Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2013 Article ID 657182 15 pageshttpdxdoiorg1011552013657182

Research ArticleDesign of Attitude Control Systems forCubeSat-Class Nanosatellite

Junquan Li Mark Post Thomas Wright and Regina Lee

Department of Earth amp Space Science and Engineering York University 4700 Keele Street Toronto ON Canada M3J 1P3

Correspondence should be addressed to Junquan Li junquanlyorkuca

Received 18 December 2012 Accepted 24 April 2013

Academic Editor Sabri Cetinkunt

Copyright copy 2013 Junquan Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

We present a satellite attitude control system design using low-cost hardware and software for a 1U CubeSat The attitude controlsystem architecture is a crucial subsystem for any satellitemission since precise pointing is often required tomeetmission objectivesThe accuracy and precision requirements are even more challenging for small satellites where limited volume mass and power areavailable for the attitude control system hardware In this proposed embedded attitude control system design for a 1U CubeSatpointing is obtained through a two-stage approach involving coarse and fine control modes Fine control is achieved through theuse of three reaction wheels or three magnetorquers and one reaction wheel along the pitch axis Significant design work has beenconducted to realize the proposed architecture In this paper we present an overview of the embedded attitude control systemdesign the verification results from numerical simulation studies to demonstrate the performance of a CubeSat-class nanosatelliteand a series of air-bearing verification tests on nanosatellite attitude control system hardware that compares the performance of theproposed nonlinear controller with a proportional-integral-derivative controller

1 Introduction

The development of nanosatellites (with a mass of 1ndash10 kg)is currently a significant trend in the area of space scienceand engineering research The development of CubeSat-classnanosatellites started in 1999 as a collaborative effort betweenCalifornia Polytechnic State University and Stanford Univer-sity and has achieved great success as a way to efficientlyconstruct and orbit small inexpensive satellites using com-mercial technology CubeSat in general is described as a classof nanosatellites ranging from 1 kg 10 times 10 times 10 cm3 andupwards in 10 cm increments of length Currently more than50 research groups around theworld are developingCubeSat-class nanosatellites for technology demonstration and scien-tific and student training missions A solid model of a typical1U CubeSat with attitude control systems (ACS) is shown inFigure 1

Full-scale satellite attitude control systems are generallytoo large or too expensive to be installed in CubeSat-classnanosatellites [1] so passive attitude control systems haveusually been used for nanosatellites in the past [2 3] Moreactive attitude control subsystems [4] in CubeSat-class nano-satellites have been implemented with the development of

suitable actuators like magnetorquers (torque coils or torquerods) and small-sized reaction wheels [5 6] An overview ofthe proposed ACS design adopted for this study is shown inFigure 2 Currently commercial nanosatellite torque rods andreaction wheels are too expensive for use in many researchnanosatellite projects The contributions of this researchare the development of ACS hardware from off-the-shelfcomponents complete simulation of the ACS system andvalidation testing of the ACS system for attitude control inthe lab environment

In this paper we first briefly describe the ACS hard-ware proposed for CubeSat-class nanosatellite missions Weoutline the hardware development of the ACS actuators inSection 2 In particular we describe the sizing and design ofthe magnetorquers More discussions on the ACS hardwareselection design and characterization for CubeSat-classnanosatellite missions currently under development at YorkUniversity can be also found in [7ndash11] In Sections 3 and 4we describe the satellite system models and the results fromthe simulation study based on this design In Section 5 weshow the ground testing results of the hardware and softwaresystem Section 6 includes future work that is plannedSection 7 concludes the paper

2 Journal of Control Science and Engineering

Reaction wheel

Magnetorquer

Figure 1 ACS (CubeSat-class nanosatellite with three reactionwheels and three torque rods)

2 CubeSat ACS Hardware

21 Attitude Sensors Attitude magnetic sensor hardware inthe current study consists of a Honeywell HMC5883L three-axis MEMS magnetometer for magnetic field measurementsAngular rate information is obtained in three axes from threeorthogonally mounted Analog Devices ADXRS614 MEMSgyroscopes The attitude control system is managed by anAT91SAM9260 32-bit ARM9 microcontroller that runsembedded Linux with 32MB SRAM and 256MB NANDFlash attached for volatile and nonvolatile storage All pro-gramming of control algorithms is accomplished in the Clanguage using the GNU C compiler for the ARM processorThe system is designed for power-efficient operation becausethere is typically less than 3W generated from the photovol-taics on a typical 1U CubeSat in low-earth orbit and a batterymust be used during eclipse periods

22 Magnetorquer Design Magnetic torque coils alsoreferred to as magnetorquers in CubeSat-class nanosatellitesprovide baseline control in many small satellites They arecommercially available in two typical configurations in loosecoils of flat-wound wire and in tightly wound coils arounda permalloy rod The rod configuration is often preferredbecause of its compactness and rigidity and the use of high-permeability 120583 materials for the core To meet the mass andpower requirements of a nanosatellite a maximummass119872of 30 g and a conservative maximum power draw 119875 of 02Wwere set and a typical maximum supply voltage 119881 between37 V and 42V was assumed to avoid having to step upvoltage on power components After combining the powerand mass equations (1) where 119877 is resistance 119882

119908is the

resistivity of the wire and 120588 is the density and solving for thecore radius 119903

119888 and length 119897

119888

119877 =

1198812

119875

119897119908

=

119877

119882119908

119872 = 1205871199032

119908119897119908120588119908+ 1205871199032

119888119897119888120588119888

(1)

The power and mass constraints were applied using (1)and a power value was estimated as the lesser of 02W and thepower dissipation was achieved at the maximum current forthe wire

1199032

119888119897119888=

119872

120587120588119888

minus

120588119908

120588119888

1199031199081198812

119875119882119908

119873119889=

4 [ln (119897119888119903119888) minus 1]

(119897119888119903119888)2minus 4 ln (119897

119888119903119888)

119863 =

119903119888119881

2119882119908

[1 +

120583119903minus 1

1 + (120583119903minus 1)119873

119889

]

(2)

Using (2) from the well-known solenoid equation andthe relations derived in [12] where 119873

119889is the demagnetizing

factor a parametric analysis of the effect of core length andcore radius on magnetic dipole moment 119863 was used todetermine the optimal length and radius of the core materialgiven the wire thickness and corresponding length to satisfythe power and dipole moment requirements Figure 3 illus-trates the effect of core sizing on generatedmagneticmomentThe number of turns is implicitly determined as the dipolemoment of the torque rod is independent of the number ofturns of wire and the core radius is also constrained to sizesthat are commercially available

To maximize the field generated with the dimensionswhile satisfying the design constraints a prototypemagnetor-quer was designed with 70mm long permalloy core and36AWG wire to provide a maximum load power of 200mWat 42 VThedesign parameters of the constructed torque rodsare shown in Table 1

In order to precisely wind 36AWG wires around a corea coil winding machine was designed and assembled usingstepper motors and L298 H-bridge drivers controlled by anATMega644Pmicrocontroller A permalloy core is rotated byonemotor while another positions a plastic feeder guide fromthe wire spool The winder shown with a completed torquerod in Figure 4 allows a torque rod to be automaticallywoundby setting the number of turns required length of the coreand thickness of thewire which determines the ratio of wind-ing speed to feeder speed

23 Reaction Wheel Design Pointing and slew maneuveringof satellites are often accomplished by a motorized rotatingmass such as a reaction wheel and momentum wheel whichprovide maneuvering torque and momentum storage [8]Reaction wheels can provide a high degree of attitude controlaccuracy with the limitation that the wheel may reach satura-tion after continued use requiring an additional momentumcontrol method such as magnetorquers to desaturate thewheel in a process known as momentum dumping

Each of the reaction wheels in the proposed ACS systemconsists of a steel cylinder that is press-fitted to the shaft of aFaulhaber brushless flat micromotor Design choices for themotor were limited to inexpensive commercial motors withlow-power consumption and the reaction wheels were sizedto provide maximummomentum storage given the mass andvolume constraints of a 1U CubeSat Three reaction wheels

Journal of Control Science and Engineering 3

Magnetometer(HMC5883L)

Rate sensors(ADXRS614)

Microcontroller(AT91SAM9G20)

ADC

Reaction wheeldrivers

Torque roddrivers

(BD6212)

Coarse sunsensors

(TSL1402)

Figure 2 Overview of proposed ACS design for a CubeSat-class nanosatellite

2 3 4 5 6 7 8005

01

015

0201

2

3

4

Core radius

Core length

Mag

netic

mom

ent

times10minus3

119883 00075119884 011119885 1302

Moment for wire radius of 011 mm

Figure 3 Magnetorquer sizing surface

Table 1 Magnetorquer parameters

Parameter Value UnitMaximum dipole moment 037 Am2

Total mass 28 gNumber of turns 6063Core diameter 57 mmWire diameter 0127 mmWire resistance 121 Ω

Maximum current 347 mA

can be used in the ACS if maximum control authority isrequired Table 2 shows the design parameters of the reactionwheels used on the proposed ACS [13] A completed reactionwheel assembly is shown in Figure 5

24 Electronic Integration of ACS Components To control thereaction wheel and magnetorquers hardware and house theattitude sensors and actuator drivers a printed circuit board(PCB) was fabricated shown in Figure 6 The board stackswith existing PC104 sized on-board computer (OBC) hard-ware and provides both IO breakout and power suppliesfor the ACS hardware It contains 33 V and 5V switchingsupplies for the ACS sensors as well as external interfaces fora battery and radio to be used specifically for air-bearing

Table 2 Reaction wheel parameters

Parameter Value UnitRotor mass 0214 kgMoment of inertia (axial) 941 times 10minus5 Kgm2

Moment of inertia (transverse) 502 times 10minus5 kgm2

Motor shaft Torque 60 times 10minus4 NmMaximum speed 1539 radsSupply voltage 37ndash42 V

ACS testing The board makes a HMC5883 three-axis mag-netometer an ADXL345 3-axis accelerometer and an ITG-3200 3-axis MEMS rate gyroscope available on the OBC I2Cbus Primary rate sensing for attitude control is accomplishedby three independent ADXRS614 rate gyro units orientedon orthogonal axes by means of right-angle IC sockets andconnected to the first three ADC channels on the OBC Thisallows accurate high-speed sampling of rotation rates for useby the attitude controller To drive the magnetorquers threeBD6212 integrated H-bridges are used controlled by threePWM channels from the OBC and three general purpose IOpins for current direction control To allow one PWM signaland one direction pin to control eachH-bridge the inputs aredemultiplexed by a SN74LVC1G8 tristate output demulti-plexer and pull-up resistors In full operation the boarddraws up to 100mW of power on average though compo-nents can be shut down as needed to conserve power if not inuse

3 System Models

31 Attitude Equations ofMotions In this section the satelliteis modelled as a rigid body with actuators that provide tor-ques about three mutually perpendicular axes that defines abody-fixed frame The equations of motion [14 15] are givenby

119869119887= minus120596times(119869119878120596119887+ 119860119894119869119908Ω) + 119860

119894120591119888+ 120591119898

+ 120591119889 (3)

where120596119887= (120596119887112059611988721205961198873)119879 is the angular velocity of the satellite

expressed in the body frame 119869119904is the inertia matrix of the

satellite 119869119908is the inertia matrix of the reaction wheel and

119869 = 119869119904minus 119860119894119869119908119860119879

119894 119860119894is the layout matrix of the reaction

4 Journal of Control Science and Engineering

Figure 4 Magnetorquer winding apparatus and completed torque rod

Figure 5 Reaction wheel assembly

wheels whose columns represent the influence of each wheelon the angular acceleration of the satelliteΩ is the velocity ofa reactionwheel 120591

