximum3) Measure the current consumption of the unit and check

that it exceeds 100 mA4) If possible, leave heater on for a few minutes, enough

to measure a temperature rise in the tank5) Turn off tank heater6) Set manifold heater duty cycle to maximum7) Measure the current consumption of the unit and check

that it exceeds 150 mA8) Turn off manifold heater9) Enable manual valve control

10) Open thruster valves A, B, C, and D for 30 s toventilate trapped atmosphere between first and secondbarriers. Note: this can affect spacecraft attitude

11) Close all thruster valves and disable manual control12) Arm all thrusters13) Wait and ensure that all thrusters reach a state where

they are preheated and ready (preheating nominal tem-perature is 40 ˝C)

14) Power off propulsion system


‚ In-orbit manoeuvres, normal use scenario1) Power on propulsion system2) Enable all thrusters3) If tank temperature is less than 0 ˝C, turn on tank

heater and wait until temperature is above 0 ˝C.4) Turn off tank heater5) Set manifold heater duty cycle to maximum6) Arm thrusters7) Wait until thrusters are preheated and ready (preheating

nominal temperature is 40 ˝C)8) Fire thrusters. Note: If burn time is expected to be more

than 5 min, enable manifold heaters whilst thrusting9) Wait until desired impulse has been reached, stop firing

and disarm thrusters10) Power off propulsion systemThe operating time of the normal use scenario clearly

depends on the firing time, but also in the time spent forheating propellant in the tank and arming thrusters, thus initialestimation of the heating rates of tank and thruster heaterswas based on the operating records of a former 3U CubeSatmission with similar orbital parameters to the MIST missionof a commercial customer of GomSpace:‚ Heating rate in tank = 180 s/˝C‚ Heating rate in thruster = 0.5 s/˝C

C. iMTQ

A magnetically stabilised satellite depends on magnetome-ters (MTM) and magnetorques (MTQ), MTM measures theEarth’s magnetic field, which is then fed to the MTQ toproduce torques to stabilise the satellite with respect to themagnetic field of Earth. Since MIST incorporates the iMTQsubsystem for autonomous detumbling and magnetic attitudecontrol, it is also proposed to use the iMTQ for NanoPropoperations; the iMTQ capabilities will allow to detumble thesatellite once the firing manoeuvre is complete.

The ISISpace’s iMTQ is a CubeSat magnetic control moduleincluding a 3-axis magnetometer, 3 magnetorquers and amicrocontroller. This subsystem is intended as a detumblingmodule based on a BDOT controller with following features,[6]:‚ Detumbling mode is performed at a fixed BDOT fre-

quency of 1, 2, 4 or 8 Hz.‚ Default BDOT algorithm gain is 104 Am2s/T‚ Actuation level in all 3-axis. Nominal value is 0.2 Am2

at 20 ˝C, 5 V‚ Maximum actuation envelope error ă 5%‚ Magnetometer accuracy ă 3 µTAn increase in BDOT frequency in principle does not

improve the detumbling performance, but only allows theBDOT algorithm to deal with higher angular rates, since ituses a first-order finite difference of the magnetic field as ameasure for the angular rate. However, there are some sideeffects since the MTM can only be sampled when the MTQis not active, so increasing the frequency will also decreasethe time that the dipole can be effected, and thus decrease thedetumbling performance. As a result, according to ISISpace,

a BDOT frequency of 8 Hz allows the BDOT controller tohandle angular rates up to 100 ˝/s.

D. IMU board - MPU6050

According to the dependability approach described in theECSS standards, it became clear to develop a FDIR strategyfor NanoProp mainly to avoid excessive rates building up tolevels that the detumble function of the iMTQ cannot handle.

An IMU device (MPU6050), particularly the embeddedMEMS gyroscope, can be used to measure the generatedangular rates whilst performing manoeuvres. Therefore, thereading from the gyroscope will allow monitoring of themotion performance of MIST for the FDIR strategy andperformance assessment of NanoProp.

The suggested MPU6050 device is an integrated 6-axis mo-tion tracking system that combines a 3-axis gyroscope, 3-axisaccelerometer, and a Digital Motion Processor (DMP). TheMPU6050 features three 16-bit analog-to-digital converters(ADCs) for digitising the gyroscope outputs and three more16-bit ADCs for digitising the accelerometer outputs, [7].

The 3-axis MEMS gyroscope has the following features:‚ Digital output X, Y, Z axis angular rate sensors with a

user-programmable full-scale range of ˘250, ˘500, ˘1000, and ˘2 000 ˝/s

‚ Sensitivity Scale Factor of 131, 65.5, 32.8, 16.4 LSB/(˝/s)for each full-scale range

‚ Integrated 16-bit ADCs enable simultaneous sampling ofgyros

‚ Enhanced bias and sensitivity temperature stability re-duces the need for user calibration

‚ Improved low-frequency noise performance‚ Digitally programmable low-pass filterIt is important to note that as the sensitivity of the gyroscope

increases, the full-scale range decreases, however, for thisstudy the gyroscope can be set at the minimum full-scalerange so the sensitivity of the gyroscope is at its best. Thiswas determined by considering that the maximum angularrate supported by the iMTQ is 100 ˝/s and the angularrates produced from firing NanoProp are foreseen at a muchlower value than the minimum full-scale range handled by theMPU6050’s internal gyroscope.

Finally, the MPU6050 device includes an internal calibra-tion configuration so there might be no need for externaltemperature sensors or filters to perform a calibration processbefore operating the gyroscope.

III. METHOD

A. NanoProp evaluation - analytical model

One of the main objectives of this study is to determinea feasible strategy to evaluate the performance of NanoProp.Clearly, firing NanoProp influences in the dynamics of thespacecraft so it is evident to first outline the Euler rotationalequations of motion shown in (6), [8]:

rIs 9ω “ ´rωs rIsω ` Lc (6)


where ω is the body angular velocity vector, I is the inertiamatrix, and Lc is the torque vector taken about the body centreof mass.

By choosing a body-fixed coordinate system that is alignedwith the principal body axes, the inertia matrix rIs will bediagonal and (6) reduces to (7)–(9), [8]:

I11 9ω1 “ ´pI33 ´ I22qω2ω3 ` L1 (7)

I22 9ω2 “ ´pI11 ´ I33qω3ω1 ` L2 (8)

I33 9ω3 “ ´pI22 ´ I11qω1ω2 ` L3 (9)

where I1, I2, and I3 are the principal moments of inertia ofthe spacecraft; ω1, ω2, and ω3 are the rotational velocitiesaround the principal axes; and L1, L2, and L3 are the externalinfluences about the centre of mass of the spacecraft which inthis study only refer to the torques produced by firing thethrusters.

For the purpose of this study, the rotational equations ofmotion need to be solved for the external torques as shown in(10)–(12). Therefore, the angular rate data, measured by theMEMS gyroscope, will allow to estimate the external torqueoutlook applied on the spacecraft. The computed torqueswill indeed provide an approximate outlook of the thrustperformance of NanoProp by taking into account the distancesof thrusters from centre of mass as described in (13).

L1 “ I11 9ω1 ` pI33 ´ I22qω2ω3 (10)

L2 “ I22 9ω2 ` pI11 ´ I33qω3ω1 (11)

L3 “ I33 9ω3 ` pI22 ´ I11qω1ω2 (12)

L “ Fˆ d (13)

The best approach to characterise the torques is by firingpairs of thrusters so that the produced torque is either wholly orpartially applied about one single axis, assuming a nonexistentor small misalignment of thrusters as illustrated in Fig. 7.Therefore, the misalignments need to be also accounted forand these can be a significant unknown (i.e. thrust vectorwith respect to nozzle mean vector, and nozzle mean vectorwith respect to thruster bracket or mounting misalignment ofbracket).

In this study, for a simple characterisation, the misalignmentof thrusters is modelled in two different ways: variationin thrust magnitude or thrust deviation from nozzle meanvector. The former is considered the main cause expected toexperience in NanoProp, shown in Fig. 8, whose maximumdifference is defined in 10%. The latter, on the other hand,describes the thrust misalignment with respect to nozzle meanvector in one plane as shown in Fig. 9.

In case the resulting torque outcome shows a significanttorque production in Z axis, which is called the roll axis,then the misalignment is in principle described by the thrustdeviation from nozzle mean vector scenario. On the otherhand, the variation in thrust magnitude scenario will in a senseproduce torques only about two axes, pitch and yaw.

Fig. 7. Torque production by firing pairs of thrusters.

Fig. 8. Variation in thrust magnitude misalignment.

Certainly, a better interpretation and characterisation ofthrust and thrust misalignment of each thruster is attainable bysetting thrusters to specific thrust levels so an expected torqueoutcome is actually screened beforehand. The inconsistenciesin thrust, expected to be minimal in NanoProp, can thereforebe determined by evaluating the resulting torque outcome fromthe Matlab/Simulink simulation developed for this study.

Once the thrust performance is figured out, the Isp can berated from each manoeuvre by using (14), where F is the totaldelivered thrust and 9m is the mass flow rate of the expendedpropellant which can be specified from dividing the propellantmass consumption over the manoeuvre time, [3]:

Isp “F

9mg0(14)

Moreover, if thrusters are firing in impulse firing mode, theIsp can be determined by using (15) since one previously de-fines the required total impulse Itot provided by each thruster,[3]:

Isp “Itot

mp g0

(15)

The simplest approach to know the propellant mass con-sumed during the manoeuvre or the total impulse attained bythe thrusters is by reading internal registers specified by theNanoProp system.


Fig. 9. Thrust deviation from nozzle mean vector misalignment.

B. Matlab/Simulink simulation

A Matlab/Simulink simulation was developed to analyse thedynamic behaviour of MIST and performance of MPU6050and iMTQ susbsystems throughout a NanoProp operation, andto test the performance of the thrust determination analyticalmodel.

1) Satellite model: The simulation first presents a kinematicand dynamic model of MIST. The evolution of the angularvelocities over time is modelled by considering the Euler ro-tational equations of motion, (7)–(9); and the attitude evolutiondue to angular velocities is described by Euler parameters(quaternions), shown in (16)–(19), since they provide a re-dundant, nonsingular attitude description, [8]:

9β0 “1

2p´β1ω1 ´ β2ω2 ´ β3ω3q (16)

9β1 “1

2p´β0ω1 ` β2ω3 ´ β3ω2q (17)

9β2 “1

2p´β0ω2 ´ β1ω3 ` β3ω1q (18)

9β3 “1

2p´β0ω3 ´ β1ω2 ` β2ω1q (19)

The latest inertia tensor proposed for MIST satellite wasincluded in the simulation which is shown in (20).

rIs “

»

–

0.051 0 00 0.037 00 0 0.0205

fi

fl kgm2 (20)

2) NanoProp model: A model for NanoProp was thenimplemented to generate external influences that will affect thedynamics and kinematics of MIST when firing the thrusters.The NanoProp model allows simulation of different firingconfigurations, including the misalignment scenarios previ-ously explained. A visualisation of the propulsion system withlabelled thrusters is shown in Fig. 10.

The locations of thrusters in NanoProp 3U are shown in Fig.11. In this study, it was assumed that NanoProp is assembledsuch that thruster A and B are placed in the +X face of MIST,and thruster A and C in the +Y face of MIST. The centrepoint of NanoProp is assumed to be aligned with the principalbody axes. Moreover, the Z-distance between the thrusters and

Fig. 10. NanoProp 3U Thruster labelling, [4].

the centre of mass was determined to be 15 cm, consideringNanoProp is positioned in the +Z face of MIST as shown inFig. 1.

