Model-in-the-Loop Simulation of the ECOSat-III Attitude

Determination and Control System

Joao Henrique Figueiredo Freitasjoao.h.freitas@tecnico.ulisboa.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

November 2016

Abstract

Ever since CubeSats were first proposed, universities have found an opportunity to engage inlow-cost space application projects. However, a large number of these satellites tend to fail theirmission. The correct functioning of a satellite and the success of the mission depends on every stage ofits development, but specially on the quantity and quality of the executed performance tests. Generally,universities do not have the necessary means or conditions to perform meticulous and extensive tests,thus diminishing the probability of success of these academic projects. In this thesis, a testing systemis proposed to examine the influence of signal transmission between the componentes of the AttitudeDetermination and Control System (ADCS) of a CubeSat, namely the ECOSat-III, on the attitudecontrol of the satellite during its mission. The goal is to provide the development team with a simpleand flexible framework to check how the required pointing of the system is affected by a real signaltransmission between the sensors, actuators, and algorithm of the ADCS, for different configurationsbeing tested. An orbit simulator is developed, which creates the necessary information for the modeledsensors to output realistic measurements to the ADCS algorithm that, in turn, sends to the actuators,also simulated, the control commands. This communication is done through a Controller Area Networkbus system. In the end, this framework operates as a Model-In-the-Loop simulation. The simulationsare performed for the ECOSat-III.Keywords: CubeSat, Attitude Determination and Control System, signal transmission, ControllerArea Network, Model-In-the-Loop

1. IntroductionOver the last few years, we have witnessed an

increased development of smaller and lighter satel-lites. Such an increase resulted in a need to definedifferent classes of these small spacecrafts. Accord-ing to Janson [1], and employing a discriminatorfor mass, satellites that weigh between 10 kg and100 kg are designated microsatellites, between 1 kgand 10 kg nanosatellites, and between 0.1 kg and1 kg picosatellites.

With a desire to provide students the possibil-ity to design a satellite, Bob Twiggs and JordiPuig-Suari developed, in 1999, a standard for amuch more specific category within nanosatellites:a CubeSat [2]. Its unit has a defined size of10 cm × 10 cm × 11 cm that weighs a maximum of1.3 kg and can be comprised of multiple units.

The development of these small and light satel-lites opened a door to universities that now havethe possibility to design, build, and launch satel-lites into orbit. From 2003 until today, hundredsof missions were done [2]. However, this kind ofprojects are complex and a lot of them fail, mostly

because of lack of tests. This issue is focused onthis work, where a framework is proposed in orderto perform tests on a CubeSat subsystem, with realsignal transmission between its components.

1.1. The ECOSat Project

The Enhanced Communications Satellite(ECOSat) is a student team of the University ofVictoria (UVic) created with the purpose of partic-ipating in the Canadian Satellite Design Challenge(CSDC). The CSDC is a competition, betweenteams of Canadian universities, that consists ondesigning and building a fully-operational 3U(three cubic units) CubeSat. The team is currentlydeveloping the ECOSat-III to participate in thisyear’s competition. Figure 1 shows a model of thesatellite.

Taking into account that the main goal of thesatellite is to perform hyperspectral imaging, a suit-able ADCS is required to guarantee the correctpointing of the camera. To answer this, a sen-sor and actuator suite — which includes a Re-action Wheel System (RWS) designed and sug-

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Figure 1: ECOSat-III model.

gested by Gomes [3] — along with attitude de-termination and control algorithms, was selectedin the work done by Rondao [4]. The attitudeof the satellite shall be determined by the un-scented quaternion Kalman filter (UQKF) algo-rithm, initialized by the constant gain geometricattitude observer (GEOB). The sensor suite se-lected is composed of a gyroscope (Silicon Sensing R©

CRS09-01), a magnetometer (PNI R© RM3100), aSun sensor (Solar MEMS R© nanoSSOC-A60), anda Global Navigation Satellite System (GNSS) re-ceiver (NovAtel R© OEM615 Dual-Frequency GNSSreceiver). The attitude of the satellite shall be con-trolled by the RWS, composed of four flywheels ina pyramidal configuration with their respective mo-tors (FAULHABER R© 1202H004BH). It will workcombined with a three-axis magnetic torquer, withsix orthogonally-oriented custom-built rods, twoper axis.