119888is the torque control provided by the reac-

tion wheel 120591119898is the torque control provided by the magne-

torquers and 120591119889is the bounded external disturbance which

is a sumof the gravity gradient 120591gravity aerodynamic 120591aero andsolar radiation pressure 120591solar disturbances

The gravity gradient disturbance is 120591gravity =

3radic1205831198901198863

2

119862119869119904119862 where 120583 is the gravitational parameter of the

Earth 119886 is the semimajor axis of the orbit and 119862119896is the

direction cosine matrix in terms of quaternionsThe aerodynamic disturbance is 120591aero = 119862

1198892120588V2119860119871

where 119862119889is the coefficient of drag for a flat plate 119860 is the

cross-sectional area causing aerodynamic drag V is the satel-lite velocity 119871 is the distance between the centre of pressureand the centre of gravity and 120588 is the atmospheric densityrelated to the altitude

The solar radiation pressure disturbance is 120591solar =

119865119904119888119860119904(1 + 119903)119871 where 119865

119904is the solar constant at the Earthrsquos

orbital distance from the Sun 119888 is the speed of light 119860119904is the

illuminated surface area and 119903 is the surface reflectance

32 Attitude Kinematics The satellite attitude kinematics isrepresented using quaternions

119902 =

1

2

(

11990241198683times3

+ 119902times

minus119902119879

)120596119887equiv

1

2

119860 (119902) 120596119887 (4)

where 119902 = (119902119879 1199024)

119879

= (1199021 1199022 1199023 1199024)119879

Coil drive bridges

Magnetometer

MEMS rate gyros

33 V5 V supplies

Figure 6 ACS sensor and actuator board

In terms of Euler angles we can also express the satelliteattitude as

[

[

120574

]

]

=

[[[[[

[

1 sin (120595) tan (120572) cos (120595) tan (120572)

0 cos (120595) minus sin (120595)

0 sin(

120595

cos (120572))

cos (120595)

cos (120572)

]]]]]

]

120596119887 (5)

where 120595 is the roll angle about the 119909-axis 120572 is the pitch angleabout the 119910-axis and 120574 is the yaw about the 119911-axis

33 SensorModels Magnetic field vectors are obtained in theorbit reference frame

1198611=

119872119890

1199033

0

times [cos (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus sin (1205960119905) sin (120598) sin (120596

119890119905)]

1198612=

minus119872119890

1199033

0

[(cos (120598) cos (119894) + sin (120598) sin (119894) cos (120596119890119905))]

1198613=

3119872119890

1199033

0

times [sin (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus2 sin (1205960119905) sin (120598) sin (120596

119890119905)]

(6)

Journal of Control Science and Engineering 5

where1205960is the angular velocity of the orbit with respect to the

inertial frame 1199030is the distance from the center of the satellite

to the center of the Earth 119894 is the orbit inclination 120576 is themagnetic dipole tilt120596

119890is the spin rate of the Earth and119872

119890is

themagnetic dipolemoment of the EarthThemagnetometermodel is

119867 = 119862119896[

[

1198611

1198612

1198613

]

]

+ 120578119898

+ 119887119898 (7)

where 119862119896is the direction cosine matrix in terms of quater-

nions 120578119898

is the zero mean Gaussian white noise of themagnetometer119861 is the vector formedwith the components ofthe Earthrsquos magnetic field in the body frame of the reference

and 119861 = 119862119896[

1198611

1198612

1198613

] 119887119898is the magnetometer bias

The angular velocity is measured from three rate gyro-scopes The model is given by

120596119892= 120596 + 119887

119892+ 120578119892

119887119892= minus119896119891119887119892+ 120578119891

(8)

where120596119892is the output of a gyroscope and120596 is the real angular

rate of the gyro 120578119892and 120578119891are Gaussian white noise 119887

119892is the

random drift of the gyro and 119896119891is the drift constant

34 ActuatorModels Reactionwheels are widely used to per-form precise satellite attitude maneuvers because they allowcontinuous and smooth control of internal torques Torquesare produced on the satellite by accelerating or deceleratingthe reaction wheels Let the torque demanded by the satellitebe denoted as 120591

119888 where 120591

119888= 119869119908(Ω +119860

119894119887) The input voltage

119890119886required to control the actuator dynamics of the reaction

wheel can be written as

119890119886= 119896119887Ω minus 119877

119887119896minus1

119905(1198601015840

119894120591119888) (9)

where 119896119905is the motor torque constant 119896

119887is the back-EMF

constant 119877119887is the armature resistance and friction in the

reaction wheels is ignoredThemaximum voltage of the reac-tion wheel is 42 V and a dead zone for the reaction wheel isestimated to be below 1V 119896

119905is 00082 119896

119887is 0007119877

119887is 05 and

the moment of inertia of the reaction wheel is 00001 kgm2

4 Control Law Design and Simulation Results

41 Satellite Attitude Control Laws Magnetic control hasbeen used over many years [16 17] for small spacecraft atti-tude control The main drawback of magnetic control is thatmagnetic torque is two-dimensional and it is only present inthe plane perpendicular to the magnetic field vector [18]Theaccuracy of satellite attitude control systems (ACS) using onlymagnetic actuators is known to be accurate on the order of04ndash05 degree [18] The satellite cannot be controlled pre-cisely in three-dimensional space using only magnetorquers[18] but the combination ofmagnetorquers with one reactionwheel expands the two-dimensional control torque possi-bilities to be three-dimensional The attitude accuracy of

the combined actuators has been compared with three reac-tion wheels-based attitude control in the references [18 19]Classical sliding mode control has also been used for mag-netic actuated spacecraft [20 21] However the proposednonlinear adaptive fuzzy sliding mode control law has neverbeen used in magnetic attitude control

To address the attitude tracking problem the attitudetracking error 119902

119890= (119902119879

119890 1199024119890)

119879

is defined as the relative orienta-tion between the body frame and the desired frame withorientation 119902

119889= (119902119879

119889 1199024119889)

119879

In order to apply the proposednonlinear controller the equations of motion are rewritten as

119902119890= 119891 (119902

119890

119902119890) + 120591119888+ 120591119898

+ 120591119889 (10)

The adaptive fuzzy sliding mode magnetic control law isgiven by

120591 = minus1198961119878 minus 120579119879120585 minus 1198962tanh(

3119870119906120589119878

120598

) (11)

120579 = 120575119878120585120579 (12)

120591ap =

120591119878

100381710038171003817100381711987821003817100381710038171003817119878

(13)

119872 = 120591ap times

119861

100381710038171003817100381711986121003817100381710038171003817

(14)

Here 120591119898

= 119872 times 119861 are the torques generated by the magne-torquers 119872 is the vector of magnetic dipoles for the threemagnetorquers and 119861 is the vector formed with the compo-nents of the Earthrsquos magnetic field in the body frame of thereference 119878 =

119902119890+ 119870119902119890is the sliding surface 120579 and 120585 are the

adaptive parameters and fuzzy weight functions generatedby the fuzzy logic systems [22] and 120575 119896

1 1198962 119870119906 120589 120598 are

positive constants used for tuning the control response

Remark 1 AFSMC controller design details can be foundin the authorrsquos previous papers [11] The design includes (1)Sliding surface design [22] and (2) fuzzy logic system design[22]

42 Simulation Results The attitude detumbling and attitudestabilization phases are considered in the ACS simulationThe B-dot algorithm PD magnetic control law and adaptivefuzzy sliding mode magnetic control law are used for thetwo phases respectively We note that the orbit used for thepresent simulation study is a 500 km circular orbit with 45∘inclination At this altitude the total disturbance torque for1U CubeSats is estimated to be on the order of 5 times 10

minus7NmThis is intended to be a slight overestimation to include asafety margin

421 Detumbling Mode and Stabilization Mode

Scenario 1 In the initial stage of ACS control the angularvelocities of the satellite are assumed to be 0169 rads as aresult of separation from the launch vehicle The ACS dampsthe angular rate by controlling three magnetorquers Thecontrol logic generally used for detumbling is called B-dot

6 Journal of Control Science and Engineering

0 02 04 06 08 1 12 14 16 18 2

0

50

100

150

200

Time (orbits)

0 01 02

0100200

Roll (deg)Pitch (deg)Yaw (deg)

minus50

minus100

minus150

minus200

minus100

minus200

Magnetic dipole 01 Am2 B-dot control

(a)

0 02 04 06 08 1 12 14 16 18 2

0

1

2

Mag

netic

torq

ue (N

m)

0 01 02

0

2minus1

minus2

minus3

minus4

minus5

times10minus6

minus2

minus4

Time (orbits)

Magnetic dipole 01 Am2 B-dot control

times10minus6

120591119861112059111986121205911198613

(b)

minus002

0

002

004

006

008

01

012

014

016

018

Ang

ular

velo

city

trac

king

erro

r (ra

ds)

0 005 015

0

005

01

015

02

0 02 04 06 08 1 12 14 16 18 2Time (orbits)

minus00501 02

Magnetic dipole 01 Am2 B-dot control

(c)

0 05 1 15 2

0

002

004

006

008

01

0 01 02

0

005minus002

minus004

minus006

minus008

minus01

Mag

netic

dip

ole (

Am2)

Time (orbits)

01

minus005

minus01

119872119909

119872119910

119872119911

Magnetic dipole 01 Am2 B-dot control

(d)

Figure 7 Scenario 1 detumbling control results

control [1] as it makes use of the derivative of the magneticfield ldquo119861rdquo For a CubeSat with moment of inertia 119869 =

diag(0002 0002 0002) kgm2 we include the external dis-turbances (aerodynamic gravity gradient and solar pres-sure) set the desired quaternion to be (0 0 0 1) set theinitial quaternion to be (01 minus01 01 09849) and assumethe magnetic dipole maximum of the rods to be 01 Am2 TheEuler angle tracking errors angular velocity tracking errorsandmagnetic torquers magnetic dipoles results are shown inFigure 7 The satellite starts at the selected tip-off rate and

after 1 orbit the angular velocities are reduced to the requiredrates before continuing with other ACS tasks

Scenario 2 Now we consider a CubeSat with the samemoment of inertia and orbit and assume the magnetic dipolemaximum of the magnetorquer to be 04Am2 with a magne-tometer sensor bias calculated by 20 lowast 10

minus4lowast rand(1) Pro-

portional-derivative (PD) magnetic control [23] laws (shownin (15)) are used in this simulation and the results over 6 orbitsare shown in Figure 8 During the first three orbits three

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

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RotatingMachinery

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Submit your manuscripts athttpwwwhindawicom

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 Journal of Control Science and Engineering

Reaction wheel

Magnetorquer

Figure 1 ACS (CubeSat-class nanosatellite with three reactionwheels and three torque rods)

2 CubeSat ACS Hardware

21 Attitude Sensors Attitude magnetic sensor hardware inthe current study consists of a Honeywell HMC5883L three-axis MEMS magnetometer for magnetic field measurementsAngular rate information is obtained in three axes from threeorthogonally mounted Analog Devices ADXRS614 MEMSgyroscopes The attitude control system is managed by anAT91SAM9260 32-bit ARM9 microcontroller that runsembedded Linux with 32MB SRAM and 256MB NANDFlash attached for volatile and nonvolatile storage All pro-gramming of control algorithms is accomplished in the Clanguage using the GNU C compiler for the ARM processorThe system is designed for power-efficient operation becausethere is typically less than 3W generated from the photovol-taics on a typical 1U CubeSat in low-earth orbit and a batterymust be used during eclipse periods

22 Magnetorquer Design Magnetic torque coils alsoreferred to as magnetorquers in CubeSat-class nanosatellitesprovide baseline control in many small satellites They arecommercially available in two typical configurations in loosecoils of flat-wound wire and in tightly wound coils arounda permalloy rod The rod configuration is often preferredbecause of its compactness and rigidity and the use of high-permeability 120583 materials for the core To meet the mass andpower requirements of a nanosatellite a maximummass119872of 30 g and a conservative maximum power draw 119875 of 02Wwere set and a typical maximum supply voltage 119881 between37 V and 42V was assumed to avoid having to step upvoltage on power components After combining the powerand mass equations (1) where 119877 is resistance 119882