Fig. 11. NanoProp 3U nozzle locations in mm, [4].

3) MPU6050 model: The dynamics of MIST will in re-ality be measured by the MEMS gyroscope contained in theMPU6050 board, thus a discrete-time IMU model, developedby Matlab, [9], was implemented to understand in particularthe operating characteristics and limitations of the gyroscope.

The main disadvantage of using a MEMS gyroscope is thatit contains error sources that need to be taken into accountin measurements: static bias and random noise. The formerdescribes errors that are generated by predictable features suchas temperature bias, nonalignment of sensor or constant offsetbias.

The latter, on the other hand, includes different types: AngleRandom Walk (ARW), Rate Random Walk (RRW), and biasinstability (Bi). ARW is characterised by the white noisespectrum of the gyroscope output, it specifies how much theangular measurement tends to drift during a certain period.RRW causes a drift in the angular rate measurement thatcan be caused by mechanical stress and temperature drift, ittends to grow as the operating time increases. Finally thebias instability is characterised by the flicker noise in the


electronics. Using (21) the mathematical model of a gyroscopecan be modelled, [10] [11]:

ωg “ ω ` ωbias ` ωARW ` ωRRW ` ωBi(21)

where ωg is the output of the gyroscope, ω is the actual angularvelocity, ωbias are the static errors, ωARW is the white noise,ωRRW is the RRW noise, and ωBi

is the flicker noise of thegyroscope.

These errors affect the accuracy of the gyroscope, therefore,it is necessary to process the noise and minimise the influenceof errors in the measurement by filtering the output from thegyroscope, therefore a discrete-time Kalman filter, designedby Matlab, [12], was implemented in the simulation, [13].The modelling of the Kalman filter in the simulation was forfunctional purposes; according to the specifications of theMPU6050, there is no need to implement such filter sincethere is already an internal filtering process.

4) iMTQ model: Once the manoeuvre is complete, thesatellite undergoes rotations in one or more of its axes whichhave to be reduced in order to orient the satellite to a givenattitude afterwards. A BDOT control algorithm, handled bythe iMTQ board, was implemented to analyse the detumblingperformance of this system.

The BDOT control relies on the application of MTQs togenerate torques opposed to the rotation rates of the satellite.The control law is described in (22), where 9B is the derivativeof the magnetic field vector B, and ω is the angular velocityvector of the satellite, [14]:

9B “ Bˆ ω (22)

The control law then creates a magnetic dipole md inthe opposite direction to the change in the magnetic field,estimated with MTM data as shown in (23), where c is theBDOT gain of the controller, [14]:

md “ ´c 9B (23)

5) General overview: In the simulation, the coordinateframes of thrusters and gyroscope board are initially con-sidered to be aligned to the body-fixed coordinate systemof MIST. However, one can adjust parameters such as theprincipal moments of inertia, position of thrusters, orientationof coordinate frames with respect to each other, etc., furtheron once MIST is finally assembled and tested, therefore,the Matlab/Simulink model offers a feasible simulation tounderstand how MIST and subsystems respond from a firingoperation.

Finally, Fig. 12 shows a functional schematic of the sim-ulation. The performance evaluation block is not included inthe simulation since it is manually solved.

C. NanoProp operating mode

This subsection assess the feasibility of operating NanoPropin two different modes: manually or automatically. The formerrefers to operating NanoProp over the KTH ground station,and the latter refers to running NanoProp at a given time

Fig. 12. Functional schematic of simulation.

during the orbit. The main operating mode for NanoPropwas determined by looking at the thermal and ground stationaccessibility analyses with respect to the internal systemoperations of NanoProp described in Section II NanoProp3U. The analysis also includes the development of powerbudgets for specific operating modes.

1) Thermal analysis: The reference orbits shown in TableIII are those used in Thermica simulations. They are adapta-tions of the original TLE set of MIST to suit the format oforbital elements in Thermica. They represent the most extremeseasonal scenarios based on a thermal standpoint: cold case(maximum distance to the Sun, 8 Feb 2018) and hot case(minimum distance to the Sun, 1 June 2018), [15].

TABLE IIIMIST REFERENCE ORBITS FOR THERMICA SIMULATIONS

Parameter 8 Feb 2018 00:00:00 UT 1 June 2018 00:00:00 UTa pkmq 7 018 7 018e 0.001 0.001i p˝q 97.943 97.943ωp p

˝q 0 0v p˝q 1.3 272.3

Results from Thermica simulations for both seasonal casesare illustrated in Fig. 13 and Fig. 14. In the thermal sim-ulations, several sensors are placed in different parts of thesystem to evaluate the temperature gradient of the wholesystem during an orbital revolution, [15]. However, for furtheranalysis, it was assumed that the temperature of the propellantin the tank is equal to the temperature gradient measured bysensor T-1031 Lower Tank.

Fig. 13. Temperature gradient of NanoProp in Cold case, [15].


Considering the temperature gradient of sensor T-1031 inthe cold case, the minimum temperature of the propellantin the tank will be approximately ´8 ˝C happening at exitfrom eclipse. On the other hand, the maximum temperature isapproximately 5 ˝C.

Fig. 14. Temperature gradient of NanoProp in Hot case, [15].

In the hot case, from the T-1031 sensor thermal analysis,the minimum temperature of propellant in tank is 4 ˝C at exitfrom eclipse; the maximum temperature is approximately 21˝C.

2) Ground station analysis: Since it is relevant to determinethe possibility of operating NanoProp over the KTH groundstation, computations of the ground station passes for the samechosen seasonal references were analysed.

Cold Case: Table IV includes all the ground station passesin a day for the cold case, starting at 00:00:00 UT on 8February 2018. The illumination column describes whetherthe communication window happens in sunlight or eclipse.The duration describes an average duration of the window.

TABLE IVCOMMUNICATION WINDOWS FOR COLD CASE

Window start Window end Illumination Duration [s]08:35 08:46 Sunlight 66010:12 10:24 Sunlight 72011:48 12:00 Sunlight 72013:25 13:33 Sunlight 48015:01 15:06 Sunlight 30016:35 16:41 Sunlight 36018:08 18:17 Eclipse 54019:42 19:54 Eclipse 72021:19 21:31 Eclipse 72022:58 23:07 Eclipse 540

As explained in Section II MIST, in the MIST referenceorbits, there are only a few long passes lasting approximately10 to 12 min so two of them were selected for examinationover the temperature gradient of sensor T-1031 as illustratedin Fig. 15:‚ Communication Window Option 1: 10:12 to 10:24‚ Communication Window Option 2: 21:19 to 21:31From Fig. 15, both communication window options are

during or close to eclipse, marked as grey zone, so the tank

Fig. 15. Occurrence of windows versus temperature gradient of propellantin Cold case.

temperature during the window opportunities will be belowthe minimum operating tank temperature of NanoProp, 0 ˝C,unless the tank heater is used to heat up the propellant.

For option 1, the beginning of communication starts 360s after exiting from eclipse. In case a manual operation ofNanoProp over the ground station is required, then it is neededto heat the propellant from ´8 ˝C to 0 ˝C in 360 s atmost. However, considering the heating rate of the tank heater,described in Section II NanoProp 3U, this heating processtakes approximately 1 440 s, more than the time allowed.

On the other hand, for option 2, in case a manual operationover the ground station is required, the best option is to startheating the propellant before, when the tank is still in eclipse.However, heating propellant in tank during eclipse is notrecommended due to internal power limitations of NanoProp.

Hot Case: Table V includes all the ground station passesin a day for the hot case, starting at 00:00:00 UT on 1 June2018.

TABLE VCOMMUNICATION WINDOWS FOR HOT CASE

Window start Window end Illumination Duration [s]07:24 07:29 Sunlight 30008:59 09:11 Sunlight 72010:36 10:48 Sunlight 72012:12 12:23 Sunlight 66013:49 13:56 Sunlight 42015:25 15:29 Sunlight 24016:58 17:05 Sunlight 42018:31 18:41 Sunlight 60020:06 20:18 Sunlight 72021:43 21:55 Sunlight 72023:24 23:30 Sunlight 360

In this case only one ground pass was selected for ex-amination over the temperature gradient of sensor T-1031 asillustrated in Fig. 16:‚ Communication Window Option 1: 10:36 to 10:48From Fig. 16, the tank temperature at the beginning of

the communication window is approximately 8 ˝C, so thereis no need to use the tank heater since the propellant isalready above the minimum temperature. As a result, a manualNanoProp operation over the ground station is possible in thehot case scenario.


Fig. 16. Occurrence of windows versus temperature gradient of propellantin Hot case.

3) Power budgets: Power budgets for each of the cold andhot options were defined to complete the feasibility analysisof NanoProp operating mode. Power levels for each of theoperating modes of NanoProp are described in Section IIIPower Levels.

Table VI shows the power budget for the communicationwindow option 1 in cold case, considering the firing of twothrusters for 10 s and heating propellant in tank from ´8 ˝Cto 0 ˝C in 1 440 s.

On the other hand, Table VII describes the power budget forthe communication window option 2, considering the firing oftwo thrusters for 10 s and heating propellant in tank from ´4˝C to 0 ˝C in 720 s.

In addition, Fig. 17 illustrates the distribution of powerlevels in a timeline for both cold scenarios where the tankheater needs to be used for heating propellant up to a particulartemperature. The timeline is not to scale.

Fig. 17. Power level timeline of Cold case scenarios.

Finally, the power budget for the hot case scenario is shownin Table VIII. It considers two thrusters firing for 10 s withoutpreviously heating the propellant in the tank because the initialtemperature of this operation is above 0 ˝C.

The power level distribution of the hot scenario is illustratedin Fig. 18. The total operating time evidently decreases sincethe tank is completely neglected in this case. The timeline isnot to scale.

Fig. 18. Power level timeline of Hot case scenario.

4) Outcomes: Based on previous analyses, mainly from thecold seasonal cases, it was determined that it is not feasibleto manually operate NanoProp over the ground station. Thistype of operation would require a high amount of power andthermal control since most of the communication windowsoccur at temperatures below 0 ˝C as well as time spans notbeing long enough to heat the propellant up to 0 ˝C beforethe beginning of the communication windows.

As a result, the viable solution is to automatically operateNanoProp when the tank temperature naturally reaches 0˝C. This type of operation avoids using the tank heater,and requires minimum power consumption and less operatingtime. In the hot case scenario, however, experiments can beperformed manually over the ground station or automatically atany other time, but it is preferable to keep automatic operationsin both seasonal cases. Consequently, the tank heater will beonly used to heat the propellant when a desirable thrust isrequested, and manifold heaters will be used for propellantconditioning and long manoeuvres.

The automatic operating mode for NanoProp then adoptsfollowing general procedure:

‚ First communication window: Upload telecommands(TC) of experiment to perform

‚ Satellite reaches 0 ˝C: The experiment will be run by theOBC, collecting data from experiment results, checkingFDIR, activating iMTQ to detumble satellite once theexperiment is complete, etc.

‚ Second communication window: Download telemetry(TM) from experiment and upload next experiment TCin case it is needed.

All experiments to be completed with NanoProp are de-scribed in Section IV Experiments and Decommissioningoperations. A few of these experiments are suggested tobe performed only during the hot case scenario because oftheir specific operating thermal requirements, however, allexperiments can be performed automatically at any time inorbit.

A Standard Operating Procedure (SOP) flowchart, describ-ing step-by-step the interaction of the OBC software withNanoProp, is also described in Section IV Standard operatingprocedure.