Since there is a 58% failure rate of academicCubeSats [5] due to student teams undervaluingsystem-level functional tests [2], this work focuseson trying to diminish the probability of errors hap-pening on the ECOSat-III by providing a frame-work to check how the ADCS performs when thereis real signal transmission between its components.

2. Background

2.1. Frames of Reference

In order to study the motion and attitude of thesatellite, a reference frame must be set. Choosingthe adequate frame of reference is essential for abetter physical understanding of the problems. Theused frames of reference are the Earth-Centered In-ertial (ECI) frame, the Earth-Centered Earth-Fixed(ECEF) frame, and the body frame.

2.1.1 Earth-Centered Inertial frame

The origin of the ECI frame of reference, I =i1, i2, i3, is fixed at the center of the Earth. i1points towards the vernal equinox, the directionfrom the Earth to the Sun when it crosses the equa-torial plane of the Earth, from south to north, onthe first day of spring. i3 is aligned with the axis ofrotation of the Earth, through the North pole. i2satisfies the right-hand rule [6]. Neither the vernalequinox nor the North pole directions are inertiallyfixed, which is why these axes are defined accordingto a specific epoch: J2000 [7].

2.1.2 Earth-Centered Earth-Fixed frame

The origin of the ECEF frame of reference, F =f1, f2, f3, is at the center of the Earth. f1 pointstowards the Greenwich meridian in the equatorialplane, f3 is aligned with the axis of rotation of theEarth, through the North pole, and f2 satisfies theright-hand rule [6].

2.1.3 Body frame

The origin of the ECOSat-III body frame of refer-ence, B = b1, b2, b3, is at the center of mass of thespacecraft. b1 points in the direction of the bottomplate adjacent to the antenna, b3 points throughthe hyperspectral imaging camera, and b2 satisfiesthe right-hand rule.

2.2. Orbital mechanics2.2.1 Two-body Problem

Correctly describing the motion of celestial bod-ies is a hard task. Newton approached the problemby combining his law of universal gravitation withhis second law of motion, obtaining the two-bodyequation of motion [8],

r = −Gm1 +m2

r3r, (1)

where r is the inertial acceleration, G = 6.674 ×10−11 N m2/kg2 is the universal gravitational con-stant, m1 and m2 are the masses of the bodies, ris the position vector of body 1 relative to body 2,and r is the distance between the objects.

Johannes Kepler, with the astronomical datagathered by his mentor, Tycho Brahe, developedthree empirical rules of planetary motion — Ke-pler’s Laws — which were later derived by IsaacNewton: each of two objects interacting gravita-tionally describe a trajectory that is a conic section,an intersection of a plane and a cone, with the cen-ter of mass at one focus; a line joining these objectssweeps out equal areas in equal intervals of time,so the angular momentum is conserved; the sum oftheir masses multiplied by the square of their periodof mutual revolution is proportional to the cube ofthe mean distance between them [8, 9].

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2.3. Keplerian orbitsWhen a body moves through space, its path de-

fines an orbit or trajectory. A Keplerian orbit isan orbit approximation in which it is assumed thatgravity is the only force acting on the two objects,the mass of the central body is much greater thanthe mass of the orbiting body, and the central bodyis a perfect sphere.

If we consider a satellite orbiting around theEarth, a Keplerian orbit is a fairly good approx-imation. Defining, approximately, µ = GM =3.986× 1014 N m2/kg as the standard gravitationalparameter of the planet Earth, where M is the massof the Earth, Eq. (1) becomes [9]

r = − µr3r. (2)

One solution of this equation results in the orbitequation on the orbital plane [10],

r =p

1 + e cos θ, (3)

where p is the semilatus rectum, the perpendiculardistance to the major axis between the focus andthe orbit, e the magnitude value of the eccentricityvector, e — a vector that points from the focus tothe point of the orbit closer to it — and θ is thetrue anomaly, the angle between r and e.