119908is the

resistivity of the wire and 120588 is the density and solving for thecore radius 119903

119888 and length 119897

119888

119877 =

1198812

119875

119897119908

=

119877

119882119908

119872 = 1205871199032

119908119897119908120588119908+ 1205871199032

119888119897119888120588119888

(1)

The power and mass constraints were applied using (1)and a power value was estimated as the lesser of 02W and thepower dissipation was achieved at the maximum current forthe wire

1199032

119888119897119888=

119872

120587120588119888

minus

120588119908

120588119888

1199031199081198812

119875119882119908

119873119889=

4 [ln (119897119888119903119888) minus 1]

(119897119888119903119888)2minus 4 ln (119897

119888119903119888)

119863 =

119903119888119881

2119882119908

[1 +

120583119903minus 1

1 + (120583119903minus 1)119873

119889

]

(2)

Using (2) from the well-known solenoid equation andthe relations derived in [12] where 119873

119889is the demagnetizing

factor a parametric analysis of the effect of core length andcore radius on magnetic dipole moment 119863 was used todetermine the optimal length and radius of the core materialgiven the wire thickness and corresponding length to satisfythe power and dipole moment requirements Figure 3 illus-trates the effect of core sizing on generatedmagneticmomentThe number of turns is implicitly determined as the dipolemoment of the torque rod is independent of the number ofturns of wire and the core radius is also constrained to sizesthat are commercially available

To maximize the field generated with the dimensionswhile satisfying the design constraints a prototypemagnetor-quer was designed with 70mm long permalloy core and36AWG wire to provide a maximum load power of 200mWat 42 VThedesign parameters of the constructed torque rodsare shown in Table 1

In order to precisely wind 36AWG wires around a corea coil winding machine was designed and assembled usingstepper motors and L298 H-bridge drivers controlled by anATMega644Pmicrocontroller A permalloy core is rotated byonemotor while another positions a plastic feeder guide fromthe wire spool The winder shown with a completed torquerod in Figure 4 allows a torque rod to be automaticallywoundby setting the number of turns required length of the coreand thickness of thewire which determines the ratio of wind-ing speed to feeder speed

23 Reaction Wheel Design Pointing and slew maneuveringof satellites are often accomplished by a motorized rotatingmass such as a reaction wheel and momentum wheel whichprovide maneuvering torque and momentum storage [8]Reaction wheels can provide a high degree of attitude controlaccuracy with the limitation that the wheel may reach satura-tion after continued use requiring an additional momentumcontrol method such as magnetorquers to desaturate thewheel in a process known as momentum dumping

Each of the reaction wheels in the proposed ACS systemconsists of a steel cylinder that is press-fitted to the shaft of aFaulhaber brushless flat micromotor Design choices for themotor were limited to inexpensive commercial motors withlow-power consumption and the reaction wheels were sizedto provide maximummomentum storage given the mass andvolume constraints of a 1U CubeSat Three reaction wheels

Journal of Control Science and Engineering 3

Magnetometer(HMC5883L)

Rate sensors(ADXRS614)

Microcontroller(AT91SAM9G20)

ADC

Reaction wheeldrivers

Torque roddrivers

(BD6212)

Coarse sunsensors

(TSL1402)

Figure 2 Overview of proposed ACS design for a CubeSat-class nanosatellite

2 3 4 5 6 7 8005

01

015

0201

2

3

4

Core radius

Core length

Mag

netic

mom

ent

times10minus3

119883 00075119884 011119885 1302

Moment for wire radius of 011 mm

Figure 3 Magnetorquer sizing surface

Table 1 Magnetorquer parameters

Parameter Value UnitMaximum dipole moment 037 Am2

Total mass 28 gNumber of turns 6063Core diameter 57 mmWire diameter 0127 mmWire resistance 121 Ω

Maximum current 347 mA

can be used in the ACS if maximum control authority isrequired Table 2 shows the design parameters of the reactionwheels used on the proposed ACS [13] A completed reactionwheel assembly is shown in Figure 5

24 Electronic Integration of ACS Components To control thereaction wheel and magnetorquers hardware and house theattitude sensors and actuator drivers a printed circuit board(PCB) was fabricated shown in Figure 6 The board stackswith existing PC104 sized on-board computer (OBC) hard-ware and provides both IO breakout and power suppliesfor the ACS hardware It contains 33 V and 5V switchingsupplies for the ACS sensors as well as external interfaces fora battery and radio to be used specifically for air-bearing

Table 2 Reaction wheel parameters

Parameter Value UnitRotor mass 0214 kgMoment of inertia (axial) 941 times 10minus5 Kgm2

Moment of inertia (transverse) 502 times 10minus5 kgm2

Motor shaft Torque 60 times 10minus4 NmMaximum speed 1539 radsSupply voltage 37ndash42 V

ACS testing The board makes a HMC5883 three-axis mag-netometer an ADXL345 3-axis accelerometer and an ITG-3200 3-axis MEMS rate gyroscope available on the OBC I2Cbus Primary rate sensing for attitude control is accomplishedby three independent ADXRS614 rate gyro units orientedon orthogonal axes by means of right-angle IC sockets andconnected to the first three ADC channels on the OBC Thisallows accurate high-speed sampling of rotation rates for useby the attitude controller To drive the magnetorquers threeBD6212 integrated H-bridges are used controlled by threePWM channels from the OBC and three general purpose IOpins for current direction control To allow one PWM signaland one direction pin to control eachH-bridge the inputs aredemultiplexed by a SN74LVC1G8 tristate output demulti-plexer and pull-up resistors In full operation the boarddraws up to 100mW of power on average though compo-nents can be shut down as needed to conserve power if not inuse

3 System Models

31 Attitude Equations ofMotions In this section the satelliteis modelled as a rigid body with actuators that provide tor-ques about three mutually perpendicular axes that defines abody-fixed frame The equations of motion [14 15] are givenby

119869119887= minus120596times(119869119878120596119887+ 119860119894119869119908Ω) + 119860

119894120591119888+ 120591119898

+ 120591119889 (3)

where120596119887= (120596119887112059611988721205961198873)119879 is the angular velocity of the satellite

expressed in the body frame 119869119904is the inertia matrix of the

satellite 119869119908is the inertia matrix of the reaction wheel and

119869 = 119869119904minus 119860119894119869119908119860119879

119894 119860119894is the layout matrix of the reaction

4 Journal of Control Science and Engineering

Figure 4 Magnetorquer winding apparatus and completed torque rod

Figure 5 Reaction wheel assembly

wheels whose columns represent the influence of each wheelon the angular acceleration of the satelliteΩ is the velocity ofa reactionwheel 120591

119888is the torque control provided by the reac-

tion wheel 120591119898is the torque control provided by the magne-

torquers and 120591119889is the bounded external disturbance which

is a sumof the gravity gradient 120591gravity aerodynamic 120591aero andsolar radiation pressure 120591solar disturbances

The gravity gradient disturbance is 120591gravity =

3radic1205831198901198863

2

119862119869119904119862 where 120583 is the gravitational parameter of the

Earth 119886 is the semimajor axis of the orbit and 119862119896is the

direction cosine matrix in terms of quaternionsThe aerodynamic disturbance is 120591aero = 119862

1198892120588V2119860119871

where 119862119889is the coefficient of drag for a flat plate 119860 is the

cross-sectional area causing aerodynamic drag V is the satel-lite velocity 119871 is the distance between the centre of pressureand the centre of gravity and 120588 is the atmospheric densityrelated to the altitude

The solar radiation pressure disturbance is 120591solar =

119865119904119888119860119904(1 + 119903)119871 where 119865

119904is the solar constant at the Earthrsquos

orbital distance from the Sun 119888 is the speed of light 119860119904is the

illuminated surface area and 119903 is the surface reflectance

32 Attitude Kinematics The satellite attitude kinematics isrepresented using quaternions

119902 =

1

2

(

11990241198683times3

+ 119902times

minus119902119879

)120596119887equiv

1

2

119860 (119902) 120596119887 (4)

where 119902 = (119902119879 1199024)

119879

= (1199021 1199022 1199023 1199024)119879

Coil drive bridges

Magnetometer

MEMS rate gyros

33 V5 V supplies

Figure 6 ACS sensor and actuator board

In terms of Euler angles we can also express the satelliteattitude as

[

[

120574

]

]

=

[[[[[

[

1 sin (120595) tan (120572) cos (120595) tan (120572)

0 cos (120595) minus sin (120595)

0 sin(

120595

cos (120572))

cos (120595)

cos (120572)

]]]]]

]

120596119887 (5)

where 120595 is the roll angle about the 119909-axis 120572 is the pitch angleabout the 119910-axis and 120574 is the yaw about the 119911-axis

33 SensorModels Magnetic field vectors are obtained in theorbit reference frame

1198611=

119872119890

1199033

0

times [cos (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus sin (1205960119905) sin (120598) sin (120596

119890119905)]

1198612=

minus119872119890

1199033

0

[(cos (120598) cos (119894) + sin (120598) sin (119894) cos (120596119890119905))]

1198613=

3119872119890

1199033

0

times [sin (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus2 sin (1205960119905) sin (120598) sin (120596

119890119905)]

(6)

Journal of Control Science and Engineering 5

where1205960is the angular velocity of the orbit with respect to the

inertial frame 1199030is the distance from the center of the satellite

to the center of the Earth 119894 is the orbit inclination 120576 is themagnetic dipole tilt120596

119890is the spin rate of the Earth and119872

119890is

themagnetic dipolemoment of the EarthThemagnetometermodel is

119867 = 119862119896[

[

1198611

1198612

1198613

]

]

+ 120578119898

+ 119887119898 (7)

where 119862119896is the direction cosine matrix in terms of quater-

nions 120578119898

is the zero mean Gaussian white noise of themagnetometer119861 is the vector formedwith the components ofthe Earthrsquos magnetic field in the body frame of the reference

and 119861 = 119862119896[

1198611

1198612

1198613

] 119887119898is the magnetometer bias

The angular velocity is measured from three rate gyro-scopes The model is given by

120596119892= 120596 + 119887

119892+ 120578119892

119887119892= minus119896119891119887119892+ 120578119891

(8)

where120596119892is the output of a gyroscope and120596 is the real angular

rate of the gyro 120578119892and 120578119891are Gaussian white noise 119887

119892is the

random drift of the gyro and 119896119891is the drift constant

34 ActuatorModels Reactionwheels are widely used to per-form precise satellite attitude maneuvers because they allowcontinuous and smooth control of internal torques Torquesare produced on the satellite by accelerating or deceleratingthe reaction wheels Let the torque demanded by the satellitebe denoted as 120591

119888 where 120591

119888= 119869119908(Ω +119860

119894119887) The input voltage

119890119886required to control the actuator dynamics of the reaction

wheel can be written as

119890119886= 119896119887Ω minus 119877

119887119896minus1

119905(1198601015840

119894120591119888) (9)

where 119896119905is the motor torque constant 119896

119887is the back-EMF

constant 119877119887is the armature resistance and friction in the

reaction wheels is ignoredThemaximum voltage of the reac-tion wheel is 42 V and a dead zone for the reaction wheel isestimated to be below 1V 119896