D. Power levels

NanoProp has local dissipations grouped as shown in TableIX. Manifold heaters are not operated independently so thementioned power requirement considers both manifolds. Onthe other hand, the power levels of thrusters and valves arevalid per thruster.

NanoProp has particular internal operating modes based onthe thruster states described in Section II NanoProp 3U: Idle,Propellant conditioning, Firing preparation, and Firing so itis important to identify the most relevant characteristics andpower requirements for each of these modes, [4] [5].

1) Idle mode: Only the main PCB is active for statuscontrol. Main PCB includes the power required to operate themain board and all four thruster boards as shown in Table X.


TABLE VIPOWER BUDGET FOR COLD CASE OPTION 1

Step Time [s] Average Power [mW] Total Energy [Ws] Mode Description5V bus Bat. bus

1 10 200 0 2 Idle System power up2 1320 200 1000 1584 Propellant Conditioning Heat propellant in tank and manifolds3 120 200 2500 3244 24 200 5000 125 Firing Preparation Prepare two thrusters for firing5 10 200 5660 59 Firing Fire two thrusters6 5 100 0 0.5 Off System power down

Total 1490 1100 14160 2095

TABLE VIIPOWER BUDGET FOR COLD CASE OPTION 2



Total 770 1100 14160 1230

TABLE VIIIPOWER BUDGET FOR HOT CASE OPTION 1



Total 165 900 12160 350

TABLE IXPOWER REQUIREMENTS OF MAIN COMPONENTS OF NANOPROP

Group Component Power [W]1 Main PCB 0.2

2 Tank heater 1Manifold heaters 1.5

3 Thruster heater 2.5Valves 0.33

TABLE XPOWER BUDGET IN IDLE MODE

Unit Power [mW]5V bus Bat. bus Sum

Main PCB 200 200Total 200 200

2) Propellant conditioning mode: This mode is used toraise the temperature (and feed pressure) of the propellant inthe tank. Thrust level is defined by the tank temperature asshown in Fig. 6.

This mode is also used to raise the temperature of man-ifolds to avoid condensation of propellant. The manifoldtemperatures shall be between tank temperature and thrustertemperature as explained in Section II NanoProp 3U.

It is recommended to use the tank heater only when:

‚ The tank temperature is below 0 ˝C (minimum operating

temperature)‚ A specific thrust level is desiredThe heater in the tank is automatically turned off when

the temperature reaches 40 ˝C to avoid overheating and over-pressure.

A general power budget is shown in Table XI.

TABLE XIPOWER BUDGET IN PROPELLANT CONDITIONING MODE


Main PCB 200 200Tank Heater 1000 1000Manifold Heaters 1500 1500Total 200 2500 2700

3) Firing preparation mode: Thrusters can only fire whenthe arming state is achieved. The heater in the thruster couldalso be used to get a minor increment in Isp. Table XIIillustrates the power budget in firing preparation mode for onethruster.

4) Firing mode: Thrust is proportional to the tank temper-ature (and feed pressure) and the number of thrusters firing.Moreover, the manifold heaters are used to compensate forheat required to evaporate propellant, this mainly happenswhen performing long firing operations. Table XIII shows thepower budget for firing one thruster.


TABLE XIIPOWER BUDGET IN FIRING PREPARATION MODE


Main PCB 200 200Tank Heater 1000 1000Manifold Heaters 1500 1500Thruster Heatera 2500 2500Total 200 5000 5200

a Thruster heater power consumption depends on number of thrusters usedfor the operation

TABLE XIIIPOWER BUDGET IN FIRING MODE


Main PCB 200 200Tank Heater 1000 1000Manifold Heaters 1500 1500Thruster Heatera 2500 2500Valvesa 330 330Total 200 5330 5530

a Thruster heater and Valves power consumption depend on number ofthrusters used for the operation

Finally, the MPU6050 board has different local dissipationsat normal operating mode depending on the equipment acti-vated for the operation as shown in Table XIV, [7]. Regardlessof the condition set up for MPU6050, the power requirementfor this system was omitted in the power budget analysis ofeach experiment since it is much smaller than the power levelsrequired by NanoProp.

TABLE XIVPOWER REQUIREMENTS OF MPU6050

Group Conditions Power [mW]1 Gyroscope + Accelerometer + DMP 142 Gyroscope + Accelerometer 133 Gyroscope only 12.5

E. Telemetry considerations

Since the operation of NanoProp and monitoring of motionof MIST will be controlled by the OBC, the need to study theregister maps of both NanoProp and MPU6050 became clear.Table XV shows a register map table of NanoProp, the lastcolumn is length in bytes (B) for both writing and reading,except for the READ ALL register whose reading length isapproximately 45 B, [5].

For this study, the relevant registers from MPU6050 are thegyroscope measurements. Each gyroscope measurement is a16-bit 2’s complement value, [16].

During an operating day of NanoProp, the system maybe fired several times, but monitoring phases between firingexperiments are also needed to regularly check the statusof the system. The data coming from both the monitoringand operating phases will be stored in an OBC’s non-volatilememory for later transmission to the ground.

TABLE XVREGISTER MAP OF NANOPROP

Name Description SizeREAD ALL Reading returns all registers 1STATREG Module status/control 1THRFIRE Thruster fire 1THRX CTRL Thruster X status/control 1THRX TEMP Thruster X temperature 1THRX PRESSURE Thruster X pressure 2THRX THRUST Thruster X thrust 2THRX IMP Thruster X total impulse counter 2THRX IMPSET Thruster X total impulse setpoint 2TANKN TEMP Tank N temperature 1TANKN PROPUSED Tank N used propellant estimate 2TANKN HEATER Tank N heater duty cycle 1MANF HEATER Manifold heater duty cycle 1TANK PASSIVATION Tank passivation 1VALVE CTRL Solenoid valve status/control 1ARM TEMP Arm/Firing temperature setpoint 1FIRMWARE REV Firmware version number 2

During the monitoring phase, the OBC will monitor thefollowing parameters:‚ Tank Temperature‚ Thruster Status‚ Thruster Temperatures

TABLE XVITELEMETRY BUDGET PER INTERROGATION IN MONITORING PHASE

Parameter Size [B]Tank Temperature 1Thruster Status 1 ¨ (4 thrusters)Thruster Temperature 1 ¨ (4 thrusters)Total 9

Samples can be collected every 5–10 minutes during themonitoring phase. The monitoring phase would produce 9 Bper reading as shown in Table XVI which gives a maximumof 2.6 kB or 1.3 kB per day as computed in (24), and (25).

9 B5 min

¨1440 min

1 day« 2.6 kB (24)

9 B10 min

¨1440 min

1 day« 1.3 kB (25)

All these samples will be collected in packets which will besent to the ground station at later opportunities. The approachis to have one packet per reading, so each monitoring packetwill have 9 B of data. As a result, the 5-min sample collectionwould generate 288 packets per day, and the 10-min collectionwould generate 144 packets during a day.

Moreover, the orbital period of MIST reference orbit isapproximately 98 min so the frequency with which these 9-Bpackets are generated per orbit is outlined in (26), and (27).

1 packet5 min

¨98 min1 orbit

« 20 packetsorbit (26)

1 packet10 min

¨98 min1 orbit

« 10 packetsorbit (27)

On the other hand, based on GomSpace recommendations,the following relevant data should be read at a higher speed,


1 Hz, during the operating phase of an experiment (Idle,Propellant conditioning, Firing preparation, Firing, Off):

‚ Tank Temperature‚ Tank Propellant Consumption‚ Thruster Status‚ Thruster Thrusts‚ Thruster Temperatures‚ Thruster Pressures‚ Thruster Total Impulses‚ Angular Rates

TABLE XVIITELEMETRY BUDGET PER INTERROGATION IN OPERATING PHASE

Parameter Size [B]Tank Temperature 1Tank Propellant Consumption 2Thruster Status 1 ¨ (4 thrusters)Thruster Thrust 2 ¨ (4 thrusters)Thruster Temperature 1 ¨ (4 thrusters)Thruster Pressure 2 ¨ (4 thrusters)Thruster Total Impulse 2 ¨ (4 thrusters)Angular Rate 2 ¨ (3 gyroscopes)Total 41

The telemetry budget for each experiment is described inSection IV Experiments and Decommissioning operations, butthe following computation just shows a general budget analysisfor the operating phase.

Every second, 41 B need to be sent as shown in Table XVIIso considering the Cold Case Option 1 operating time as anexample, it generates 61 kB as described in (28).

„

8 Bthruster

1 s¨ p4 thrustersq `

3 Btank

1 s`

6 Bgyro

1 s

¨1490 s « 61 kB (28)

The approach is to have one packet per experiment, yet thecontent size of a packet sent to ground station is limited to amaximum of 214 B so the results from this experiment wouldbe stored in approximately 286 packets.

According to GomSpace, it might be more feasible touse the READ ALL register for collection of those relevantparameters during the operating phase since the representationof those parameters for a specific time slot is more accuratethan the process of independently getting those values.

However, the size of data sent to OBC per interrogationwould be 51 B as shown in Table XVIII.

TABLE XVIIITELEMETRY BUDGET PER INTERROGATION IN OPERATING PHASE USING

READ ALL REGISTER

Parameter Size [B]All NanoProp parameters 45Angular Rate 2 ¨ (3 gyroscopes)Total 51

Therefore, considering the same operating time as before,76 kB of data are generated which lead to have approximately356 packets as computed in (29).

„

45 B1 s

`6 Bgyro

1 s

¨ 1490 s « 76 kB (29)

Finally, the decision for data collection during the operatingphase depends upon the characteristics of the OBC and generalMIST mission design.

F. FDIR Analysis

A FDIR process ensures the safety and availability ofthe spacecraft by avoiding irreversible loss of the nominalmission after the occurrence of a failure. Since the operationof NanoProp will be mostly automatic, it was clear the needof a FDIR function executed by the OBC.

Appendix A shows a FDIR analysis of NanoProp at space-craft level in the occurrence of failures systematically identi-fied by a Failure Mode and Effects Analysis (FMEA) describedin Appendix B. The FDIR analysis is based on guidelinesdefined by ECSS-Q-ST-30C Space product assurance standard.

There are some important details to consider when the FDIRanalysis is inspected:

1) Manifold heaters are not operated independently so thementioned failures consider both manifolds. On the otherhand, the failures for thrusters are valid per thruster.

2) Based on the heating rate estimates for tank and thrusterheaters, described in Section II NanoProp 3U, heatingvariables were defined. T0 is the initial temperature ofthe propellant which is measured by the tank tempera-ture sensor. Tf is the final desirable temperature of thepropellant. Since the heating rates are just estimates, theactual rates and offsets will be determined by performinga specific experiment in space:‚ T1 = 180 s + TBD s‚ T3 = 0.5 s + TBD s‚ T1MAX = r| Tf ´ T0 | ¨180 ss ` TBD s‚ T3MAX = r| Tf ´ T0 | ¨0.5 ss ` TBD s

G. Propellant mass determination

The wet mass of NanoProp clearly decreases as propellant isconsumed so it is important to keep track of this consumptionin order to have a better insight of the actual status andperformance of the system. Even though it is difficult tomeasure the exact propellant mass at any phase during aspace mission, a bookkeeping method was characterised todetermine the propellant mass evolution during the MISTmission.

1) Bookkeeping: This method involves determination ofpropellant consumed during each manoeuvre by on-groundrecording of all manoeuvre data, [17].