As stated by the first Kepler’s law, the orbit of anobject is a conic section specificed by the eccentric-ity: if e = 0, the orbit is a circle; if 0 < e < 1, theorbit is an ellipse; if e = 1, the orbit is a parabola;and if e > 1, it is a hyperbola. However, only theellipse and hyperbola orbits occur in nature [9, 10].

One way to define the characteristics of the orbitis through the use of Keplerian elements. The orbitsize is defined by the semi-major axis, a, and theshape by the eccentricity, e. The orbital plane ori-entation is characterized by the inclination, i, andthe right ascension of the ascending node (RAAN),Ω. The former is the angle between the orbitaland reference planes, and their intersection is calledthe line of nodes — it connects the ascending anddescending nodes, the points where the satellitecrosses the equator going from south to north orvice-versa, respectively. The latter is the angle be-tween the vernal equinox and the ascending nodevector, measured in the reference plane. The rota-tional orientation within the orbital plane is definedby the argument of perigee, $, the angle betweenthe ascending node and eccentricity vectors. Fi-nally, the position of the satellite is specified by thetrue anomaly, θ, measured in the direction of mo-tion.

2.4. Orbit PerturbationsA satellite does not actually move on a Keplerian

motion: its real orbit deviates slightly at each in-stant, due to sources not acknowledged in Kepler’s

assumptions: non-spherical mass distribution, non-gravitational forces, third body interactions, andrelativistic mechanics. The third body interactionsare the influences caused by the interaction withother celestial bodies, and they are not significantfor a satellite in low Earth orbit (LEO). The rela-tivistic effects can also be neglected for a satellite,since it moves very slowly compared to the speed oflight [9, 11].

The equation of motion of a spacecraft aroundthe central body, including the perturbations, canbe presented in the form [10]

r = −∇U + f , (4)

where U is the gravitational potential field and fis the force vector per unit mass resultant of othersources of perturbations.

2.4.1 Non-spherical mass distributionThe Earth does not have a spherically symmet-

ric mass distribution, due to its rotation it presentsa flattening at the poles [12]. This causes the tra-jectory of the spacecraft to deviate because of thenon-uniform gravitational potencial, or geopoten-tial, field of the Earth.

Spherical harmonics can be used to form a geopo-tential model and are split into three: zonal, sec-torial, and tesseral harmonics. The first dividethe Earth model into longitude independent zones,leading to axial symmetry about the axis throughthe poles, while the second are independent of thelatitude. The last produce a tiled pattern [11].

2.4.2 Non-gravitational forcesNon-gravitational perturbing forces are frictional

forces, being the atmospheric drag and the solar ra-diation pressure (SRP) the most significant at LEO.

A spacecraft at that altitude is still in contactwith air molecules, which cause friction on the sur-face of the body, removing energy to the orbit. Al-though hard to model, an approximation can bedone for the drag force, fd, in body frame [8],

(fd)B = −1

2ρCdAp

m(v)B(v)B, (5)

being ρ the air density, Cd the drag coefficient, Ap

the total projected area of the satellite, m the massof the satellite, v the air velocity relative to thesurface of the satellite, and v its magnitude.

A satellite orbiting the Earth is also influenced bydifferent radiation sources, being solar radiation thedominant effect [10]. When electromagnetic radia-tion reflects on the spacecraft, it exchanges momen-tum that causes a perturbation on its trajectory.

The SRP influence, fSRP , can be expressed, inbody frame, by [13]

(fSRP )B = −psAp(s)B, (6)

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where ps = 4.5× 10−6 N/m2

is, approximately, themean SRP, and s the unit vector that points fromthe satellite to the Sun.