119905is 00082 119896

119887is 0007119877

119887is 05 and

the moment of inertia of the reaction wheel is 00001 kgm2

4 Control Law Design and Simulation Results

41 Satellite Attitude Control Laws Magnetic control hasbeen used over many years [16 17] for small spacecraft atti-tude control The main drawback of magnetic control is thatmagnetic torque is two-dimensional and it is only present inthe plane perpendicular to the magnetic field vector [18]Theaccuracy of satellite attitude control systems (ACS) using onlymagnetic actuators is known to be accurate on the order of04ndash05 degree [18] The satellite cannot be controlled pre-cisely in three-dimensional space using only magnetorquers[18] but the combination ofmagnetorquers with one reactionwheel expands the two-dimensional control torque possi-bilities to be three-dimensional The attitude accuracy of

the combined actuators has been compared with three reac-tion wheels-based attitude control in the references [18 19]Classical sliding mode control has also been used for mag-netic actuated spacecraft [20 21] However the proposednonlinear adaptive fuzzy sliding mode control law has neverbeen used in magnetic attitude control

To address the attitude tracking problem the attitudetracking error 119902

119890= (119902119879

119890 1199024119890)

119879

is defined as the relative orienta-tion between the body frame and the desired frame withorientation 119902

119889= (119902119879

119889 1199024119889)

119879

In order to apply the proposednonlinear controller the equations of motion are rewritten as

119902119890= 119891 (119902

119890

119902119890) + 120591119888+ 120591119898

+ 120591119889 (10)

The adaptive fuzzy sliding mode magnetic control law isgiven by

120591 = minus1198961119878 minus 120579119879120585 minus 1198962tanh(

3119870119906120589119878

120598

) (11)

120579 = 120575119878120585120579 (12)

120591ap =

120591119878

100381710038171003817100381711987821003817100381710038171003817119878

(13)

119872 = 120591ap times

119861

100381710038171003817100381711986121003817100381710038171003817

(14)

Here 120591119898

= 119872 times 119861 are the torques generated by the magne-torquers 119872 is the vector of magnetic dipoles for the threemagnetorquers and 119861 is the vector formed with the compo-nents of the Earthrsquos magnetic field in the body frame of thereference 119878 =

119902119890+ 119870119902119890is the sliding surface 120579 and 120585 are the

adaptive parameters and fuzzy weight functions generatedby the fuzzy logic systems [22] and 120575 119896

1 1198962 119870119906 120589 120598 are

positive constants used for tuning the control response

Remark 1 AFSMC controller design details can be foundin the authorrsquos previous papers [11] The design includes (1)Sliding surface design [22] and (2) fuzzy logic system design[22]

42 Simulation Results The attitude detumbling and attitudestabilization phases are considered in the ACS simulationThe B-dot algorithm PD magnetic control law and adaptivefuzzy sliding mode magnetic control law are used for thetwo phases respectively We note that the orbit used for thepresent simulation study is a 500 km circular orbit with 45∘inclination At this altitude the total disturbance torque for1U CubeSats is estimated to be on the order of 5 times 10

minus7NmThis is intended to be a slight overestimation to include asafety margin

421 Detumbling Mode and Stabilization Mode

Scenario 1 In the initial stage of ACS control the angularvelocities of the satellite are assumed to be 0169 rads as aresult of separation from the launch vehicle The ACS dampsthe angular rate by controlling three magnetorquers Thecontrol logic generally used for detumbling is called B-dot

6 Journal of Control Science and Engineering

0 02 04 06 08 1 12 14 16 18 2

0

50

100

150

200

Time (orbits)

0 01 02

0100200

Roll (deg)Pitch (deg)Yaw (deg)

minus50

minus100

minus150

minus200

minus100

minus200

Magnetic dipole 01 Am2 B-dot control

(a)

0 02 04 06 08 1 12 14 16 18 2

0

1

2

Mag

netic

torq

ue (N

m)

0 01 02

0

2minus1

minus2

minus3

minus4

minus5

times10minus6

minus2

minus4

Time (orbits)

Magnetic dipole 01 Am2 B-dot control

times10minus6

120591119861112059111986121205911198613

(b)

minus002

0

002

004

006

008

01

012

014

016

018

Ang

ular

velo

city

trac

king

erro

r (ra

ds)

0 005 015

0

005

01

015

02

0 02 04 06 08 1 12 14 16 18 2Time (orbits)

minus00501 02

Magnetic dipole 01 Am2 B-dot control

(c)

0 05 1 15 2

0

002

004

006

008

01

0 01 02

0

005minus002

minus004

minus006

minus008

minus01

Mag

netic

dip

ole (

Am2)

Time (orbits)

01

minus005

minus01

119872119909

119872119910

119872119911

Magnetic dipole 01 Am2 B-dot control

(d)

Figure 7 Scenario 1 detumbling control results

control [1] as it makes use of the derivative of the magneticfield ldquo119861rdquo For a CubeSat with moment of inertia 119869 =

diag(0002 0002 0002) kgm2 we include the external dis-turbances (aerodynamic gravity gradient and solar pres-sure) set the desired quaternion to be (0 0 0 1) set theinitial quaternion to be (01 minus01 01 09849) and assumethe magnetic dipole maximum of the rods to be 01 Am2 TheEuler angle tracking errors angular velocity tracking errorsandmagnetic torquers magnetic dipoles results are shown inFigure 7 The satellite starts at the selected tip-off rate and

after 1 orbit the angular velocities are reduced to the requiredrates before continuing with other ACS tasks

Scenario 2 Now we consider a CubeSat with the samemoment of inertia and orbit and assume the magnetic dipolemaximum of the magnetorquer to be 04Am2 with a magne-tometer sensor bias calculated by 20 lowast 10

minus4lowast rand(1) Pro-

portional-derivative (PD) magnetic control [23] laws (shownin (15)) are used in this simulation and the results over 6 orbitsare shown in Figure 8 During the first three orbits three

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

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SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 3

Magnetometer(HMC5883L)

Rate sensors(ADXRS614)

Microcontroller(AT91SAM9G20)

ADC

Reaction wheeldrivers

Torque roddrivers

(BD6212)

Coarse sunsensors

(TSL1402)

Figure 2 Overview of proposed ACS design for a CubeSat-class nanosatellite

2 3 4 5 6 7 8005

01

015

0201

2

3

4

Core radius

Core length

Mag

netic

mom

ent

times10minus3

119883 00075119884 011119885 1302

Moment for wire radius of 011 mm

Figure 3 Magnetorquer sizing surface

Table 1 Magnetorquer parameters

Parameter Value UnitMaximum dipole moment 037 Am2

Total mass 28 gNumber of turns 6063Core diameter 57 mmWire diameter 0127 mmWire resistance 121 Ω

Maximum current 347 mA

can be used in the ACS if maximum control authority isrequired Table 2 shows the design parameters of the reactionwheels used on the proposed ACS [13] A completed reactionwheel assembly is shown in Figure 5

24 Electronic Integration of ACS Components To control thereaction wheel and magnetorquers hardware and house theattitude sensors and actuator drivers a printed circuit board(PCB) was fabricated shown in Figure 6 The board stackswith existing PC104 sized on-board computer (OBC) hard-ware and provides both IO breakout and power suppliesfor the ACS hardware It contains 33 V and 5V switchingsupplies for the ACS sensors as well as external interfaces fora battery and radio to be used specifically for air-bearing

Table 2 Reaction wheel parameters

Parameter Value UnitRotor mass 0214 kgMoment of inertia (axial) 941 times 10minus5 Kgm2

Moment of inertia (transverse) 502 times 10minus5 kgm2

Motor shaft Torque 60 times 10minus4 NmMaximum speed 1539 radsSupply voltage 37ndash42 V

ACS testing The board makes a HMC5883 three-axis mag-netometer an ADXL345 3-axis accelerometer and an ITG-3200 3-axis MEMS rate gyroscope available on the OBC I2Cbus Primary rate sensing for attitude control is accomplishedby three independent ADXRS614 rate gyro units orientedon orthogonal axes by means of right-angle IC sockets andconnected to the first three ADC channels on the OBC Thisallows accurate high-speed sampling of rotation rates for useby the attitude controller To drive the magnetorquers threeBD6212 integrated H-bridges are used controlled by threePWM channels from the OBC and three general purpose IOpins for current direction control To allow one PWM signaland one direction pin to control eachH-bridge the inputs aredemultiplexed by a SN74LVC1G8 tristate output demulti-plexer and pull-up resistors In full operation the boarddraws up to 100mW of power on average though compo-nents can be shut down as needed to conserve power if not inuse

3 System Models

31 Attitude Equations ofMotions In this section the satelliteis modelled as a rigid body with actuators that provide tor-ques about three mutually perpendicular axes that defines abody-fixed frame The equations of motion [14 15] are givenby

119869119887= minus120596times(119869119878120596119887+ 119860119894119869119908Ω) + 119860

119894120591119888+ 120591119898

+ 120591119889 (3)

where120596119887= (120596119887112059611988721205961198873)119879 is the angular velocity of the satellite

expressed in the body frame 119869119904is the inertia matrix of the

satellite 119869119908is the inertia matrix of the reaction wheel and

119869 = 119869119904minus 119860119894119869119908119860119879

119894 119860119894is the layout matrix of the reaction

4 Journal of Control Science and Engineering

Figure 4 Magnetorquer winding apparatus and completed torque rod

Figure 5 Reaction wheel assembly

wheels whose columns represent the influence of each wheelon the angular acceleration of the satelliteΩ is the velocity ofa reactionwheel 120591

119888is the torque control provided by the reac-

tion wheel 120591119898is the torque control provided by the magne-

torquers and 120591119889is the bounded external disturbance which

is a sumof the gravity gradient 120591gravity aerodynamic 120591aero andsolar radiation pressure 120591solar disturbances

The gravity gradient disturbance is 120591gravity =

3radic1205831198901198863

2

119862119869119904119862 where 120583 is the gravitational parameter of the

Earth 119886 is the semimajor axis of the orbit and 119862119896is the

direction cosine matrix in terms of quaternionsThe aerodynamic disturbance is 120591aero = 119862

1198892120588V2119860119871

where 119862119889is the coefficient of drag for a flat plate 119860 is the

cross-sectional area causing aerodynamic drag V is the satel-lite velocity 119871 is the distance between the centre of pressureand the centre of gravity and 120588 is the atmospheric densityrelated to the altitude

The solar radiation pressure disturbance is 120591solar =

119865119904119888119860119904(1 + 119903)119871 where 119865

119904is the solar constant at the Earthrsquos

orbital distance from the Sun 119888 is the speed of light 119860119904is the

illuminated surface area and 119903 is the surface reflectance

32 Attitude Kinematics The satellite attitude kinematics isrepresented using quaternions

119902 =

1

2

(

11990241198683times3

+ 119902times

minus119902119879

)120596119887equiv

1

2

119860 (119902) 120596119887 (4)

where 119902 = (119902119879 1199024)

119879

= (1199021 1199022 1199023 1199024)119879

Coil drive bridges

Magnetometer

MEMS rate gyros

33 V5 V supplies

Figure 6 ACS sensor and actuator board

In terms of Euler angles we can also express the satelliteattitude as

[

[

120574

]

]

=

[[[[[

[

1 sin (120595) tan (120572) cos (120595) tan (120572)

0 cos (120595) minus sin (120595)

0 sin(

120595

cos (120572))

cos (120595)

cos (120572)

]]]]]

]

120596119887 (5)

where 120595 is the roll angle about the 119909-axis 120572 is the pitch angleabout the 119910-axis and 120574 is the yaw about the 119911-axis

33 SensorModels Magnetic field vectors are obtained in theorbit reference frame

1198611=

119872119890

1199033

0

times [cos (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus sin (1205960119905) sin (120598) sin (120596

119890119905)]

1198612=

minus119872119890

1199033

0

[(cos (120598) cos (119894) + sin (120598) sin (119894) cos (120596119890119905))]

1198613=

3119872119890

1199033

0

times [sin (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus2 sin (1205960119905) sin (120598) sin (120596

119890119905)]

(6)