Bookkeeping usually takes into account the propellant massflow rate generated by each thruster. The mass flow rateallows one to compute the propellant mass required for amanoeuvre by integrating it over the manoeuvre time. Theremaining propellant mass is then computed by substractingthe mass consumed for that specific operation to the massvalue determined before the operation, [18]. Additionally,


the bookkeeping method can be developed on the MISTmission by just continuously reading the internal propellantconsumption register of NanoProp, mentioned in Table XV,each time a manoeuvre is performed.

On-ground bookkeeping is a feasible and practical way todetermine the propellant mass of NanoProp during the MISTmission. As primary strategy, reading the internal register ofNanoProp is proposed since there is no need for additionalequipment, yet inaccuracies can build up over time, thus themass flow rate practice, first requiring the computation ofthe performance of NanoProp, will be used as an alternativesolution to support the readings given by NanoProp.

H. Decommissioning plan

In order to meet the objectives of the ESA Space DebrisMitigation (SDM) policy, MIST-NanoProp operations shall bedesigned according to the following requirements, [17]:‚ Clearance of the LEO protected region

No space system left in LEO for more than 25 yearsafter the end of mission. It is necessary to design a spacesystem able to clear (after the mission) the LEO ProtectedRegion by performing deorbit operations or place thespace system in an orbit where natural orbital decayallows re-entry within 25 years.

‚ Re-entry casualty risk mitigationIt is necessary to ensure that the re-entry casualty riskdoes not exceed 10´4 for any re-entry event (controlledor uncontrolled re-entry).

‚ End of mission (EoM) passivationRemoval of stored energy to prevent debris generationafter end of mission. Necessary to implement measuresfor depleting the stored energy in the space system at endof mission.

As a result, Fig. 19 is the general flowchart that MISTshould follow to comply with the ESA SDM Policy.

Fig. 19. End Of Life deorbit strategies, [19].

Firstly, the orbit propagation analysis, illustrated in Fig. 20,shows that the selected reference orbit of MIST, described inSection II MIST, has sufficiently low altitude to ensure re-entryin about 16.5 years according to the ESA DRAMA tool andthe following spacecraft parameters: random tumbling cross-section area (seen as the average area), [20], spacecraft massas well as the drag and the reflectivity coefficient which aresummarised in Table XIX.

The re-entry casualty risk for MIST mission can be analysedfrom a spacecraft re-entry survival analysis, and also computedin the DRAMA tool. Fig. 22 shows a general survival analysisduring an uncontrolled re-entry into the atmosphere for some

Fig. 20. Orbit life time of MIST reference orbit.

TABLE XIXSPACECRAFT PARAMETERS FOR DRAMA-ORBIT PROPAGATION

ANALYSIS

Parameter ValueA 0.0615 m2

m 3 kgCD 2.2Cr 1.2

components of MIST which are simulated as simple boxesmade of default materials provided by the DRAMA library asillustrated in Fig. 21 and Table XX.

Fig. 21. MIST model for re-entry survival analysis.

TABLE XXSPACECRAFT MODEL FOR DRAMA-RE-ENTRY SURVIVAL ANALYSIS

Component Material Mass [kg]Frame Al-Li 2195 0.36Solar Panels GaAs 1Top Stack TiAl6v4 0.41Middle Stack Al-Li 2195 1.07Bottom Stack Al-Li 2195 0.38

Assuming the re-entry initiates as soon as the altitudeis around 120 km, all components are burned up into theatmosphere, except for the top stack which actually simulatesbeing NanoProp. However, DRAMA tool indicates the totalcasualty probability under the 1D projection for this simulationis 6.5¨10´6 which is lower than 10´4, thus an uncontrolledre-entry can be performed for MIST which leads to design apassivation plan for NanoProp.

Finally, the passivation plan for NanoProp needs to imple-ment measures such as venting, depletion burns or depressuri-sation for depleting the stored energy in the propulsion tankat end of mission to avoid from further adding to the spacedebris generation problem, [17].


Fig. 22. Re-entry survival analysis of MIST.

IV. RESULTS

A. Experiments

Once the features of each of the fundamental operatingprocedures for NanoProp were outlined, experiments thatNanoProp will perform during the MIST mission were char-acterised. The experiments, effective from the commissioningstage to the decommissioning stage, aim to assess the per-formance of the propulsion system, but also to evaluate thefunction of other subsystems by performing attitude and orbitalmanoeuvres:Commissioning stage‚ System function verification‚ Heating rate definition

Operating stage‚ Performance assessment via Indefinite firing mode‚ Performance assessment via Impulse firing mode‚ Translation assessment‚ Eccentricity change manoeuvre‚ Altitude change manoeuvre

Decommissioning stage‚ Venting‚ Depletion/Disposal manoeuvre

1) System function verification: Objective: To ensure thatthe system is operational after launch and spacecraft detum-bling.

Procedure: All equipment is tested. This experiment can beperformed manually during ground contact or automaticallyby the OBC. During the verification, in case it is needed, theiMTQ board is used to detumble the satellite. The step-by-stepdescription of this procedure is outlined in Table XXI.

The power budget and timeline of power levels are shownin Table XXII and Fig. 23.

Fig. 23. Power level timeline for System function verification.

This experiment would require the following information:‚ Tank Temperature‚ Tank Heater Current Consumption*‚ Manifold Heater Current Consumption*‚ Thruster Heater Current Consumption*‚ Thruster Status‚ Thruster Temperature‚ Thruster Pressure‚ Angular Rates*It was assumed the size of these parameters is 1 B. Size of

others are described in Section III Telemetry considerations.Samples can be collected every 5 s. As computed in (35),

378 B are generated and will be stored in approximately 2packets since the content size of a packet is limited to 214 B.

The size per interrogation of each step of the experiment iscomputed in (30)–(34).

TestTank “2 B5 s

¨ 360 s “ 144 B (30)

TestManifolds “1 B5 s

¨ 30 s “ 6 B (31)

TestValves&Gyro “14 B5 s

¨ 30 s “ 84 B (32)

TestEnable “12 B5 s

¨ 30 s “ 72 B (33)

TestArm “3 B5 s

¨ 30 s “ 18 B (34)

rTestTank ` TestManifolds ` TestValves&Gyro ` TestEnable

`TestArm ¨ p4 thrustersqs “ 378 B (35)

2) Heating rate definition: Objective: To verify the pro-posed heating rate estimates and to determine the FDIR offsetsfor heating processes in tank and thruster.

Procedure: This experiment can be performed manuallyduring ground contact or automatically by the OBC. Thestep-by-step description of this procedure is outlined in TableXXIII.

The power budget and timeline of power levels are shownin Table XXIV and Fig. 24.

Fig. 24. Power level timeline for Heating rate definition.

This experiment would require the following information.‚ Tank Temperature‚ Thruster Status‚ Thruster TemperatureSamples can be collected every 5 s. As computed in (38),

120 B are generated and will be stored in 1 packet.


TABLE XXIPROCEDURE FOR SYSTEM FUNCTION VERIFICATION

Step Test Verification method Success criteria Comments

1Activate tank heaterDuty cycle = 95%t = 360 s

Temperature sensor

Heater currentconsumption

Tank temperatureincrease is observable

Measured heater currentconsumption exceeds 100 mA

Turn off tank heater after test

2

Activate manifoldheatersDuty cycle = 95%t = 30 s


Measured heater currentconsumption exceeds 150 mA Turn off manifold heaters after test

3

Open the foursecond barrier valvesActivate the gyro boardt = 30 s

Pressure sensors

Gyro board signals

Thruster pressures areobservable

Produced angular rates areobservable

To open the valves, first enable manual valve control(TANK PASSIVATION)

It is advised to have a delay of minimum 10 ms betweeneach valve opening to limit the peak power consumption

Close valves and disable manual valve control after test

This step can affect the S/C attitude, iMTQ is used fordetumbling the S/C

4 “Enable” all thrusterst = 30 s

Temperature sensors

Pressure sensors

Thruster temperatures andpressures are observable

5 “Arm” thruster At = 30 s

Temperature sensor


Thruster status

Thruster temperature increaseis observable

Measure heater currentconsumption exceeds 100 mA

Ensure that thruster A reaches “Ready” state

6 “Arm” thruster Bt = 30 s

Temperature sensor


Thruster status



Ensure that thruster B reaches “Ready” state

7 “Arm” thruster Ct = 30 s

Temperature sensor


Thruster status



Ensure that thruster C reaches “Ready” state

8 “Arm” thruster Dt = 30 s

Temperature sensor


Thruster status



Ensure that thruster D reaches “Ready” state

The size per interrogation of each step of the experiment iscomputed in (36), and (37).

TestTank “1 B5 s

¨ 360 s “ 72 B (36)

TestArm “2 B5 s

¨ 30 s “ 12 B (37)

rTestTank ` TestArm ¨ p4 thrustersqs “ 120 B (38)

3) Performance assessment via Indefinite firing mode:Objective: to assess the performance and misalignment ofthrusters.

Procedure: After verification and heating rate definitionof the system, some indefinite-firing-mode experiments areperformed to determine the thrust, thrust misalignment andspecific impulse of the propulsion system.

Based on the Section III NanoProp evaluation - analyticalmodel, the strategy is to fire pairs of thrusters for 1 min andevaluate the gyro board response to determine the influenceof thrusters in the spacecraft rotation. In each fire, the pair ofthrusters is set at equal “arm” temperature to produce uniformthrust. The spacecraft should be stabilised using the iMTQboard after each manoeuvre experiment in order to evaluatethe detumble controller of the iMTQ board.

Therefore, the strategy is to fire each thruster a couple oftimes to precisely differentiate the performance of the thrusterin respect of the others; assuming a nonexistent or minimalmisalignment of thrusters, this strategy is prepared in a waythat the torque is applied about one axis as illustrated in Fig.7 when Thrusters A & B are simultaneously firing.

The following firing configurations were determined basedon Fig. 10:

1) Fire thruster A & B2) Fire thruster A & C


TABLE XXIIPOWER BUDGET FOR SYSTEM FUNCTION VERIFICATION

Step Time [s] Average Power [mW] Total Energy [Ws] Total Energy [Wh] Description5V bus Bat. bus

1 10 200 0 2 5.5¨10´4 System power up2 360 200 1000 432 0.12 Test tank3 30 200 1500 51 1.4¨10´2 Test manifolds4 30 200 1320 46 1.3¨10´2 Open valves and Test gyro board5 30 200 0 6 1.7¨10´3 “Enable” thrusters6 30 200 2500 81 2.3¨10´2 “Arm” thruster A7 30 200 2500 81 2.3¨10´2 “Arm” thruster B8 30 200 2500 81 2.3¨10´2 “Arm” thruster C9 30 200 2500 81 2.3¨10´2 “Arm” thruster D

10 5 100 0 0.5 1.4¨10´4 System power downTotal 585 862 0.24

TABLE XXIIIPROCEDURE FOR HEATING RATE DEFINITION

Step Test Verification method Success criteria Comments

1Activate tank heaterDuty cycle = 95%t = 360 s

Temperature sensor

Tank temperatureincrease is observable

Heating rate is determinedfrom timer evaluation

Turn off tank heater after test

2 “Arm” thruster At = 30 s

Temperature sensor

Thruster status



To “arm” the thruster A, first enable the thruster

Ensure that thruster A reaches “Ready” state

3 “Arm” thruster Bt = 30 s

Temperature sensor

Thruster status



To “arm” the thruster B, first enable the thruster

Ensure that thruster B reaches “Ready” state

4 “Arm” thruster Ct = 30 s

Temperature sensor

Thruster status



To “arm” the thruster C, first enable the thruster

Ensure that thruster C reaches “Ready” state

5 “Arm” thruster Dt = 30 s

Temperature sensor

Thruster status



To “arm” the thruster D, first enable the thruster

Ensure that thruster D reaches “Ready” state

3) Fire thruster C & D4) Fire thruster B & DTwo more firing configurations can be tested to analyse

the performance of thrusters through the production of zerorotations about axes, assuming nonexistent or minimal mis-alignment as well:

1) Fire thruster A & D2) Fire thruster B & CAccording to the outcomes of the Section III NanoProp

operating mode, these experiments are performed automat-ically by the OBC when the tank temperature reaches theminimum operating temperature (0 ˝C) in both the cold andhot scenarios.