2.5. Disturbance TorquesWhile perturbation forces influence the orbit of

the satellite, disturbance torques influence its atti-tude. The most significant disturbance torques arecaused by external sources: gravitational, aerody-namic, SRP, and magnetic [9].

2.5.1 Gravitational torqueAs stated before, the gravitational field of the

Earth is not uniform causing a torque about its cen-ter of mass. This torque, τg, is defined, in bodyframe, by [13]

(τg)B = 3( µr3

)(o)×B (J)B (o)B, (7)

where r is the distance between the center of massof the body and the center of mass of the Earth, Jis the second moment of inertia, and o = −r/r.

As a side note, (a)× represents the cross-productmatrix of the vector a = (a1, a2, a3),

(a)× =

0 −a3 a2a3 0 −a1−a2 a1 0

. (8)

2.5.2 Aerodynamic torqueThe transfer of momentum between air molecules

and the satellite, during their collision, also causesa torque on the latter. The aerodynamic torque,τd, is defined, in body frame, by [13]

(τd)B = ρ(v)2BAp(cp)×B (v)B, (9)

where v is the magnitude of the velocity of the airrelative to the center of mass of the body, cp isthe position vector of the center of pressure, andv = v/v.

2.5.3 SRP torqueThe SRP also applies a torque due to the corpus-

cular nature of the photons that transfer momen-tum at the moment of collision with the surface. Itis expressed, in the body-frame, by [13]

(τSRP )B = (cp)B × (fSRP )B. (10)

2.5.4 Magnetic torqueAnother kind of torque applied to the satellite

is the magnetic one, τm. This disturbance torqueis caused by the interaction between the net mag-netic moment of the spacecraft, mm, and an exter-nal magnetic field, B, in this case the Earth’s. It isexpressed, in body frame, by

(τm)B = (mm)B × (B)B. (11)

3. Propagator SelectionIn order to develop an orbit simulator, a method

to determine the position of the spacecraft mustbe selected. The special perturbations is a methodthat resorts to step-by-step numerical integration ofa selected parameter. It is a really flexible tool, asit can be applied to any orbit with any number ofperturbations.

3.1. Special PerturbationsThe most used methods are: Cowell, Encke, and

variation-of-parameters.Cowell’s method is very simple, the position of

the body is found by numerically integrating twicethe equation of motion (4). Its main advantagesare the straightforwardness and how easy it is to beapplied. It is also flexible, as it can be applied toa great variety of problems and many perturbationforces can be included [14].

Encke’s method consists in integrating devia-tions, or differential accelerations, from a referenceposition, instead of the total acceleration. The ref-erence orbit, which must be rectified occasionally,is the trajectory the spacecraft would assume if alldisturbing forces instantly stopped acting on it [15].

The variation-of-parameters is a method whichintegrates the variation of a set of parameters of areference orbit. This technique requires a continu-ous rectification of the reference orbit [14].

3.1.1 Method selectionAlthough Encke’s and variation-of-parameters

methods are faster than Cowell’s, the simplicity andflexibility of the latter makes it the most appropri-ate choice. Besides, the accuracy depends greatlyon the numerical integration process.

3.2. Numerical Integration TechniquesAll of the previous methods to determine the po-

sition of the satellite, need an integration process.An accurate technique must then be chosen to beapplied on the selected orbit calculation method.

3.2.1 TechniquesSimulink R© has various numerical integration

methods included; therefore, since it is the soft-ware that is used in this work, some of thosemethods are compared and the most adequate se-lected: Euler; Heun; Bogacki-Shampine (BS); 4thorder Runga-Kutta (RK4); 5th order Runga-KuttaDormand-Prince (RK-DP5); and 8th order Runga-Kutta Dormand-Prince (RK-DP8).

3.2.2 TestingTwo tests of the selected numerical integration

techniques are presented. The first corresponds tothe accuracy of the solution and the second to theorbit integration time. Both cases are applied ona Cowell propagator of an unperturbed LEO orbit

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with the (proposed by the ECOSat mission designteam) initial elements displayed in Table 1.