Journal of Control Science and Engineering 5

where1205960is the angular velocity of the orbit with respect to the

inertial frame 1199030is the distance from the center of the satellite

to the center of the Earth 119894 is the orbit inclination 120576 is themagnetic dipole tilt120596

119890is the spin rate of the Earth and119872

119890is

themagnetic dipolemoment of the EarthThemagnetometermodel is

119867 = 119862119896[

[

1198611

1198612

1198613

]

]

+ 120578119898

+ 119887119898 (7)

where 119862119896is the direction cosine matrix in terms of quater-

nions 120578119898

is the zero mean Gaussian white noise of themagnetometer119861 is the vector formedwith the components ofthe Earthrsquos magnetic field in the body frame of the reference

and 119861 = 119862119896[

1198611

1198612

1198613

] 119887119898is the magnetometer bias

The angular velocity is measured from three rate gyro-scopes The model is given by

120596119892= 120596 + 119887

119892+ 120578119892

119887119892= minus119896119891119887119892+ 120578119891

(8)

where120596119892is the output of a gyroscope and120596 is the real angular

rate of the gyro 120578119892and 120578119891are Gaussian white noise 119887

119892is the

random drift of the gyro and 119896119891is the drift constant

34 ActuatorModels Reactionwheels are widely used to per-form precise satellite attitude maneuvers because they allowcontinuous and smooth control of internal torques Torquesare produced on the satellite by accelerating or deceleratingthe reaction wheels Let the torque demanded by the satellitebe denoted as 120591

119888 where 120591

119888= 119869119908(Ω +119860

119894119887) The input voltage

119890119886required to control the actuator dynamics of the reaction

wheel can be written as

119890119886= 119896119887Ω minus 119877

119887119896minus1

119905(1198601015840

119894120591119888) (9)

where 119896119905is the motor torque constant 119896

119887is the back-EMF

constant 119877119887is the armature resistance and friction in the

reaction wheels is ignoredThemaximum voltage of the reac-tion wheel is 42 V and a dead zone for the reaction wheel isestimated to be below 1V 119896

119905is 00082 119896

119887is 0007119877

119887is 05 and

the moment of inertia of the reaction wheel is 00001 kgm2

4 Control Law Design and Simulation Results

41 Satellite Attitude Control Laws Magnetic control hasbeen used over many years [16 17] for small spacecraft atti-tude control The main drawback of magnetic control is thatmagnetic torque is two-dimensional and it is only present inthe plane perpendicular to the magnetic field vector [18]Theaccuracy of satellite attitude control systems (ACS) using onlymagnetic actuators is known to be accurate on the order of04ndash05 degree [18] The satellite cannot be controlled pre-cisely in three-dimensional space using only magnetorquers[18] but the combination ofmagnetorquers with one reactionwheel expands the two-dimensional control torque possi-bilities to be three-dimensional The attitude accuracy of

the combined actuators has been compared with three reac-tion wheels-based attitude control in the references [18 19]Classical sliding mode control has also been used for mag-netic actuated spacecraft [20 21] However the proposednonlinear adaptive fuzzy sliding mode control law has neverbeen used in magnetic attitude control

To address the attitude tracking problem the attitudetracking error 119902

119890= (119902119879

119890 1199024119890)

119879

is defined as the relative orienta-tion between the body frame and the desired frame withorientation 119902

119889= (119902119879

119889 1199024119889)

119879

In order to apply the proposednonlinear controller the equations of motion are rewritten as

119902119890= 119891 (119902

119890

119902119890) + 120591119888+ 120591119898

+ 120591119889 (10)

The adaptive fuzzy sliding mode magnetic control law isgiven by

120591 = minus1198961119878 minus 120579119879120585 minus 1198962tanh(

3119870119906120589119878

120598

) (11)

120579 = 120575119878120585120579 (12)

120591ap =

120591119878

100381710038171003817100381711987821003817100381710038171003817119878

(13)

119872 = 120591ap times

119861

100381710038171003817100381711986121003817100381710038171003817

(14)

Here 120591119898

= 119872 times 119861 are the torques generated by the magne-torquers 119872 is the vector of magnetic dipoles for the threemagnetorquers and 119861 is the vector formed with the compo-nents of the Earthrsquos magnetic field in the body frame of thereference 119878 =

119902119890+ 119870119902119890is the sliding surface 120579 and 120585 are the

adaptive parameters and fuzzy weight functions generatedby the fuzzy logic systems [22] and 120575 119896

1 1198962 119870119906 120589 120598 are

positive constants used for tuning the control response

Remark 1 AFSMC controller design details can be foundin the authorrsquos previous papers [11] The design includes (1)Sliding surface design [22] and (2) fuzzy logic system design[22]

42 Simulation Results The attitude detumbling and attitudestabilization phases are considered in the ACS simulationThe B-dot algorithm PD magnetic control law and adaptivefuzzy sliding mode magnetic control law are used for thetwo phases respectively We note that the orbit used for thepresent simulation study is a 500 km circular orbit with 45∘inclination At this altitude the total disturbance torque for1U CubeSats is estimated to be on the order of 5 times 10

minus7NmThis is intended to be a slight overestimation to include asafety margin

421 Detumbling Mode and Stabilization Mode

Scenario 1 In the initial stage of ACS control the angularvelocities of the satellite are assumed to be 0169 rads as aresult of separation from the launch vehicle The ACS dampsthe angular rate by controlling three magnetorquers Thecontrol logic generally used for detumbling is called B-dot

6 Journal of Control Science and Engineering

0 02 04 06 08 1 12 14 16 18 2

0

50

100

150

200

Time (orbits)

0 01 02

0100200

Roll (deg)Pitch (deg)Yaw (deg)

minus50

minus100

minus150

minus200

minus100

minus200

Magnetic dipole 01 Am2 B-dot control

(a)

0 02 04 06 08 1 12 14 16 18 2

0

1

2

Mag

netic

torq

ue (N

m)

0 01 02

0

2minus1

minus2

minus3

minus4

minus5

times10minus6

minus2

minus4

Time (orbits)

Magnetic dipole 01 Am2 B-dot control

times10minus6

120591119861112059111986121205911198613

(b)

minus002

0

002

004

006

008

01

012

014

016

018

Ang

ular

velo

city

trac

king

erro

r (ra

ds)

0 005 015

0

005

01

015

02

0 02 04 06 08 1 12 14 16 18 2Time (orbits)

minus00501 02

Magnetic dipole 01 Am2 B-dot control

(c)

0 05 1 15 2

0

002

004

006

008

01

0 01 02

0

005minus002

minus004

minus006

minus008

minus01

Mag

netic

dip

ole (

Am2)

Time (orbits)

01

minus005

minus01

119872119909

119872119910

119872119911

Magnetic dipole 01 Am2 B-dot control

(d)

Figure 7 Scenario 1 detumbling control results

control [1] as it makes use of the derivative of the magneticfield ldquo119861rdquo For a CubeSat with moment of inertia 119869 =

diag(0002 0002 0002) kgm2 we include the external dis-turbances (aerodynamic gravity gradient and solar pres-sure) set the desired quaternion to be (0 0 0 1) set theinitial quaternion to be (01 minus01 01 09849) and assumethe magnetic dipole maximum of the rods to be 01 Am2 TheEuler angle tracking errors angular velocity tracking errorsandmagnetic torquers magnetic dipoles results are shown inFigure 7 The satellite starts at the selected tip-off rate and

after 1 orbit the angular velocities are reduced to the requiredrates before continuing with other ACS tasks

Scenario 2 Now we consider a CubeSat with the samemoment of inertia and orbit and assume the magnetic dipolemaximum of the magnetorquer to be 04Am2 with a magne-tometer sensor bias calculated by 20 lowast 10

minus4lowast rand(1) Pro-

portional-derivative (PD) magnetic control [23] laws (shownin (15)) are used in this simulation and the results over 6 orbitsare shown in Figure 8 During the first three orbits three

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

4 Journal of Control Science and Engineering

Figure 4 Magnetorquer winding apparatus and completed torque rod

Figure 5 Reaction wheel assembly

wheels whose columns represent the influence of each wheelon the angular acceleration of the satelliteΩ is the velocity ofa reactionwheel 120591

119888is the torque control provided by the reac-

tion wheel 120591119898is the torque control provided by the magne-

torquers and 120591119889is the bounded external disturbance which

is a sumof the gravity gradient 120591gravity aerodynamic 120591aero andsolar radiation pressure 120591solar disturbances

The gravity gradient disturbance is 120591gravity =

3radic1205831198901198863

2

119862119869119904119862 where 120583 is the gravitational parameter of the

Earth 119886 is the semimajor axis of the orbit and 119862119896is the

direction cosine matrix in terms of quaternionsThe aerodynamic disturbance is 120591aero = 119862

1198892120588V2119860119871

where 119862119889is the coefficient of drag for a flat plate 119860 is the

cross-sectional area causing aerodynamic drag V is the satel-lite velocity 119871 is the distance between the centre of pressureand the centre of gravity and 120588 is the atmospheric densityrelated to the altitude

The solar radiation pressure disturbance is 120591solar =

119865119904119888119860119904(1 + 119903)119871 where 119865

119904is the solar constant at the Earthrsquos

orbital distance from the Sun 119888 is the speed of light 119860119904is the

illuminated surface area and 119903 is the surface reflectance

32 Attitude Kinematics The satellite attitude kinematics isrepresented using quaternions

119902 =

1

2

(

11990241198683times3

+ 119902times

minus119902119879

)120596119887equiv

1

2

119860 (119902) 120596119887 (4)

where 119902 = (119902119879 1199024)

119879

= (1199021 1199022 1199023 1199024)119879

Coil drive bridges

Magnetometer

MEMS rate gyros

33 V5 V supplies

Figure 6 ACS sensor and actuator board

In terms of Euler angles we can also express the satelliteattitude as

[

[

120574

]

]

=

[[[[[

[

1 sin (120595) tan (120572) cos (120595) tan (120572)

0 cos (120595) minus sin (120595)

0 sin(

120595

cos (120572))

cos (120595)

cos (120572)

]]]]]

]

120596119887 (5)

where 120595 is the roll angle about the 119909-axis 120572 is the pitch angleabout the 119910-axis and 120574 is the yaw about the 119911-axis

33 SensorModels Magnetic field vectors are obtained in theorbit reference frame

1198611=

119872119890

1199033

0

times [cos (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus sin (1205960119905) sin (120598) sin (120596

119890119905)]

1198612=

minus119872119890

1199033

0

[(cos (120598) cos (119894) + sin (120598) sin (119894) cos (120596119890119905))]

1198613=

3119872119890

1199033

0

times [sin (1205960119905) (cos (120598) sin (119894) minus sin (120598) cos (119894) cos (120596

119890119905))

minus2 sin (1205960119905) sin (120598) sin (120596

119890119905)]

(6)

Journal of Control Science and Engineering 5

where1205960is the angular velocity of the orbit with respect to the

inertial frame 1199030is the distance from the center of the satellite

to the center of the Earth 119894 is the orbit inclination 120576 is themagnetic dipole tilt120596

119890is the spin rate of the Earth and119872

119890is

themagnetic dipolemoment of the EarthThemagnetometermodel is

119867 = 119862119896[

[

1198611

1198612

1198613

]

]

+ 120578119898

+ 119887119898 (7)

where 119862119896is the direction cosine matrix in terms of quater-

nions 120578119898

is the zero mean Gaussian white noise of themagnetometer119861 is the vector formedwith the components ofthe Earthrsquos magnetic field in the body frame of the reference

and 119861 = 119862119896[

1198611

1198612

1198613

] 119887119898is the magnetometer bias

The angular velocity is measured from three rate gyro-scopes The model is given by