The power budget is shown in Table XXV, but the timelineof power levels is the same as the one described in Fig. 18since the tank is not used in this experiment.

These experiments will follow the strategy described inSection III Telemetry considerations for an operating phase,thus 41 B need to be sent to the OBC every second, as shownin Table XVII.

Considering the operating time proposed for this kind ofexperiment, it generates 8.8 kB as described in (39). Thecontent size of a packet is limited to 214 B so the results ofeach experiment will be stored in approximately 42 packets.

„

8 Bthruster


3 Btank

1 s`

6 Bgyro

1 s

¨215 s « 8.8 kB (39)

On the other hand, 11 kB are generated by each experiment,as computed in (40), in case the READ ALL register is usedfor data collection as explained in Section III Telemetry con-siderations. For this alternative, the results of each experimentwill be stored in approximately 52 packets.

„

45 B1 s

`6 Bgyro

1 s

¨ 215 s « 11 kB (40)

4) Performance assessment via Impulse firing mode: Ob-jective: to assess the performance of thrusters and to verifythe results from Performance assessment via Indefinite firingmode experiment.


TABLE XXIVPOWER BUDGET FOR HEATING RATE DEFINITION

Step Time [s] Average Power [mW] Total Energy [Ws] Total Energy [Wh] Description5V bus Bat. bus

1 10 200 0 2 5.5¨10´4 System power up2 360 200 1000 432 0.12 Tank heating3 30 200 2500 81 2.3¨10´2 “Arm” thruster A4 30 200 2500 81 2.3¨10´2 “Arm” thruster B5 30 200 2500 81 2.3¨10´2 “Arm” thruster C6 30 200 2500 81 2.3¨10´2 “Arm” thruster D7 5 100 0 0.5 1.4¨10´4 System power down

Total 495 759 0.21

TABLE XXVPOWER BUDGET FOR PERFORMANCE ASSESSMENT VIA INDEFINITE FIRING MODE

Step Time [s] Average Power [mW] Total Energy [Ws] Total Energy [Wh] Mode Description5V bus Bat. bus

1 10 200 0 2 5.5¨10´4 Idle System power up2 120 200 1500 204 0.06 Propellant Conditioning Heat propellant in manifolds3 20a 200 5000 104 0.03 Firing Preparation Prepare two thrusters for firing4 60 200 5660 352 0.1 Firing Fire two thrusters5 5 100 0 0.5 1.4¨10´4 Off System power down

Total 215 662 0.19a The firing preparation time depends on the initial temperature of thrusters; however, it is assumed that the minimum initial temperature that thrustersexpect is 0 ˝C, leading to 20 s for arming thrusters at most

Procedure: Impulse-firing-mode experiments are performedto primarily determine the specific impulse and the exhaustvelocity of thrusters.

The tank temperature will always be set at the same tem-perature so pressure and thrust delivered by thrusters remainthe same. This strategy allows the synchronisation of the firingstop of thrusters with the condition that total impulse setpointand “arm” temperature of all thrusters are the same.

Fire pairs of thrusters and evaluate the gyro board responseto determine the influence of thrusters in the spacecraft ro-tation. The spacecraft should be stabilised using the iMTQboard after each manoeuvre experiment in order to evaluatethe detumble controller of the iMTQ board. These experimentswill follow the same 6 firing configurations described in thePerformance assessment via Indefinite firing mode experiment.

The firing time in these experiments is defined by theselected tank temperature and total impulse setpoints. To getobservable results, the tank temperature is set at 10 ˝C so thethrust delivered by each thruster is 1 mN, and the total impulsesetpoint is set at 150 mNs in each thruster, thus a firing timeof 2.5 min is expected.

Because of the nature of the MIST mission, these experi-ments are also performed automatically by the OBC in bothcold and hot scenarios, but only when the tank temperaturenaturally reaches a minimum temperature of 5 ˝C to reducepropellant conditioning mode operating time.

The power budget is shown in Table XXVI, but the timelineof power levels is the same as the one described in Fig. 17since the tank is used to heat the propellant such that thrustersattain a specific thrust level.

These experiments will follow the strategy described inSection III Telemetry considerations for an operating phase,thus considering the operating time proposed for this kind ofexperiment, each manoeuvre generates 44.5 kB as described

in (41). The results of each experiment will be stored inapproximately 208 packets.

„

8 Bthruster


3 Btank

1 s`

6 Bgyro

1 s

¨1 085 s « 44.5 kB (41)

On the other hand, 55.3 kB are generated by each experi-ment, as computed in (42), in case the READ ALL register isused for data collection. The results of each experiment willbe stored in approximately 259 packets.

„

45 B1 s

`6 Bgyro

1 s

¨ 1 085 s « 55.3 kB (42)

5) Translation assessment: Objective: to verify how bal-anced the satellite is when all four thrusters are firing.

Procedure: In the tower position, fire (´U direction) allfour thrusters in impulse-firing-mode and evaluate the gyroboard response to determine the influence of thrusters inthe spacecraft rotation. The spacecraft should be stabilisedusing the iMTQ board after the manoeuvre experiment in caseangular rates are produced.

The tank temperature will be set at a specific temperatureso pressure and thrust delivered by thrusters are the same forall of them. This strategy allows to synchronise the firing stopof thrusters with the condition that total impulse setpoint and“arm” temperature of all thrusters are the same.

The firing time in this experiment is defined by the selectedtank temperature and total impulse setpoints. To get observableresults, the tank temperature is set at 10 ˝C so the thrustdelivered by each thruster is 1 mN, and the total impulse


TABLE XXVIPOWER BUDGET FOR PERFORMANCE ASSESSMENT VIA IMPULSE FIRING MODE


1 10 200 0 2 5.5¨10´4 Idle System power up2 780a 200 1000 936 0.26 Propellant Conditioning Heat propellant in tank

and manifolds3 120a 200 2500 324 0.094 20b 200 5000 104 0.03 Firing Preparation Prepare two thrusters for firing5 150 200 5660 880 0.24 Firing Fire two thrusters6 5 100 0 0.5 1.4¨10´4 Off System power down

Total 1085 2246 0.62a The propellant conditioning (heating propellant in tank) time depends on the initial temperature of tank. Therefore, to reduce the heating time, it isassumed that this mode starts when the initial tank temperature is 5 ˝C, leading to 900 s for heating propellant in tank at mostb The firing preparation time depends on the initial temperature of thrusters; however, it is assumed that the minimum initial temperature that thrustersexpect is 0 ˝C, leading to 20 s for arming thrusters at most

setpoint is set at 120 mNs in each thruster, thus a firing timeof 2 min is expected.

Because of the nature of the experiment, it is recommendedthat this experiment is only scheduled during the hot case sce-nario to reduce the influence of power and thermal limitations;the proposed starting temperature for propellant conditioningmode is now set at 8 ˝C. Considering only the hot scenario,the experiment can be performed either automatically by theOBC at any time or manually during a pass over the groundstation.

Table XXVII shows the power budget for this experimentand Fig. 17 represents the power level timeline.

This experiment will follow the strategy described in Sec-tion III Telemetry considerations for an operating phase, thusconsidering the operating time proposed for this experiment,it generates 21.2 kB as described in (43). The results of thisexperiment will be stored in approximately 100 packets.

„

8 Bthruster


3 Btank

1 s`

6 Bgyro

1 s

¨515 s « 21.2 kB (43)

On the other hand, 26.3 kB are generated by this experiment,as computed in (44), in case the READ ALL register is usedfor data collection. The data will be stored in approximately123 packets.

„

45 B1 s

`6 Bgyro

1 s

¨ 515 s « 26.3 kB (44)

In case the thrust difference is larger than 10%, thismisalignment shall be compensated for for longer firingburns. This can be done by selecting different total impulseset points for each thruster so the firing time variationscompensate the imbalance of the spacecraft during a four-thruster manoeuvre.

6) Eccentricity change manoeuvre: Objective: to evaluatethe delivered ∆V and to measure the change in orbit eccen-tricity.

Procedure: A ∆V manoeuvre is performed in the radialdirection (´U direction) to attain a minimum eccentricitychange without altering the period of the orbit.

The change after the manoeuvre experiment is monitored bythe space track application in order to evaluate the performanceof the system for determining orbital changes.

“Arm” temperature is set equal for all thrusters to produceuniform thrust. The spacecraft should be stabilised using theiMTQ board after the manoeuvre experiment in case angularrates are produced.

The maximum traceable total impulse provided by onethruster is around 6.5 Ns since its counter register is stored in a16-bit integer, therefore, the maximum traceable total impulseprovided by all four thrusters firing is around 25 Ns. By using(45), the ∆V is computed, [3]. The maximum ∆V from a 3-kg CubeSat is about 8.2 m/s, considering the specific impulseof NanoProp is 50 s and mass of propellant is 50 g, as shownin Table II.

∆V “ Isp g0 lnˆ

m0

mf

˙

(45)

Using (46), the burn time of a manoeuvre is determined,[3]. The total burn time to get the maximum traceable totalimpulse, when all four thrusters are firing at 1 mN, is around104 min which is not recommended to be performed since itrequires extreme operating, power and thermal control.

tburn “Itot

F(46)

mp “Itot

Isp g0

(47)

Alternatively, if a burn is made within the line-of-sight ofthe ground station, then the ∆V manoeuvre could last about10 min. Using (45), (46), and (47), it is determined that thisoperation would generate a total impulse of 2.4 Ns and ∆V =0.8 m/s, assuming the thrusters produce 1 mN of thrust eachand mp is the mass of propellant consumed for that specifictotal impulse.

As a result, all four thrusters are fired in indefinite-firing-mode for 10 min towards the Earth (´U direction), andthe change in orbit eccentricity is measured to evaluate thedelivered ∆V.

Because of the nature of the experiment, it is recommendedthat this experiment is only scheduled during the hot case


TABLE XXVIIPOWER BUDGET FOR TRANSLATION ASSESSMENT


1 10 200 0 2 5.5¨10´4 Idle System power up2 240a 200 1000 288 0.08 Propellant Conditioning Heat propellant in tank

and manifolds3 120a 200 2500 324 0.094 20b 200 10000 204 0.06 Firing Preparation Prepare four thrusters for firing5 120 200 11320 1382 0.38 Firing Fire four thrusters6 5 100 0 0.5 1.4¨10´4 Off System power down

Total 515 2200 0.61a The propellant conditioning (heating propellant in tank) time depends on the initial temperature of tank. Therefore, to reduce the heating time, it isassumed that this mode starts when the initial tank temperature is 8 ˝C, leading to 360 s at most for heating propellant in tank up to 10 ˝Cb The firing preparation time depends on the initial temperature of thrusters; however, it is assumed that the minimum initial temperature that thrustersexpect is 0 ˝C, leading to 20 s for arming thrusters at most

scenario to reduce the influence of power and thermal limita-tions. Considering only the hot scenario, the experiment canbe performed either automatically by the OBC or manuallyduring a pass over the ground station.