Orbit element Symbol Value Unit

Semi-major axis a 7 178 137 mEccentricity e 0 –Inclination i 51.65

RAAN Ω 45.65

Argument of perigee $ 141.82

True anomaly θ 0

Table 1: Initial orbit elements.

Considering the nature of this work, a simulationas accurate as possible provides a more reliable test-ing environment for the ECOSat-III ADCS. In orderto determine the solution accuracy of each integra-tion method, a calculation of the absolute error ofthe position and velocity is done. The orbit gener-ated by a Cowell propagator, throughout 30 days,with a fixed time step of 60 s, is compared to the or-bit generated by the General Mission Analysis Tool(GMAT), with the same conditions.

The polynomial regression of the resulting abso-lute error of the i1 position coordinate is shown inFig. 2 for easier visualization of the order of mag-nitude of the error. Since the other position coor-dinates and the velocities in every direction presentthe same behavior, their results are not displayed.

Figure 2: Absolute error of the position along i1,for each numerical integration technique.

The integration speed test has the purpose ofcomparing the time spent on each numerical tech-nique and examining its evolution with the fixedtime step. The test is done on the same orbit, butfor 7 days. The result is shown in Fig. 3.

3.2.3 Technique selectionThe speed test results reveal that all of the meth-

ods are sufficiently fast, considering the nature ofthe proposed simulation.

Observing Fig. 2, it can be seen that the higherthe order of the integration process, the higher the

Figure 3: Total integration time of each numericalintegration technique, for different step sizes.

accuracy. Euler has a very significant error, reach-ing orders of magnitude of 107 m. Although it isthe fastest method, the Euler technique is too in-accurate to be used. The same goes for Heun andBogacki-Shampine processes.

The RK4 is a good method to apply on short-term situations, but, on a long-term basis, the ac-cumulated error makes it a not good enough option.

The choice then falls on the last two methods:RK-DP5 and RK-DP8. These are pretty accurate,reaching maximum absolute position errors of ap-proximately 10 m, which is actually really good con-sidering the nature of the problem. A faster sim-ulation may be of interest for practical purposes;however, the difference in time is not too much tobe considered a decisive factor on the choice. Hence,the RK-DP8 is the chosen numerical integrationmethod, as it shows the best accuracy results.

4. Hardware Configuration

As the goal is to test the influence of the sig-nal transmission, between the components of theADCS, on the pointing control, it is important tounderstand how the used bus communication sys-tem, the Controller Area Network (CAN), works.

4.1. Controller Area Network

CAN is an internal communications network thatconnects devices with each other without the needof a master to control their activities, as every nodeis independent. It is used to exchange short mes-sages, like sensor data, which are broadcast to allthe network. Therefore, it is an independent, multi-master message broadcast system [16, 17].

It was developed by Robert Bosch GmbH, orig-inally intended for the automotive industry, in or-der to replace the complex wiring with a simpletwo-wire bus. As the number of vehicle devices in-creased, the number and length of wires increasedas well, making it harder to find faults in the net-

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work [17]. CAN addresses this issue by connectingevery node to a single communication bus.

4.1.1 CAN physical layer

The physical layer defines how the bits are en-coded into signals transmitted over the wires. Inthis case, the physical medium is a single twistedpair of wires, where one of the wires is called theCAN LOW and the other is the CAN HIGH.

With a Non Return to Zero (NRZ) bit encoding— there is no rest state — a recessive bit, or 1, istransmitted by both wires at 2.5 V, while a domi-nant bit, or 0, is transmitted when CAN HIGH is at3.5 V and CAN LOW at 1.5 V. This is representedin Figure 4.

Figure 4: Encoding of bits on a CAN bus [16].

In order to suppress signal reflections that happenat the bus, as a consequence of imperfections in thecable, the bus must be terminated at both ends withresistors [16].

4.1.2 CAN data layer

The data layer is concerned with the structure ofthe frames (messages), the arbitration process, thesynchronization, and the error handling.