120596119892= 120596 + 119887

119892+ 120578119892

119887119892= minus119896119891119887119892+ 120578119891

(8)

where120596119892is the output of a gyroscope and120596 is the real angular

rate of the gyro 120578119892and 120578119891are Gaussian white noise 119887

119892is the

random drift of the gyro and 119896119891is the drift constant

34 ActuatorModels Reactionwheels are widely used to per-form precise satellite attitude maneuvers because they allowcontinuous and smooth control of internal torques Torquesare produced on the satellite by accelerating or deceleratingthe reaction wheels Let the torque demanded by the satellitebe denoted as 120591

119888 where 120591

119888= 119869119908(Ω +119860

119894119887) The input voltage

119890119886required to control the actuator dynamics of the reaction

wheel can be written as

119890119886= 119896119887Ω minus 119877

119887119896minus1

119905(1198601015840

119894120591119888) (9)

where 119896119905is the motor torque constant 119896

119887is the back-EMF

constant 119877119887is the armature resistance and friction in the

reaction wheels is ignoredThemaximum voltage of the reac-tion wheel is 42 V and a dead zone for the reaction wheel isestimated to be below 1V 119896

119905is 00082 119896

119887is 0007119877

119887is 05 and

the moment of inertia of the reaction wheel is 00001 kgm2

4 Control Law Design and Simulation Results

41 Satellite Attitude Control Laws Magnetic control hasbeen used over many years [16 17] for small spacecraft atti-tude control The main drawback of magnetic control is thatmagnetic torque is two-dimensional and it is only present inthe plane perpendicular to the magnetic field vector [18]Theaccuracy of satellite attitude control systems (ACS) using onlymagnetic actuators is known to be accurate on the order of04ndash05 degree [18] The satellite cannot be controlled pre-cisely in three-dimensional space using only magnetorquers[18] but the combination ofmagnetorquers with one reactionwheel expands the two-dimensional control torque possi-bilities to be three-dimensional The attitude accuracy of

the combined actuators has been compared with three reac-tion wheels-based attitude control in the references [18 19]Classical sliding mode control has also been used for mag-netic actuated spacecraft [20 21] However the proposednonlinear adaptive fuzzy sliding mode control law has neverbeen used in magnetic attitude control

To address the attitude tracking problem the attitudetracking error 119902

119890= (119902119879

119890 1199024119890)

119879

is defined as the relative orienta-tion between the body frame and the desired frame withorientation 119902

119889= (119902119879

119889 1199024119889)

119879

In order to apply the proposednonlinear controller the equations of motion are rewritten as

119902119890= 119891 (119902

119890

119902119890) + 120591119888+ 120591119898

+ 120591119889 (10)

The adaptive fuzzy sliding mode magnetic control law isgiven by

120591 = minus1198961119878 minus 120579119879120585 minus 1198962tanh(

3119870119906120589119878

120598

) (11)

120579 = 120575119878120585120579 (12)

120591ap =

120591119878

100381710038171003817100381711987821003817100381710038171003817119878

(13)

119872 = 120591ap times

119861

100381710038171003817100381711986121003817100381710038171003817

(14)

Here 120591119898

= 119872 times 119861 are the torques generated by the magne-torquers 119872 is the vector of magnetic dipoles for the threemagnetorquers and 119861 is the vector formed with the compo-nents of the Earthrsquos magnetic field in the body frame of thereference 119878 =

119902119890+ 119870119902119890is the sliding surface 120579 and 120585 are the

adaptive parameters and fuzzy weight functions generatedby the fuzzy logic systems [22] and 120575 119896

1 1198962 119870119906 120589 120598 are

positive constants used for tuning the control response

Remark 1 AFSMC controller design details can be foundin the authorrsquos previous papers [11] The design includes (1)Sliding surface design [22] and (2) fuzzy logic system design[22]

42 Simulation Results The attitude detumbling and attitudestabilization phases are considered in the ACS simulationThe B-dot algorithm PD magnetic control law and adaptivefuzzy sliding mode magnetic control law are used for thetwo phases respectively We note that the orbit used for thepresent simulation study is a 500 km circular orbit with 45∘inclination At this altitude the total disturbance torque for1U CubeSats is estimated to be on the order of 5 times 10

minus7NmThis is intended to be a slight overestimation to include asafety margin

421 Detumbling Mode and Stabilization Mode

Scenario 1 In the initial stage of ACS control the angularvelocities of the satellite are assumed to be 0169 rads as aresult of separation from the launch vehicle The ACS dampsthe angular rate by controlling three magnetorquers Thecontrol logic generally used for detumbling is called B-dot

6 Journal of Control Science and Engineering

0 02 04 06 08 1 12 14 16 18 2

0

50

100

150

200

Time (orbits)

0 01 02

0100200

Roll (deg)Pitch (deg)Yaw (deg)

minus50

minus100

minus150

minus200

minus100

minus200

Magnetic dipole 01 Am2 B-dot control

(a)

0 02 04 06 08 1 12 14 16 18 2

0

1

2

Mag

netic

torq

ue (N

m)

0 01 02

0

2minus1

minus2

minus3

minus4

minus5

times10minus6

minus2

minus4

Time (orbits)

Magnetic dipole 01 Am2 B-dot control

times10minus6

120591119861112059111986121205911198613

(b)

minus002

0

002

004

006

008

01

012

014

016

018

Ang

ular

velo

city

trac

king

erro

r (ra

ds)

0 005 015

0

005

01

015

02

0 02 04 06 08 1 12 14 16 18 2Time (orbits)

minus00501 02

Magnetic dipole 01 Am2 B-dot control

(c)

0 05 1 15 2

0

002

004

006

008

01

0 01 02

0

005minus002

minus004

minus006

minus008

minus01

Mag

netic

dip

ole (

Am2)

Time (orbits)

01

minus005

minus01

119872119909

119872119910

119872119911

Magnetic dipole 01 Am2 B-dot control

(d)

Figure 7 Scenario 1 detumbling control results

control [1] as it makes use of the derivative of the magneticfield ldquo119861rdquo For a CubeSat with moment of inertia 119869 =

diag(0002 0002 0002) kgm2 we include the external dis-turbances (aerodynamic gravity gradient and solar pres-sure) set the desired quaternion to be (0 0 0 1) set theinitial quaternion to be (01 minus01 01 09849) and assumethe magnetic dipole maximum of the rods to be 01 Am2 TheEuler angle tracking errors angular velocity tracking errorsandmagnetic torquers magnetic dipoles results are shown inFigure 7 The satellite starts at the selected tip-off rate and

after 1 orbit the angular velocities are reduced to the requiredrates before continuing with other ACS tasks

Scenario 2 Now we consider a CubeSat with the samemoment of inertia and orbit and assume the magnetic dipolemaximum of the magnetorquer to be 04Am2 with a magne-tometer sensor bias calculated by 20 lowast 10

minus4lowast rand(1) Pro-

portional-derivative (PD) magnetic control [23] laws (shownin (15)) are used in this simulation and the results over 6 orbitsare shown in Figure 8 During the first three orbits three

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

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Active and Passive Electronic Components

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 5

where1205960is the angular velocity of the orbit with respect to the

inertial frame 1199030is the distance from the center of the satellite

to the center of the Earth 119894 is the orbit inclination 120576 is themagnetic dipole tilt120596

119890is the spin rate of the Earth and119872

119890is

themagnetic dipolemoment of the EarthThemagnetometermodel is

119867 = 119862119896[

[

1198611

1198612

1198613

]

]

+ 120578119898

+ 119887119898 (7)

where 119862119896is the direction cosine matrix in terms of quater-

nions 120578119898

is the zero mean Gaussian white noise of themagnetometer119861 is the vector formedwith the components ofthe Earthrsquos magnetic field in the body frame of the reference

and 119861 = 119862119896[

1198611

1198612

1198613

] 119887119898is the magnetometer bias

The angular velocity is measured from three rate gyro-scopes The model is given by

120596119892= 120596 + 119887

119892+ 120578119892

119887119892= minus119896119891119887119892+ 120578119891

(8)

where120596119892is the output of a gyroscope and120596 is the real angular

rate of the gyro 120578119892and 120578119891are Gaussian white noise 119887

119892is the

random drift of the gyro and 119896119891is the drift constant

34 ActuatorModels Reactionwheels are widely used to per-form precise satellite attitude maneuvers because they allowcontinuous and smooth control of internal torques Torquesare produced on the satellite by accelerating or deceleratingthe reaction wheels Let the torque demanded by the satellitebe denoted as 120591

119888 where 120591

119888= 119869119908(Ω +119860

119894119887) The input voltage

119890119886required to control the actuator dynamics of the reaction

wheel can be written as

119890119886= 119896119887Ω minus 119877

119887119896minus1

119905(1198601015840

119894120591119888) (9)

where 119896119905is the motor torque constant 119896

119887is the back-EMF

constant 119877119887is the armature resistance and friction in the

reaction wheels is ignoredThemaximum voltage of the reac-tion wheel is 42 V and a dead zone for the reaction wheel isestimated to be below 1V 119896

119905is 00082 119896

119887is 0007119877

119887is 05 and

the moment of inertia of the reaction wheel is 00001 kgm2

4 Control Law Design and Simulation Results

41 Satellite Attitude Control Laws Magnetic control hasbeen used over many years [16 17] for small spacecraft atti-tude control The main drawback of magnetic control is thatmagnetic torque is two-dimensional and it is only present inthe plane perpendicular to the magnetic field vector [18]Theaccuracy of satellite attitude control systems (ACS) using onlymagnetic actuators is known to be accurate on the order of04ndash05 degree [18] The satellite cannot be controlled pre-cisely in three-dimensional space using only magnetorquers[18] but the combination ofmagnetorquers with one reactionwheel expands the two-dimensional control torque possi-bilities to be three-dimensional The attitude accuracy of

the combined actuators has been compared with three reac-tion wheels-based attitude control in the references [18 19]Classical sliding mode control has also been used for mag-netic actuated spacecraft [20 21] However the proposednonlinear adaptive fuzzy sliding mode control law has neverbeen used in magnetic attitude control

To address the attitude tracking problem the attitudetracking error 119902

119890= (119902119879

119890 1199024119890)

119879

is defined as the relative orienta-tion between the body frame and the desired frame withorientation 119902

119889= (119902119879

119889 1199024119889)

119879

In order to apply the proposednonlinear controller the equations of motion are rewritten as

119902119890= 119891 (119902

119890

119902119890) + 120591119888+ 120591119898

+ 120591119889 (10)

The adaptive fuzzy sliding mode magnetic control law isgiven by

120591 = minus1198961119878 minus 120579119879120585 minus 1198962tanh(

3119870119906120589119878

120598

) (11)

120579 = 120575119878120585120579 (12)

120591ap =

120591119878

100381710038171003817100381711987821003817100381710038171003817119878

(13)

119872 = 120591ap times

119861

100381710038171003817100381711986121003817100381710038171003817

(14)

Here 120591119898

= 119872 times 119861 are the torques generated by the magne-torquers 119872 is the vector of magnetic dipoles for the threemagnetorquers and 119861 is the vector formed with the compo-nents of the Earthrsquos magnetic field in the body frame of thereference 119878 =

119902119890+ 119870119902119890is the sliding surface 120579 and 120585 are the

adaptive parameters and fuzzy weight functions generatedby the fuzzy logic systems [22] and 120575 119896

1 1198962 119870119906 120589 120598 are

positive constants used for tuning the control response

Remark 1 AFSMC controller design details can be foundin the authorrsquos previous papers [11] The design includes (1)Sliding surface design [22] and (2) fuzzy logic system design[22]