To produce 1 mN on each thruster, in automatic operation,the OBC will start the experiment when the tank naturallyreaches 10 ˝C, so there is no need to use the tank heater.

On the other hand, in manual operation, the manoeuvrecould start at the beginning of the communication windowsince the expected tank temperature at this point is closeenough to 10 ˝C according to Section III NanoProp operatingmode, so there is no need to use the tank heater, yet themanifold heaters must be switched on during the entire longburn experiment to reduce the pressure and temperature dropas propellant is consumed.

The power budget for this experiment is shown in TableXXVIII. The power level timeline for this type of experimentis illustrated in Fig. 25.

Fig. 25. Power level timeline for Eccentricity change manoeuvre.

This experiment will follow the strategy described in Sec-tion III Telemetry considerations for an operating phase, thusconsidering the operating time proposed for this experiment,31 kB are generated as described in (48). The results of thisexperiment will be stored in approximately 145 packets.

„

8 Bthruster


3 Btank

1 s`

6 Bgyro

1 s

¨755 s « 31 kB (48)

On the other hand, in case the READ ALL register is usedfor data collection, 38.5 kB are generated by this experiment ascomputed in (49). The results will be stored in approximately180 packets.

„

45 B1 s

`6 Bgyro

1 s

¨ 755 s « 38.5 kB (49)

Finally, considering that this manoeuvre is performed attower position towards the Earth in ´U direction (radialmanoeuvre), the satellite will attain a small eccentricitychange without altering the period of the orbit. Followingboth solutions described in Appendix C, the attained ∆e «0.000053–0.000159, considering the MIST reference orbitparameters of Table I.

7) Altitude change manoeuvre: Objective: to evaluate thedelivered ∆V and to measure the change in orbit period aswell as semi-major axis and, consequently, the altitude.

Procedure: A ∆V manoeuvre is performed along the veloc-ity vector direction (+V) to attain a semi-major axis changeconsequently altering the period of the orbit.

The change after the manoeuvre experiment is monitored bythe space track application in order to evaluate the performanceof the system for determining orbital changes.


Considering that the burn is also made within the line-of-sight of the ground station, the operation would generate a totalimpulse of 2.4 Ns and ∆V = 0.8 m/s, assuming the thrustersproduce 1 mN of thrust each.

As a result, all four thrusters are fired in indefinite-firing-mode for 10 min along the velocity vector direction (+V), andthe change in orbital period or semi-major axis is measuredto evaluate the delivered ∆V.

Because of the nature of the experiment, it is recommendedthat this experiment is only scheduled during the hot casescenario to reduce the influence of power and thermal limita-tions. Considering only the hot scenario, the experiment canbe performed either automatically by the OBC or manuallyduring a pass over the ground station.

To produce 1 mN on each thruster, in automatic operation,the OBC will start the experiment when the tank naturallyreaches 10 ˝C, so there is no need to use the tank heater.

On the other hand, in manual operation, the manoeuvrecould start at the beginning of the communication windowsince the expected tank temperature at this point is closeenough to 10 ˝C according to Section III NanoProp operatingmode, so there is no need to use the tank heater, yet the


TABLE XXVIIIPOWER BUDGET FOR ECCENTRICITY CHANGE MANOEUVRE


1 10 200 0 2 5.5¨10´4 Idle System power up2 120a 200 1500 204 0.06 Propellant Conditioning Heat propellant in manifolds

3 20b 200 11500 234 0.07 Firing PreparationPrepare four thrusters for firing

Continue heating propellantin manifolds

4 600 200 12820 7812 2.17 FiringFire four thrusters

Continue heating propellantin manifolds

5 5 100 0 0.5 1.4¨10´4 Off System power downTotal 755 8253 2.3

a Since this experiment will be performed for more than 5 minutes, the heaters in the manifolds are switched on during the entire experiment to keep astable pressure and temperature. It is assumed that tank temperature is around 10 ˝C, tank heater will be only used in case the 10 ˝C criterion is not metb The firing preparation time depends on the initial temperature of thrusters; however, it is assumed that the minimum initial temperature that thrustersexpect is 0 ˝C, leading to 20 s for arming thrusters at most

manifold heaters must be switched on during the entire longburn experiment to reduce the pressure and temperature dropas propellant is consumed.

Since this experiment has the same requirements as theEccentricity change manoeuvre experiment, the power budgetand timeline of this experiment are represented in TableXXVIII, and Fig. 25. Moreover, the telemetry budgets for thisexperiment are described in (48) or (49).

Finally, considering that this manoeuvre is performed in thearrow position along the velocity vector direction (+V), thesatellite will attain a semi-major axis change consequentlyaltering the period from the original orbit. Based on thesolution described in Appendix C, the attained ∆a « 1.5 kmand ∆Tp « 0.031 min, considering the MIST reference orbitparameters of Table I.

However, in order to perform this manoeuvre, the satelliteneeds to be orientated with the thrust vector along the orbitalmotion (+V axis) so it is important to verify whether the ADCSsystem can produce and control this attitude change from thenominal attitude of MIST (tower position) to arrow position.For instance, the ADCS system is able to position MIST in aspecific attitude by selecting which axis to point towards Nadir,but since the system is only able to control Nadir pointing,MIST could rotate along the axis pointing Nadir at arrowposition, but also it might be slightly complex to keep theleast inertia axis towards the orbital motion direction.

B. Decommissioning operations

Based on the strategy described in Section III Decommis-sioning plan, the passivation plan for NanoProp propellanttank should implement one or more of the following operationsfor depleting the stored energy at end of mission:‚ Venting‚ Depletion manoeuvres(s)‚ Depressurisation at least down to a level such that no

bursts can occur due to over-pressure or temperatureAccording to Fig. 20, NanoProp can just perform the

venting operation since MIST is initially within the 25-yearnatural decay limit so there is no need to do any disposalmanoeuvre, but it is important to control the unpredictable

attitude result from this operation and assure the stability ofthe satellite afterwards.

On the other hand, performing depletion manoeuvres allowthe consumption of the remaining propellant and, conse-quently, depressurise the tank, but most importantly they couldalso reduce the time of natural decay for MIST by performingthese manoeuvres opposite to the direction of motion.

In any case, it is considered that the remaining mass ofpropellant in the tank is about 70% of the initial propellantmass at End Of Life (EOL).

1) Venting: Objective: to remove stored energy to preventdebris generation after end of mission.

Procedure: To open the valves, first enable the manual valvecontrol placed in the tank passivation register.

Open the two first barrier valves to thrusters A+B and C+Drespectively, then open all four second barrier valves withoutheating the propellant in tank, manifolds or thrusters.

Using (50) and (51), an approximate operating time forthe venting operation was computed, [3]. Assuming that theremaining mass of propellant mp at EOL is approximately 35g, it would take 2 min at most to expel the propellant out tospace. It was also assumed that the venting exhaust velocityis 10 m/s and a nominal thrust of 1 mN per thruster.

9m “F

ve(50)

t “mp

9m(51)

However, it is recommended to perform an extra 2-minventing operation in the following orbit since the efficiency tovent the last amount of propellant is poor due to the possibleice-cold state of propellant.

Finally, evaluate the gyro board response to determine theinfluence of venting in the spacecraft rotation. The spacecraftshould be stabilised using the iMTQ board after the ventingoperation is complete.

This operation can be performed manually during groundcontact or automatically by the OBC in both the cold and hotscenarios.


The power budget and power level timeline are shown inTable XXIX and Fig. 26.

Fig. 26. Power level timeline for Venting operation.

Even though the venting operation does not require firingthe propulsion system, it is recommended that this operationcollects the following relevant data with samples collected ata frequency of 1 Hz. Therefore, every second, 31 B need tobe sent to the OBC as shown in Table XXX.‚ Tank Temperature‚ Tank Propellant Consumption‚ Thruster Thrust‚ Thruster Temperature‚ Thruster Pressure‚ Tank Passivation‚ Valve Control‚ Angular RatesConsidering the operating time proposed for this operation,

4.2 kB are generated as described in (52). The results of theoperation will be stored in approximately 20 packets.

r5 Bthruster


3 Btank

1 s`

6 Bgyro

1 s`

`2 Bventing

1 ss ¨ 135 s « 4.2 kB (52)

On the other hand, in case the READ ALL register is usedfor data collection, 7 kB are generated by this operation ascomputed in (53). The results will be stored in approximately33 packets.

„

45 B1 s

`6 Bgyro

1 s

¨ 135 s « 7 kB (53)

2) Depletion/Disposal manoeuvre: Objective: to removestored energy to prevent debris generation after end of mission,and to place the spacecraft in an orbit where natural orbitaldecay allows re-entry in less than 25 years.

Procedure: A “braking” ∆V manoeuvre is performed alongthe velocity vector direction (´V) to attain a semi-major axischange placing the satellite in a lower orbit leading to adecrease in the natural lifetime of MIST.

The change after the manoeuvre operation is monitored bythe space-track application in order to evaluate the perfor-mance of the system for determining orbital changes.


By using (45), it is determined that the maximum attainable∆V provided by this manoeuvre is 5.6 m/s, consideringthe specific impulse is 50 s, 1 mN of thrust delivered per

thruster, and 15 g of propellant already consumed in previousexperiments which yields to m0 = 2.985 kg.

Following the analytical method described in Appendix C,a 5.6 m/s manoeuvre will place MIST in a final orbit whosesemi-major axis is about 7 012 km, taking into account an a0= 7 021.94 km which was generated by the Altitude changemanoeuvre experiment.

Using (54) and (55) a burn time for this operation is com-puted, [3]. Since NanoProp has low thrust performance, thestrategy is to perform this manoeuvre continuously, resultingin a spiral-type trajectory whose total burn time is 70 min,assuming each thruster delivers 1 mN of thrust, that is notrecommended to do since it requires extreme operating, powerand thermal control.

acc «F

m0(54)

tburn “µacc

´

a´120 ´ a

´12f

¯

(55)

Alternatively, it is possible to subdivide the overall “brak-ing” manoeuvre into several submanoeuvres performed withinthe line-of-sight of the ground station, then each ∆V sub-manoeuvre will be 0.8 m/s as described in the Eccentricitychange manoeuvre experiment when all thrusters deliver 1 mNof thrust.

As a result, 7 submanoeuvres are performed. For eachsubmanoeuvre all four thrusters are fired in indefinite-firing-mode for 10 minutes opposite to the velocity vector direction(´V), and the change in orbital period is measured to evaluatethe delivered ∆V.

Because of the nature of these operations, it is recommendedthat these operations are only scheduled during the hot casescenario to reduce the influence of power and thermal limi-tations. Considering only the hot scenario, the operations canbe performed either automatically by the OBC or manuallyduring a pass over the ground station.

To produce 1 mN on each thruster, in automatic operation,the OBC will start the operations when the tank naturallyreaches 10 ˝C, so there is no need to use the tank heater.

On the other hand, in manual operation, the submanoeuvrescould start at the beginning of the communication windowsince the expected tank temperature at this point is closeenough to 10 ˝C according to Section III NanoProp operatingmode, so there is no need to use the tank heater, yet themanifold heaters must be switched on during the entire longburn experiment to reduce pressure and temperature drop aspropellant is consumed.