In CAN communication there are four types offrames: data, remote, error, and overload frames.The data frame is the type of message that containsinformation (up to 8 bytes) from a node, while theremote frame requests transmission of data. Theerror frame transmits detected errors and the over-load frame requests delay in a transmission [16, 18].

Any data or remote frame contains an identifier(ID) that distinguishes the source, for the receiverto decide wether to process the message or ignore it.Several CAN specifications have been released andCAN 2.0, divided in two parts, is the latest. PartA is the specification of the standard format, char-acterized by an 11-bit ID, and part B the extendedformat, with a 29-bit ID.

As a multi-master network, any node in a CANbus is able to send frames at any time; however,this leads to possible conflicts of messages beingtransmitted at the same time. This situation ishandled through an arbitration process, that deter-mines which message has priority by comparing the

IDs: if two nodes are sending a frame and one ofthem sends a recessive ID bit while the other sendsa dominant bit, the latter will have priority [19].

Synchronization between every node is achievedwith a process called bit stuffing: when five consec-utive bits with the same polarity are transmitted, abit of opposite polarity is inserted.

An error is flagged whenever a node detects acorrupted message, which must be aborted and thenretransmitted. When the error is found, the nodesends an Active Error flag (six dominant bits). Ifit keeps sending errors, it starts sending a PassiveError flag (six recessive bits). For a long period oferrors, the node is considered faulty and goes BusOff — it is disconnected from the bus [18].

4.2. Hardware DevicesIn order to implement the CAN system, an inter-

face device is used — the Vector R© CANcaseXL. Itworks as a CAN/USB interface and it connects thehost computer to the CAN bus. It is supported bySimulink R©. An analyzer tool is also useful to moni-tor the bus in real-time, as well as logging all of thecommunication. The tool used is the Microchip R©

CAN Bus Analyzer. These devices are connectedto the computer that will host the framework, bya set of cables with DE-9 connectors, as shown inFigure 5.

Figure 5: The computer hosting the framework, inthe middle; the Microchip R© CAN Bus Analyzer, onthe left, and the Vector R© CANcaseXL, on the right.

5. Framework ImplementationThe work done by Rondao [4] is modified and

improved for a practical way to simulate and test areal message exchange between the components ofthe ADCS. The point is to make the algorithm workas a stand-alone system and test the influence of realsignal transmission between the algorithm and thesensors/actuators, through a CAN bus. Essentially,the propagator induces the modeled sensors to out-put realistic data to the algorithm that processes itand sends to the actuators the commands. Figure6 displays the main systems of this framework: the

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spacecraft mechanics simulator, the hardware mod-els, the ADCS algorithm, and the CAN system.

Figure 6: Systems of the framework: spacecraft me-chanics simulator (left), hardware models (middle),ADCS (right), and CAN communication (bottom).

5.1. Initial Conditions Menu

The framework requires the user to set variousparameters and initial conditions, before startingthe simulation. These parameters are related to thespacecraft itself, the orbit, the hardware models,and the CAN bus. It is done in a way that minimalchanges inside the subsystems are required.

5.2. Spacecraft Mechanics Simulation

The spacecraft mechanics simulation, adaptedfrom Rondao [4], is based on the theory and equa-tions detailed in Section 2. The purpose of this sys-tem is to generate the orbital motion of the satel-lite around the Earth. This simulation provides thenecessary information for the sensors to output themeasurements required by the ADCS.

5.3. Hardware Models

This subsystem generates the measurements thesensors would output to the algorithm under realconditions. It also simulates the actuators opera-tion. It is important that the measurements aresimilar to what is expected from the real messages.

First of all, it is relevant to define the data type ofeach signal. The magnetometer, the sun sensor, andthe gyroscope are defined to transmit the measure-ments of each component in 16-bit signed integers,as well as the actuators inputs. The GNSS receiveris defined to transmit in double data type.