42 Simulation Results The attitude detumbling and attitudestabilization phases are considered in the ACS simulationThe B-dot algorithm PD magnetic control law and adaptivefuzzy sliding mode magnetic control law are used for thetwo phases respectively We note that the orbit used for thepresent simulation study is a 500 km circular orbit with 45∘inclination At this altitude the total disturbance torque for1U CubeSats is estimated to be on the order of 5 times 10

minus7NmThis is intended to be a slight overestimation to include asafety margin

421 Detumbling Mode and Stabilization Mode

Scenario 1 In the initial stage of ACS control the angularvelocities of the satellite are assumed to be 0169 rads as aresult of separation from the launch vehicle The ACS dampsthe angular rate by controlling three magnetorquers Thecontrol logic generally used for detumbling is called B-dot

6 Journal of Control Science and Engineering

0 02 04 06 08 1 12 14 16 18 2

0

50

100

150

200

Time (orbits)

0 01 02

0100200

Roll (deg)Pitch (deg)Yaw (deg)

minus50

minus100

minus150

minus200

minus100

minus200

Magnetic dipole 01 Am2 B-dot control

(a)

0 02 04 06 08 1 12 14 16 18 2

0

1

2

Mag

netic

torq

ue (N

m)

0 01 02

0

2minus1

minus2

minus3

minus4

minus5

times10minus6

minus2

minus4

Time (orbits)

Magnetic dipole 01 Am2 B-dot control

times10minus6

120591119861112059111986121205911198613

(b)

minus002

0

002

004

006

008

01

012

014

016

018

Ang

ular

velo

city

trac

king

erro

r (ra

ds)

0 005 015

0

005

01

015

02

0 02 04 06 08 1 12 14 16 18 2Time (orbits)

minus00501 02

Magnetic dipole 01 Am2 B-dot control

(c)

0 05 1 15 2

0

002

004

006

008

01

0 01 02

0

005minus002

minus004

minus006

minus008

minus01

Mag

netic

dip

ole (

Am2)

Time (orbits)

01

minus005

minus01

119872119909

119872119910

119872119911

Magnetic dipole 01 Am2 B-dot control

(d)

Figure 7 Scenario 1 detumbling control results

control [1] as it makes use of the derivative of the magneticfield ldquo119861rdquo For a CubeSat with moment of inertia 119869 =

diag(0002 0002 0002) kgm2 we include the external dis-turbances (aerodynamic gravity gradient and solar pres-sure) set the desired quaternion to be (0 0 0 1) set theinitial quaternion to be (01 minus01 01 09849) and assumethe magnetic dipole maximum of the rods to be 01 Am2 TheEuler angle tracking errors angular velocity tracking errorsandmagnetic torquers magnetic dipoles results are shown inFigure 7 The satellite starts at the selected tip-off rate and

after 1 orbit the angular velocities are reduced to the requiredrates before continuing with other ACS tasks

Scenario 2 Now we consider a CubeSat with the samemoment of inertia and orbit and assume the magnetic dipolemaximum of the magnetorquer to be 04Am2 with a magne-tometer sensor bias calculated by 20 lowast 10

minus4lowast rand(1) Pro-

portional-derivative (PD) magnetic control [23] laws (shownin (15)) are used in this simulation and the results over 6 orbitsare shown in Figure 8 During the first three orbits three

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

6 Journal of Control Science and Engineering

0 02 04 06 08 1 12 14 16 18 2

0

50

100

150

200

Time (orbits)

0 01 02

0100200

Roll (deg)Pitch (deg)Yaw (deg)

minus50

minus100

minus150

minus200

minus100

minus200

Magnetic dipole 01 Am2 B-dot control

(a)

0 02 04 06 08 1 12 14 16 18 2

0

1

2

Mag

netic

torq

ue (N

m)

0 01 02

0

2minus1

minus2

minus3

minus4

minus5

times10minus6

minus2

minus4

Time (orbits)

Magnetic dipole 01 Am2 B-dot control

times10minus6

120591119861112059111986121205911198613

(b)

minus002

0

002

004

006

008

01

012

014

016

018

Ang

ular

velo

city

trac

king

erro

r (ra

ds)

0 005 015

0

005

01

015

02

0 02 04 06 08 1 12 14 16 18 2Time (orbits)

minus00501 02

Magnetic dipole 01 Am2 B-dot control

(c)

0 05 1 15 2

0

002

004

006

008

01

0 01 02

0

005minus002

minus004

minus006

minus008

minus01

Mag

netic

dip

ole (

Am2)

Time (orbits)

01

minus005

minus01

119872119909

119872119910

119872119911

Magnetic dipole 01 Am2 B-dot control

(d)

Figure 7 Scenario 1 detumbling control results

control [1] as it makes use of the derivative of the magneticfield ldquo119861rdquo For a CubeSat with moment of inertia 119869 =

diag(0002 0002 0002) kgm2 we include the external dis-turbances (aerodynamic gravity gradient and solar pres-sure) set the desired quaternion to be (0 0 0 1) set theinitial quaternion to be (01 minus01 01 09849) and assumethe magnetic dipole maximum of the rods to be 01 Am2 TheEuler angle tracking errors angular velocity tracking errorsandmagnetic torquers magnetic dipoles results are shown inFigure 7 The satellite starts at the selected tip-off rate and

after 1 orbit the angular velocities are reduced to the requiredrates before continuing with other ACS tasks

Scenario 2 Now we consider a CubeSat with the samemoment of inertia and orbit and assume the magnetic dipolemaximum of the magnetorquer to be 04Am2 with a magne-tometer sensor bias calculated by 20 lowast 10

minus4lowast rand(1) Pro-

portional-derivative (PD) magnetic control [23] laws (shownin (15)) are used in this simulation and the results over 6 orbitsare shown in Figure 8 During the first three orbits three

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 7

0 1 2 3 4 5 6

0

50

100

150

200Roll-pitch-yaw

Time (orbits)

4 5 6

0

001

002

Detumbling mode B-dotminus50

minus100

minus150

minus200

minus001

minus002

3-axis pure magnetic control

(a)

0 1 2 3 4 5 6

0

002

004

006

008

01

012

014

016

018Angular velocity

3 302 304

0

001

Detumbling mode B-dot

Time (orbits)

minus002

minus001

minus002

3-axis pure magnetic control

Ang

ular

velo

city

max

(01

69 ra

ds=

10 de

gs)

02

01

00 0005 001

(b)

0 1 2 3 4 5 6

0

01

02

03

04Magnetic moment

0 0005 001 56 58 6

0 1

2

Detumbling mode B-dot

minus01

minus02

minus03

minus04

Mag

netic

dip

ole (

Am2)

3-axis pure magnetic control

Time (orbits)

minus1

1

119872119909

119872119910

119872119911

times10minus404

020

minus02

minus04

(c)

0 1 2 3 4 5 6

0

05

1

15

2

25

3Detumbling mode B-dot

minus05

times10minus4

Time (orbits)

3-axis pure magnetic controlM

agne

tic fi

eld

in b

ody

fram

e (T)

Body frame

119861111986121198613

(d)

Figure 8 Scenario 2 detumbling mode and stable mode control results

magnetorquers are used for the detumbling mode In thesecond three orbits three magnetorquers and one reactionwheel are used for the stable mode The attitude controlaccuracy is less than 002 degree while using the PDmagneticcontrol laws

120591119898

= 119872 times 119861

119872 = 1198701120596119887times 119861

119872 = 1198701120596119887times 119861 + 119870

2119902 times 119861

(15)

422 Attitude Stabilization Mode Nadir and Limb Pointingwith Three Magnetorquers and One Pitch Reaction WheelNext we consider the second stage of nanosatellite controlwith a low initial angular velocity after detumbling and large

slew angle target for limb and nadir pointing The configura-tionwith threemagnetorquers and one flywheel [24] has beenused formany years In a real nanosatellite mission hardwarefailures of the reaction wheels are very common [19] Whenthere are two wheel failures the ACS can be switched fromusing three reaction wheels to three magnetorquers and onereaction wheel and attitude control accuracy maintainedusing this methodThe adaptive fuzzy slidingmodemagneticcontrol laws are shown in (11)ndash(14) The attitude controlaccuracy using the nonlinear adaptive fuzzy sliding modecontrol law will be more robust to the external disturbancesthan using the PD magnetic control law in (15)

Scenario 3 An ACS using one reaction wheel and threemagnetorquers as actuators for limbpointingwith the desired

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Control Science and Engineering

0 2 4 6 8 10 12

01020304050607080

Roll-pitch-yaw tracking errors

Time (orbits)

minus10

minus20

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

minus01

1198981

(Am2)

Time (orbits)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Time (orbits)

Magnetic moment y-axis

(c)

0 05 1 15 2 25 3 35

0

005

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Time (orbits)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

20

40

60

80

100

Whe

el sp

eed

(rad

s)

minus20

minus40

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

08

06

04

02

0

minus02

minus04

minus06

minus08

minus1

Time (orbits)

(f)

Figure 9 Scenario 3 limb pointing control results using one reaction wheel and three magnetorquers

quaternion set to (0 05736 0 08192) is examined usingAFSMC over 10 orbits The wheel dead zone is not consid-ered here The initial quaternion is (01 minus01 01 09849)

and initial angular velocity is (00169 00169 00169) radsConsidering only the pitch reaction wheel is available thenumerical simulations demonstrate that the proposed tech-nique achieves a high pointing accuracy (lt009 degree)for small satellites The magnetic dipoles from the three

magnetorquers attitude tracking errors wheel speed andwheel voltage are shown in Figure 9

Scenario 4 AnACS using one reaction wheel and threemag-netorquers as actuators for nadir pointing with the desiredquaternion that is set to (0 0 0 1) is examined using AFSMCover 10 orbits The wheel dead zone is assumed to be plusmn10VThe initial quaternion is (01 minus01 01 09849) and initial

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 9

0 2 4 6 8 10 12

0

10

20

30

40Roll-pitch-yaw tracking errors

minus10

minus20

Time (orbits)

(a)

0 2 4 6 8 10 12

0

005

01

015

02

025

03

minus005

Time (orbits)

1198981

(Am2)

Magnetic moment x-axis

(b)

0 2 4 6 8 10 12Time (orbits)

03

02

01

0

minus01

minus02

minus03

minus04

1198982

(Am2)

Magnetic moment y-axis

(c)

0

005

0 2 4 6 8 10 12Time (orbits)

minus005

minus01

minus015

minus02

minus025

minus03

1198983

(Am2)

Magnetic moment z-axis

(d)

0 2 4 6 8 10 12

0

Whe

el sp

eed

(rad

s)

minus10

minus20

minus30

minus40

minus50

minus60

Time (orbits)

(e)

0 2 4 6 8 10 12

Whe

el vo

ltage

(V)

minus01

minus02

minus03

minus04

minus05

minus06

minus07

minus08

minus09

minus1

Time (orbits)

(f)

Figure 10 Scenario 4 nadir pointing control results using one reaction wheel and three magnetorquers

angular velocity is (00169 00169 00169) rads The pitchreaction wheel and three magnetorquers are usedThese sim-ulations demonstrate that the proposed technique can alsoachieve high accuracy (lt009 degree with all disturbances)pointing control for small satellites The magnetic dipolesof the three magnetorquers attitude tracking errors wheelspeed andwheel voltage are shown in Figure 10 It takes about40 orbits for the wheel speed to increase from 0 to 2000 rpm(209 rads)

423 Attitude Stabilization Mode Nadir Pointing withThree Reaction Wheels

Scenario 5 An ACS using three reaction wheels as actua-tors for nadir pointing with the desired quaternion set to(0 0 0 1) is examined using AFSMC over 01 orbits Thewheel dead zone is assumed to be plusmn10V The initial quater-nion is (01 minus01 01 09849) and initial angular velocityis (00169 00169 00169) rads This configuration can also

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Control Science and Engineering

0 001 002 003 004 005 006 007 008 009 01

0

5

10

15Roll-pitch-yaw tracking error with three reaction wheels

Ang

le (d

eg)