Since these operations have the same requirements as theEccentricity change manoeuvre experiment, the power budgetand timeline are represented in Table XXVIII, and Fig. 25.Moreover, the telemetry budgets for these operations aredescribed in (48) or (49).

After performing the complete depletion/disposal manoeu-vre operation, the decay time of MIST would be reduced downto 15 years since the disposal orbit is 7 012 km. Fig. 27shows the 15-year natural lifetime of MIST as a function ofaltitude computed in DRAMA tool by ESA and consideringthe spacecraft parameters described in Table XIX.


TABLE XXIXPOWER BUDGET FOR VENTING OPERATION


1 10 200 0 2 5.5¨10´4 Idle System power up2 120 200 1320a 183 0.05 Open all valves3 5 100 0 0.5 1.4¨10´4 Off System power down

Total 135 186 0.05a It is advised to have a delay of minimum 10 ms between each valve opening to limit the peak power consumption

TABLE XXXTELEMETRY BUDGET PER INTERROGATION IN VENTING OPERATION

Parameter Size [B]Tank Temperature 1Tank Propellant Consumption 2Thruster Thrust 2 ¨ (4 thrusters)Thruster Temperature 1 ¨ (4 thrusters)Thruster Pressure 2 ¨ (4 thrusters)Tank Passivation 1Valve Control 1Angular Rate 2 ¨ (3 gyroscopes)Total 31

Fig. 27. Orbit life time of MIST after depletion/disposal manoeuvre.

As a result, the depletion/disposal manoeuvre would de-crease the natural decay time of MIST about 1.5 years,considering that the initial natural lifetime of MIST was 16.5years as determined in Section III Decommissioning plan.Finally, in order to perform these operations, the satelliteneeds to be orientated with the thrust vector along the orbitalmotion so it is important to verify whether the ADCS systemcan produce and control an attitude change from the nominalattitude of MIST (tower position) to arrow position.

C. Standard operating procedure

A special operating mode to fire NanoProp is clearlyneeded, thus a SOP was designed as a flowchart to describethe interaction between the OBC and NanoProp.

Folder “NanoProp SOP”, placed in MIST Dropbox/M174-NanoProp, shows in detail the main SOP for one thrusteraccording to the set of modes of NanoProp: Idle, PropellantConditioning, Firing, Firing Preparation and Off. The aim ofthis flowchart is to provide a general understanding of how

to operate NanoProp. The SOP needs to be shaped accordingto the operating requirements of the experiments described inSection IV Experiments and Decommissioning operations.

D. Simulation Example

In order to have a better understanding of how the operationof NanoProp influences the dynamic behaviour of MIST andhow other subsystems operate according to the outcomesinduced by NanoProp, a Matlab/Simulink simulation of theexperiment Performance assessment via Indefinite firing modewas performed.

According to Section IV Experiments, the objective of thisexperiment is to assess the performance and misalignment ofthrusters by firing pairs of thrusters, thus firing configuration(Fire thruster A & B) with variation in thrust magnitudemisalignment was selected. Considering that the maximumforeseen misalignment between thrusters is 10%, Thruster Ais set to fire at 0.9 mN and Thruster B at 1 mN for 1 min.Fig. 28 illustrates this scenario.

Fig. 28. Firing thruster A and B with variation in thrust misalignment.

From Fig. 28, it is clear that the simulated misalignmentbetween thrusters A and B will produce pitch and yaw rota-tions, the main torque will be applied around the Y axis anda small torque will be generated about the X axis, therefore,considering the distances illustrated in Fig. 11, the torquesapplied into the system are shown in Table XXXI.

Table XXXII summarises the most important parameters forMIST, NanoProp, MPU6050, and iMTQ models to run theexperiment.

Fig. 29 shows the dynamic performance of MIST overthe operating time. Since the main torque is applied about


TABLE XXXITORQUE OVERVIEW

Thruster Lx [Nm] Ly [Nm] Lz [Nm]A ´3.24¨10´5 3.06¨10´5 0B 3.6¨10´5 3.4¨10´5 0

Total 3.6¨10´6 6.46¨10´5 0

TABLE XXXIIINITIAL PARAMETERS FOR SIMULATION

Parameter ValueMIST

Ix 0.051 kgm2

Iy 0.037 kgm2

Iz 0.0205 kgm2

wx 10´3 rad/swy 0 rad/swz 0 rad/sβ0 1β1 0β2 0β3 0

NanoPropFA 0.9 mNFB 1 mNFC 0 mNFD 0 mNtburn 1 mindA [34 36 150] mmdB [34 ´36 150] mmdC [´34 36 150] mmdD [´34 ´36 150] mm

MPU6050-Gyrofsampling 10 Hz

Full scale range ˘250 ˝/sSensistivity scale factor 131 LSB/(˝/s)

ωbias 0 ˝/sωARW 0.005 p˝sq

?Hz

ωRRW 0 p˝sq?

HzωBi

0 ˝/siMTQ

fsampling 8 Hzc 104 Am2s/T

md 0.2 Am2

Actuation error 5 %Magnetometer accuracy 3 µT

the Y axis, ωy holds the highest angular velocity evolution.Even though the torques are only applied about X and Yaxes, there is still a minimum rotation generated about theZ axis which needs to be controlled by the iMTQ system.However, all produced angular velocities are much smallerthan the maximum angular rate handled by the iMTQ, thusthis experiment does not compromise the control of MISTafterwards.

As shown in Fig. 29, it is important to perform a calibrationin gyroscope before the start of the experiment in order toreduce errors in measurements generated by static bias andrandom noise.

Once the angular velocities are measured and filtered bythe gyroscope, the torques are computed on-ground. Fig. 30shows the resulting torque outcome produced by the torqueevaluation model.

Assuming a zero misalignment scenario for this experiment,it is expected to see no torques about X and Z axes, but Ly

= 6.8¨10´5 Nm. Instead, the resulting torque outcome from

the simulation shows torque generations about X and Y axesindicating that there is a misalignment between thrusters asexpected.

By evaluating these outcomes, it can first be determinedthat the misalignment between thrusters is minimum sincethe torque generated about Y axis is similar to the valueexpected for the zero misalignment scenario. Second, it can beconcluded that the misalignment between thrusters is causeddue to variation in thrust magnitude because there is no torquegenerated about Z axis, moreover, since the torque generatedabout the X axis is positive, it can be defined that Thruster Adelivers less thrust with respect to Thruster B.

Then, the torque results from the model concentrate aroundthe values defined in Table XXXI, therefore, the torque eval-uation model is able to provide a detailed overview of thethruster performance of NanoProp.

On the other hand, Fig. 31 shows the kinematic performanceof MIST over the operating time. The computation indicatesthe spacecraft rotates mainly about the Y axis as NanoProp isfiring. Once the manoeuvre is complete, MIST will be rotated180˝ with respect to the initial X and Z references axes.

Finally, once the experiment is complete, the iMTQ isactivated to detumble the satellite from the final angularvelocities produced by the manoeuvre. Fig. 32 shows theBDOT detumble operation of MIST.

Considering that the orbital period of MIST reference orbitis approximately 98 min, the iMTQ will take about 2.5 orbitsto detumble MIST so it can be orientated to a given attitudeafterwards.

V. DISCUSSION AND FUTURE WORK

Based on this study, the NanoProp propulsion system is ableto provide a wide range of manoeuvres for a 3U CubeSat,but the application of those in space will mainly dependon thermal, power, and telemetry budgets developed for aspecific mission, and in this case, since MIST is still underdevelopment, the proposed mission experiments offer a stronginitial understanding and guideline of the requirements andlimitations considered for the operation of NanoProp accord-ing to the requirements of the MIST mission.

Clearly, the need for a special operating mode for the OBCsoftware to run NanoProp is crucial to effectively performthe proposed mission experiments. Therefore, the developedoperating procedures such as the telemetry and FDIR analysisof NanoProp, together with the developed SOP, provide afeasible strategy to design the interaction between the OBCand NanoProp. Moreover, proposed mission experiments, in-cluding their power and telemetry budgets, present the basisfor developing more practical system engineering budgets forthe MIST mission.

According to the results presented in this study and thelatest engineering budgets developed for MIST mission, theoperation of NanoProp can be performed as proposed inthe study. Yet, there are some specific operating details thatneed a further examination such as the opportunity to operateNanoProp during a ground station pass, the attitude change toperform manoeuvres in the arrow position or the implementa-tion and operation of the IMU board in the MIST satellite.


Fig. 29. Angular velocity evolution over time. The measurements generated by the gyroscope will serve as inputs for iMTQ model and Torque evaluationmodel

Fig. 30. Torque estimation. Kalman filters were also generated to reduce the noise in the torque evaluation model. Tuning of filters might be necessary forbetter measurements.

In case it is desired to run some of the allowed missionexperiments of NanoProp over the ground station, a completesystem engineering budget, including the requirements of theother experiments in operation, is needed to determine thefeasibility of this strategy. Fortunately, the study points outthat all proposed mission experiments of NanoProp can beautomatically performed at any time during the orbit.

Moreover, the required attitude change for arrow manoeu-vres depends on the feasibility of the ADCS system andgeneral power requirements of MIST to perform and controlthis attitude change. This condition actually questions thepossibility of performing the suggested depletion manoeuvre atEOL of the mission which yields to consider the venting strat-egy as the primary option for passivation plan for NanoProp.

On the other hand, functional testing is needed to verify theoperating characteristics mentioned in this study for the IMUboard. It is particularly important to inspect the filtering pro-cess included in the system so one can have a better outlook on

the needs and limitations of the embedded gyroscope board toread the induced angular rates. Similarly, the implementationof a functional testing campaign for NanoProp may be usefulto understand the performance and operating requirementsof the system, and most importantly, to validate the resultsproposed in this study.

Finally, according to the mentioned simulation example, theMatlab/Simulink model offers a feasible practice to understandthe dynamic and kinematic interaction between NanoProp andthe satellite, but in order to have a more realistic outlook, theimplementation of other external perturbations in the environ-ment of the spacecraft such as solar pressure or atmosphericdrag should be considered in the simulation. They can clearlyalter the angular rates induced by firing NanoProp, althoughto a minor extent. Moreover, the option to develop a moresensible firing model for NanoProp can be significant for thesimulation. For instance, a pulse of exhaust propellant is ingeneral in the shape of a steep thrust peak at the instant of


Fig. 31. Attitude evolution over time. The attitude reference is Euler Angles described in XYZ sequence.

Fig. 32. Detumble operation over time.

firing followed by a tail after the instant of the firing stopping.This special behaviour and some minor delays after sendinga firing or stop firing command can shape the thrust levelsdelivered by NanoProp.

VI. CONCLUSION

A propulsion system clearly improves the performance ofthe mission by adding more functionalities to the spacecraftsuch as attitude and orbital manoeuvres, station keepingcontrol, decommissioning strategy or interplanetary travel.However, it is important to notice that the accessibility tothese functionalities mainly depend on the type of propul-sion system selected for the mission and the profile of themission itself to be performed, therefore, the implementationof a propulsion system in a satellite definitely requires anexhaustive understanding of the performance and internaloperating requirements of the system as well as definitionof the objectives and operating characteristics of the spacemission.

As a result, a feasibility study and mission plan for thepropulsion system need to be developed at early stage of themission design in order to develop a spacecraft qualified tocomplete its mission objectives as demanded. For that reason,the results of this study, effective from the commissioningstage to the decommissioning stage, aim to determine theprocedures and experiments to operate and evaluate the per-formance of the NanoProp 3U propulsion system according tothe mission profile of the MIST 3U CubeSat satellite.