Relative to the prior work, only the outputs ofthe magnetometer, sun sensor, and gyroscope weremodified in order to respect the definitions estab-lished before. On the other hand, the GNSS re-ceiver model has to be fully created, as it was notincluded in the previous hardware suite. The modelis depicted in Figure 7.

The actuators models were also slightly changed.Instead of computing here the required voltage foreach wheel or rod, that calculation is done by the

Figure 7: Simulink R© model of the GNSS receiver.

algorithm and received via CAN as an input. Sincethe data type of these inputs is defined as 16-bitsigned integer, the computed voltages must be con-verted on an integer scale. The determined value isrepresented by a fraction of the maximum voltagemultiplied by the maximum 16-bit integer value.

5.4. ECOSat-III ADCS Algorithm

The algorithm is assembled with new subsystemsas a consequence of the introduction of the CANcommunication: one to convert the sensors data andanother to predict the actuators behavior and cal-culate the required voltages. The main function ofthe converter subsystem is to interpret the receivedsensors data, which are stored in non-dimensional16-bit integer counts. The position measurementsmust be changed from latitude, longitude, and alti-tude coordinates back to the ECI frame.

This ADCS suite does not include accelerometers;therefore, the acceleration must be calculated byderiving twice the position measured by the GPS.However, the Simulink R© differentiator does not per-form well with noisy data. The solution is to filterthe measurements by setting a cutoff frequency, upto which every signal is allowed to pass, blocking thehigher frequencies caused by the noise — low-passfilter. Through manual tuning, a 4th order low-pass Butterworth filter with a cutoff frequency of1.6 rad/s is set, providing an adequate attenuationof the signals. However, there is a late transientresponse, causing bad results during that period.This issue is solved by setting constant the initialconditions of position, velocity, and acceleration un-til the filtered signal is closer to the expected.

5.5. CAN Communication

The Vehicle Network Toolbox is used to set upthe CAN communication between the hardwaremodels and the ADCS algorithm. This toolbox con-tains several blocks with which it is possible to cre-ate and/or simulate the message exchange.

Before describing the system, it is useful to definehow the messages are arranged. The magnetometeroutputs messages with three signals, one per axis.

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Since each component has 16 bits, a message with3× 16 bits is generated from this device. The samehappens for the gyroscope readings and magnetor-quer inputs. The RWS receives four 16-bit signals,which can be assembled as 8 bytes data frames. Fi-nally, the GNSS receiver must output each coordi-nate in separate messages with 8 bytes each.

In order to set the message transmission system,the CAN Configuration block must be inserted toconfigure the channel. Then, the signals must bepacked into CAN messages, with the help of theCAN Pack block, and sent to the configured chan-nel, through the CAN Transmit block. Figure 8shows an example, relative to the transmission fromthe ADCS algorithm to the actuators.

Figure 8: Simulink R© model of the CAN messagetransmission system of the algorithm.

The messages are received through the CAN Re-ceive block, which have to be unpacked into sig-nals through the CAN Unpack block, which mustbe placed in a Function-Call block. Figure 9 depictsthe reception system of the actuators.

Figure 9: Simulink R© model of the CAN messagereception system of the actuators.

6. Model-in-the-Loop Test ResultsThe ECOSat-III ADCS with a real CAN com-

munication, configured between its components, istested. It is important to understand if the systemperforms as expected by design.

6.1. Simulation ParametersThe tests are done using the developed

Simulink R© framework and hardware configurationwith the orbit parameters defined in Table 1. TheRK-DP8 integrator is selected with a fixed step-sizeof 0.1 s, for a period of 1 728 s. The initial epoch isset as January 1st, 2018, at 0h00. The CAN busspeed is set at 500 kbps. This test is done for thenominal operation mode of the ADCS, where thesatellite is required to align the hyperspectral cam-era with nadir, from an initial random orientation,and keep that alignment throughout the orbit.

6.2. ResultsThe measurements sent from the sensors to the

ADCS algorithm, during the simulation, are col-lected and displayed along with the measurementsfrom the no-CAN bus alternative, in order for acomparison to be done. This alternative representsthe performance expected by design. Figures 10, 11,and 12 present the data transmitted by the magne-tometer, the sun sensor, and the gyroscope, respec-tively.

Figure 10: Magnetometer measurements.

Figure 11: Sun sensor measurements.

Figure 12: Gyroscope measurements.

Besides the previous results, the acceleration cal-culation, in Figure 13, from the position measure-ments are also a case of study. The initialization ofthe position, velocity, and acceleration are displayedin Figure 14.

The pointing requirement is the main driver ofthe design of the ECOSat-III ADCS; therefore,it is important to observe the pointing accuracyachieved by it. Figure 15 displays the pointing errorobtained throughout the simulation.

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Figure 13: Determined acceleration.

(a) Position along i1. (b) Velocity along i1.

(c) Position along i2. (d) Velocity along i2.

(e) Position along i3. (f) Velocity along i3.

(g) Acceleration.

Figure 14: Initialization of the position, velocity,and acceleration.

6.3. Discussion

The difference between the approach taken in thiswork and the model without a communication bus,is that a real bus induces delay in every transmis-sion. This delay and other problems related to sig-

Figure 15: Attitude pointing error.

nal transmission, such as lost or corrupted data,may reduce the performance of the system undertest. As seen in the results, the method withoutCAN suggests a smooth data collection, while theother demonstrates a rougher behavior. The delayscause the algorithm to process the data and cal-culate the commands at a time later than the ex-pected by the former approach. This later responseimpacts what the sensors measure, as the actuatorsact later than predicted. However, the measureddata oscillation over the wanted outcome tends todiminish and get closer to the expected value.

The acceleration computation test shows greatresults taking into account the conditions of the cal-culation. Without the low-pass Butterworth filtersto smooth the GNSS receiver measurements, thecomputations would result in large errors.

Another interesting point of these calculations isthe initialization operation that follows a processof introducing an initial value that is constant overa certain period of time and then changes to theoutcome of the low-pass Butterworth filter. Thisimposition is required as the filtered data startsfrom zero, causing issues on the performance of theADCS when it starts operating. It is possible tosee, in Figure 14, that after a short period of time,the filtered data tends to the expected outcome.

Finally, the pointing accuracy achieved by theECOSat-III ADCS, displayed in Figure 15, demon-strates a similar behavior to the designed outcome.There is also a later change of attitude compared tothe no-CAN alternative due to the delay of the com-mands processed by the algorithm, causing a laterresponse of the actuators. This is especially notice-able around 300 s of the simulation. Nevertheless,the ADCS is still able to provide a pointing accu-racy under the specified requirement (4.78) fromaround the same time as previously.

7. Conclusions

A testing system of the ECOSat-III ADCS withreal signal transmission, using CAN, between itscomponents was developed. The work started withthe selection of an orbit propagator method to pro-vide a simulated environment, as realistic as pos-

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sible, for the ADCS. The Cowell method was se-lected based on how simple it is, and the numericalintegration technique chosen for the process, froma list of the techniques included in Simulink R©, wasthe RK-DP8. A hardware configuration of the CANbus was then set, to be used with the testing frame-work developed on Simulink R©. In the end, the sys-tem was tested and the ADCS proved to be able toachieve the requirement imposed (4.78). The pro-posed testing system is flexible and adjustable, witha menu that allows the team to easily change thesimulation conditions and the hardware parametersof the ADCS. This way, the team is provided withan useful tool for future tests. Therefore, the maingoal of this work was successfully done.

AcknowledgementsI would like to thank my supervisor, Dr. Afzal

Suleman, for providing me the opportunity to workin the Center for Aerospace Research, at the Univer-sity of Victoria, where I had the chance to contactand collaborate with a real satellite design team,the ECOSat team. I would also like to addressmy appreciation to Cass Hussmann, who helped methroughout the development of my work, to the restof the ECOSat team, and to all of the members ofthe Center for Aerospace Research.

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