Finally, the presented results in this study also indicate acontinuous interaction of the propulsion system with othersubsystems on-board the satellite. The conditions to operatea subsystem evidently impact the conditions to run othersas well as the general affordability of the space mission,therefore constant evaluation of the thermal, telemetry andpower budgets need to be performed so that all elements inthe spacecraft work together towards the development of acomplete and safe space mission.


ACKNOWLEDGMENTS

Foremost, I would like to express my special gratitude to mysupervisors Sven Grahn and Johan Sundqvist whose expertise,consistent guidance, and endless advices helped me to bringthis study into success.

Moreover, I would like to thank to the MIST project and allmy fellow teammates for giving me the opportunity to be partof a unique group developing a satellite that will be flyingin space very soon. For a year and a half, I have attainedimmense memories and experiences that certainly will inspirein my future and personal projects.

I would also like to thank to GomSpace and the entire stafffor their sincere guidance and help for completing this study.

Special thanks to CONACYT for giving me the opportunityand financial support to develop my graduate studies abroad.

My deepest appreciation belongs to my family, especiallymy parents Alejo and Dulce and my sister Karla, for givingme unlimited support and encouragement to undertake thiswonderful adventure. You have always been by my sidedespite the physical distance that sometimes separates us, butremember in a few years we will be talking about light yearsaway.

REFERENCES

[1] E. Kulu. Nanosats database. [Online]. Available: https://www.nanosats.eu/

[2] S. Grahn, “Mist project handbook.” [Online]. Avail-able: https://www.dropbox.com/s/6nhq4mxds8trc7d/MIST M512 002version 7 20190114 MIST Project Handbook.pdf?dl=0

[3] W. E. Wiesel, Spaceflight Dynamics. Beavercreek, Ohio: AphelionPress, 2010.

[4] GomSpace, “Interface control document: Nanoprop 3u propulsion mod-ule.” [Online]. Available: https://www.dropbox.com/s/lmlv721p3s1onac/20480ICD%20v1%20Interface%20Control%20Document.pdf?dl=0

[5] ——, “User manual: Nanoprop 3u.” [Online]. Available: https://www.dropbox.com/s/g3nbuvviy8uh09z/v3%20User%20Manual.pdf?dl=0

[6] ISIS, “imtq user manual.” [Online]. Available: https://www.dropbox.com/s/ivhxzpzt4temlcx/ISIS.iMTQ.User%20Manual.v1.5.E.pdf?dl=0

[7] InvenSense. Mpu-6000 and mpu-6050 product specification.[Online]. Available: https://invensense.tdk.com/wp-content/uploads/2015/02/MPU-6000-Datasheet1.pdf

[8] H. Schaub and J. L. Junkins, Analytical Mechanics of Space Systems.Blacksburg, Virginia: AIAA Education Series, 2009.

[9] Matlab, “Imu.” [Online]. Available: https://se.mathworks.com/help/nav/ref/imu.html

[10] L. Larsson, “Design of spacecraft attitude determination system usingmems sensors,” Master’s thesis, KTH Royal Institute of Technology,2016.

[11] Matlab, “Inertial sensor noise analysis using allan vari-ance.” [Online]. Available: https://se.mathworks.com/help/nav/ug/inertial-sensor-noise-analysis-using-allan-variance.html

[12] ——, “Kalman filter.” [Online]. Available: https://se.mathworks.com/help/control/ref/kalmanfilter.html

[13] H. D. Shuo Cai, Yunfeng Hu and H. Chen, “A noise reductionmethod for mems gyroscope based on direct modeling and kalmanfilter,” Acta Astronautica, vol. 51, no. 31, pp. 172–176, 2018.DOI:10.1016/j.ifacol.2018.10.032.

[14] S. Chandrashekar, “De-tumbling analysis of mist satellite.” [Online].Available: https://www.dropbox.com/s/svur07oee5a9c8o/MIST M160005 version 1 20160215 De-tumbling%20Analysis%20of%20MIST%20Satellite%20 %20Shreyas%20Chandrashekar.pdf?dl=0

[15] R. Scholtes, “Thermal analysis 2019 final report.” [On-line]. Available: https://www.dropbox.com/s/blzg4hb6x1xdvqy/MISTThermal Analysis 2019 Robin Scholtes.pdf?dl=0

[16] InvenSense. Mpu-6000 and mpu-6050 register map and descriptions.[Online]. Available: https://invensense.tdk.com/wp-content/uploads/2015/02/MPU-6000-Register-Map1.pdf

[17] ESA. Esa space debris mitigation compliance verification guidelines.[Online]. Available: https://copernicus-masters.com/wp-content/uploads/2017/03/ESSB-HB-U-002-Issue119February20151.pdf

[18] F. S. Thomas Uhlig and M. Schmidhuber. Spacecraftoperations. [Online]. Available: https://link.springer.com/book/10.1007%2F978-3-7091-1803-0

[19] ESA. Esa requirements on eol de-orbit. [Online].Available: https://indico.esa.int/event/73/attachments/2543/2948/ESARequirements on EOL De-orbit.pdf

[20] D. Brundin, “Mist, minimum and maximum orbit life time.”[Online]. Available: https://www.dropbox.com/s/m35icn02mwy576v/MIST M531 005 version 2 20151129 Minimum and Maximumlifetime.pdf?dl=0

[21] E. Butikov, “Relative motion of orbiting bodies,” American Jour-nal of Physics - AMER J PHYS, vol. 69, pp. 63–67, 2001.DOI:10.1119/1.1313520.

[22] S. M. A. Ruggiero, P. Pergola and M. Andrenucci, “Low-thrust maneu-vers for the efficient correction of orbital elements,” 2011.

[23] R. A. Bettinger and J. T.Black, “Mathematical relation between thehohmann transfer and continuous-low thrust maneuvers,” Acta Astro-nautica, vol. 96, pp. 42–44, 2014. DOI:10.1016/j.actaastro.2013.11.020.


APPENDIX AFAULT DETECTION ISOLATION AND RECOVERY ANALYSIS


APPENDIX BFAILURE MODE AND EFFECTS ANALYSIS

To increase the reliability of the MIST-NanoProp mission,it is important to first perform an FMEA analysis in orderto systematically identify potential failures in products (func-tional and hardware) and processes and subsequently set anadequate FDIR policy. This FMEA analysis only considersthose potential failures that might occur in following equip-ment during the operation of NanoProp. The effects of thesefailures are assessed at spacecraft level.‚ Tank Temperature Sensor and Tank Heater‚ Manifold Heaters‚ Thruster Temperature Sensors and Thruster Heaters‚ Gyroscope Board


APPENDIX CORBITAL MANOEUVRE ANALYSIS

This appendix shows the analytical methods to calculatethe orbital changes when performing two types of orbitalmanoeuvres: radial and along velocity vector.

Moreover, the appendix analyses the feasibility of the No-vAtel OEM615 GPS receiver and the Space Track softwaretool to detect the orbital changes expected to see for the MISTmission.

A. Radial Manoeuvre

A radial ∆V manoeuvre will attain a small eccentricitychange without altering the period from the original orbit, [21].

Considering the orbital parameters for MIST which aredescribed in Table I and R0 = 6 378.15 km, the altitudes ofapogee and perigee are:

hp “ 635.28 km ha “ 649.32 km

The two solutions below determine the eccentricity changesfrom a ∆V = 0.8 m/s manoeuvre to be performed for theMIST mission.

1) Solution 1:

∆h “∆V Tp

2π“

0.8 m/s ¨ 5 854.07 s2π

« 745.36 m

∆e1 “∆h

ha ` hp ` 2 R0“ 0.000053

ef “ ∆e1 ` e0 “ 0.001053

2) Solution 2: Using (56), it is also possible to computethe total velocity increment, for quasi-circular orbits, requiredto realize a net eccentricity change from an initial value e0 toa final value ef , [22].

∆V “2

3

c

µa

ˇ

ˇarcsin pe0q ´ arcsin pef qˇ

ˇ (56)

ef,1 “ sin

ˆ

arcsin pe0q `∆V3

2

c

a

µ

˙

ef,2 “ ´ sin

ˆ

∆V3

2

c

a

µ´ arcsin pe0q

˙

ef,1 “ 0.001159 or ef,2 “ 0.00084

| ∆e2 |“ 0.000159

The differences between ∆e solutions are in the magnitude10´4, therefore, it is determined that both approaches aresufficiently correct. As a result, the ∆e from solution 2 (∆e2= 0.000159) can be considered the maximum possible ∆eattained by this manoeuvre.

Finally, both eccentricity changes are compared with theeccentricity evolution of the former ESTCube-1 CubeSat mis-sion which was determined by the Space Track software as

Fig. 33. Eccentricity evolution for ESTCube-1 mission computed in SpaceTrack software.

illustrated in Fig. 33. The ∆e1 = 0.000053 is shown as a redarrow and ∆e2 = 0.000159 is shown as a green arrow.

Both eccentricity changes are also compared with the ec-centricity evolution determined by the OEM615 GPS receiveron-board the GOMX-4B CubeSat mission when performing an8 cm/s manoeuvre as shown in Fig. 34. Data were providedby GomSpace. The ∆e of this manoeuvre is smaller than theminimum changes expected to see from a 0.8 m/s manoeuvreto be performed for the MIST mission.

Fig. 34. Eccentricity evolution in GOMX-4B mission after performing an 8cm/s manoeuvre.

B. Along velocity vector ManoeuvreOn the contrary, a ∆V manoeuvre parallel to the orbit

velocity vector will produce a change in both period and semi-major axis, [21].

By using (57), the required velocity increment, for quasi-circular orbit, to obtain a change in semi-major axis is com-puted, [22] [23]:

∆V “

c

µa0´

c

µaf

(57)


af “µ

´b

µa0´∆V

¯2

Considering one more time the orbital parameters of TableI and a ∆V = 0.8 m/s manoeuvre to be performed for theMIST mission.

af “ 7 021.94 km

∆a « 1.5 km

Finally, this type of ∆V manoeuvre will also produce achange in the orbital period.

Tp “ 2π

d

a3

µ“ 5 855.94 s “ 97.6 min

∆Tp « 0.031 min

As shown in Fig. 35, the green arrow represents the ∆Tp =0.03 min to see for the MIST mission which is compared withthe period evolution of the ESTCube-1 mission determined bythe Space Track software.

Fig. 35. Nodal period evolution for ESTCube-1 mission computed in SpaceTrack software.

On the other hand, the ∆a «1.5 km is compared with thesemi-major axis evolution of the GOMX-4B CubeSat whenperforming an 8 cm/s manoeuvre as shown in Fig. 36. Datawas determined by the on-board OEM615 GPS as well. Thesemi-major axis change is smaller than the expected change tosee from a 0.8 m/s manoeuvre to be performed for the MISTmission.

In conclusion, both the NovAtel OEM615 GPS receiverand the Space Track ground tracking software tool are ableto detect the orbital changes produced from ∆V = 0.8 m/smanoeuvres which are planned to be performed on MIST inthe ˘ U direction (satellite at tower orientation) and in the ˘V direction (satellite at arrow orientation).

However, the precision of the GPS is not necessarily thelimiting factor in orbit determination. A strategy must bedeveloped for sampling the GPS in multiple positions alongthe orbit to exceed the accuracy of a single point navigationsolution.

Fig. 36. Semi-major axis evolution in GOMX-4B mission after performinga 8 cm/s manoeuvre.

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