05

1015

013 0132 0134 0136 0138 014

02468

minus5

minus10

minus15

minus5

minus10

minus150 02 04 06 08 1

times10minus3

minus2

times10minus3

Time (orbits)

Figure 11 Scenario 5 nadir pointing control results using three wheels Euler angle tracking errors

0 002 004 006 008 01 012 014 016

0

2

4

6

8Control input with AFSMC

Con

trolle

r (N

m)

times10minus3

minus2

minus4

minus6

minus8

Time (orbits)

Figure 12 Scenario 5 nadir pointing control results using threewheels control input

achieve high attitude control accuracy (lt0008 degree with alldisturbances) The reaction wheel attitude control laws use(11) and (12) The settling time is shorter and the pointingaccuracy is higher than that achieved using only three mag-netorquers and one reaction wheel as actuators Howeverthe power consumption is higher than using three magnetor-quers and one reactionwheelTheEuler angle tracking errorscontrol inputs wheel speeds and wheel voltages are shown inFigures 11 12 13 and 14

5 Satellite Attitude Control SystemHardware Testing

51 Spherical Air-Bearing Testbed for Satellite Attitude ControlSystems The ground testing of the proposed CubeSat ACSdesignwas performed at YorkUniversity using a nanosatelliteattitude control testbed This facility consists of a sphericalair-bearing platform [25 26] suspended upon a thin layer ofair providing a full three degrees of freedom with negligiblefriction for ACS testing The platform includes a manualbalancing system and platform electronics that include anon-board computer (OBC)wireless transceiver for telemetryreference inertial measurement unit (IMU) power distribu-tion board and batteries The air-bearing system used for 1UCubeSat testing is shown in Figure 15

52 Ground Test Results ACS Testing Results withThree Reac-tion Wheel Actuators Nonlinear attitude control has beenexplored widely in theory [14 27 28] In real satellite appli-cations nonlinear controllers are usually not selected due totheir complexity of design We have tested nonlinear controlalgorithms [11]with our spherical air-bearing systemWenowtest the proposed control method (from (11) and (12)) on thissystem using the sensors and ACS board described above andthree-axis reaction wheel actuation A PID control law is alsoused for comparison on the same hardware The control lawsare programmed in the C language and the OBC runs theLinux operating system More details of the implementationcan be also found in [11] Here we will show air-bearingsystem test results with a 1U CubeSat The design parametersof the control laws used are given in Tables 3 and 4

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 11

0 002 004 006 008 01 012 014 016

0

200

400

600Wheel speed with AFSMC

Whe

el sp

eed

(rad

s)

minus200

minus400

minus600

Time (orbits)

Figure 13 Scenario 5 nadir pointing control results using three wheels wheel speed

0

1

2

3

4Wheel voltages with AFSMC

Whe

el vo

ltage

(V)

0 002 004 006 008 01 012 014 016Time (orbits)

minus1

minus2

minus3

minus4

minus5

Figure 14 Scenario 5 nadir pointing control results using three wheels wheel voltage

119909 119910

119911

Figure 15 Air-bearing ACS ground testing system

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Control Science and Engineering

0 50 100 150 200

0

20

40

60

80

100AFSMC tracking error

Time (s)

Erro

r (de

g)

RollPitchYaw

minus20

(a)

0 50 100 150 200

0

1

2AFSMC control input

Time (s)

Roll-

pitc

h-ya

w-c

ontro

l

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(b)

0 20 40 60 80 100 120 140 160 180 200

0

1

2

3AFSMC wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 20 40 60 80 100 120 140 160 180 200

0

500

1000

1500AFSMC wheel speed

Time (s)

Whe

el sp

eed

(rad

s)

minus500

minus1000

minus1500

minus2000

minus2500

minus3000

RollPitchYaw

(d)

Figure 16 Air-bearing AFSMC controller results

Table 3 PID controller parameters for air bearing testing

Name ValuesProportional parameters 003Integral parameters 00001Derivative parameters 011

Figures 16 and 17 show the attitude tracking errorsAFSMCPID control output signals reaction wheel voltagesand reaction wheel velocities for a 90 degree yaw slew of thesystem about the 119911-axis while maintaining 0 degrees of roll

Table 4 AFSMC controller parameters for air bearing testing

Name ValuesSliding surface gain 000001 100Fuzzy membership function 1 1Adaptive gains 120575 119870

119906 120589 120598 01 036 001 2

AFSMC parameter 1198961

0004AFSMC parameter 119896

200025

and pitch Due to the difficulty of perfectly balancing theair-bearing system a gravitational disturbance larger than

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 13

0 50 100 150 200

0

20

40

60

80

100PID tracking error

Time (s)

Erro

r (de

g)

minus20

RollPitchYaw

(a)

0 50 100 150 200

PID control input

Time (s)

Torq

ue fr

actio

n

1

05

0

minus05

minus1

minus15

minus2

RollPitchYaw

(b)

0 50 100 150

0

1

2PID wheel voltage

Time (s)

Whe

el v

olta

ge (V

)

minus1

minus2

minus3

minus4

minus5

RollPitchYaw

(c)

0 50 100 150

0

500PID wheel speed

Time (s)

Whe

el sp

eed

(rad

s) minus500

minus1000

minus1500

minus2000

minus2500

RollPitchYaw

(d)

Figure 17 Air-bearing PID controller results

normal in size is considered to be present about the 119909 and 119910

rotational axes Compared to the PID controller the AFSMCcontroller uses nearly the same gain and has much bettertracking performance under these conditions

6 Future Work

While the ground test demonstrates the effective and promis-ing control accuracy of the proposedACS design it is difficult

to predict the performance of pure and hybrid magneticcontrol as the Earthrsquos magnetic field present in the test facilityis constant and invariant with many sources of additionalmagnetic noise The next step in the development of acomplete ACS test facility is the addition of a Helmholtz cagefor magnetic control tests The magnetic cage and the air-bearing system in the lab are shown in Figure 18 and arepresently being prepared for air-bearing magnetic controltesting Future work will demonstrate the effectiveness ofmagnetic control in further ground testing

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Journal of Control Science and Engineering

Figure 18 Helmholtz cage for magnetic field generation

7 Conclusion

In this paper the proposed attitude control system designwillallow inexpensive and capable satellites to be developed foracademic use The proposed attitude control system usesthree reaction wheels as actuators or one wheel with threemagnetorquers as actuators The hardware designs of theactuators and embedded attitude control systems are alsodescribed for prototype development Five different scenariosof numerical simulation results for a 1U CubeSat-class nano-satellite show the effectiveness of the proposed attitude con-trol design for detumbling and attitude pointing purposesThe ground testing results in this paper provide a promisingcomparison of an adaptive fuzzy slidingmode controller witha conventional proportional-integral-derivative controller fora 1U CubeSat-class nanosatellite The nanosatellite testinghardware can be also extended for use in 2U or 3U CubeSat-class nanosatellites in the future

Acknowledgments

The authors gratefully acknowledge the support provided byCOM DEV Ltd NSERC MITACS and OCE The authorswould also like to acknowledge the work of M Cannata IProper T Ustrzycki G Benari and H Hakima in this paper

References

[1] YW Jan and J C Chiou ldquoAttitude control system for ROCSAT-3microsatellite a conceptual designrdquoActa Astronautica vol 56no 4 pp 439ndash452 2005

[2] M Ovchinnikov V Penrsquokov O Norberg and S BarabashldquoAttitude control system for the first Swedish nanosatellitelsquoMUNINrsquordquo Acta Astronautica vol 46 no 2 pp 319ndash326 2000

[3] M I Martinelli and R S S Pena ldquoPassive 3 axis attitude controlof MSU-1 pico-satelliterdquo Acta Astronautica vol 56 no 5 pp507ndash517 2005

[4] G P Candini F Piergentili and F Santoni ldquoMiniaturized atti-tude control system for nanosatellitesrdquo Acta Astronautica vol81 pp 325ndash334 2005

[5] T Xiang T Meng HWang K Han and Z H Jin ldquoDesign andon-orbit performance of the attitude determination and controlsystem for the ZDPS-1A pico-satelliterdquo Acta Astronautica vol77 pp 82ndash196 2012

[6] M Abdekrahman and S Y Park ldquoIntegrated attitude determi-nation and control system via magnetic measurements andactuationrdquo Acta Astronautica vol 69 no 3-4 pp 168ndash185 2011

[7] M Cannata Development of a sun vector determination algo-rithm for Cubesat-Class spacecraft [MS thesis] Dept of Earthand Space Science and Engineering York University TorontoCanada 2010

[8] I Proper Reaction wheel design construction and qualificationtesting [MS thesis] Dept of Earth and Space Science andEngineering York University Toronto Canada 2010

[9] J Li M A Post and R Lee ldquoReal time fault tolerant nonlinearattitude control system for nanosatellite applicationrdquo in AIAAInfotechAerospace 2012 Conference pp 19ndash21 Garden GroveCalif USA 2012

[10] J Li M A Post and R Lee ldquoNanosatellite air bearing testsof fault-tolerant sliding-mode attitude control with UnscentedKalman Filterrdquo in AIAA Guidance Navigation and ControlConference Minnesota Minneapolis Minn USA 2012

[11] J Li M A Post and R Lee ldquoNanosatellite attitude air bearingsystem using variable structure controlrdquo in IEEE 25th AnnualCanadian Conference on Electrical and Computer EngineeringMontreal Canada May 2012

[12] M F Mehrjardi andM Mirshams ldquoDesign and manufacturingof a researchmagnetic torquer RodrdquoContemporary EngineeringSciences vol 3 no 5 pp 227ndash236 2010

[13] T Ustrzycki Spherical air bearing testbed for nanosatellite atti-tude control development [MS thesis] Dept of Earth and SpaceScience and Engineering York University Toronto Canada2011

[14] C H Won ldquoComparative study of various control methods forattitude control of a LEO satelliterdquo Aerospace Science and Tech-nology vol 5 pp 323ndash333 1999

[15] J Y Lin S Ko and C K Ryoo ldquoFault tolerant control ofsatellites with four reaction wheelsrdquo Control Engineering Prac-tice vol 16 no 10 pp 1250ndash1258 2008

[16] E Silani andM Lovera ldquoMagnetic spacecraft attitude control asurvey and some new resultsrdquo Control Engineering Practice vol13 no 3 pp 357ndash371 2005

[17] C J Dameran ldquoHybrid magnetic attitude control gain selec-tionrdquo Proceedings of the Institution of Mechanical Engineers Gvol 223 no 8 pp 1041ndash1047 2009

[18] Z Q Zhou ldquoSpacecraft attitude tracking and maneuver usingcombined magnetic actuatorsrdquo in AIAA Guidance Navigationand Control Conference Toronto Ontario Canada August2010

[19] J R Forbes and C J Damaren ldquoGeometric approach to space-craft attitude control usingmagnetic andmechanical actuationrdquoJournal of Guidance Control and Dynamics vol 33 no 2 pp590ndash595 2010

[20] RWisniewski Satellite attitude control usingmagnetic actuationonly [PhD thesis] Dissertation Dept of Control EngineeringAalborg University Denmark 1996

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 15

[21] PWang Y B Shtessel andYQWang ldquoSatellite attitude controlusing only magnetorquersrdquo in Proceeding of the 13th Southeast-ern Symposium on System Theory West Virginia UniversityMorgantown WVa USA March 1998

[22] J Li and K D Kumar ldquoFault tolerant attitude synchronizationcontrol during formation flyingrdquo Journal of Aerospace Engineer-ing vol 24 no 3 pp 251ndash263 2011

[23] D V Guerrant Design and analysis of fully magnetic controlfor picosatellite stabilization [MS thesis] California PolytechnicState University 2005

[24] MChen S J Zhang F R Liu andY C Zhang ldquoCombined atti-tude control of small satellite using One flywheel and magnetictorquersrdquo in Proceedings of the 2nd International Sympo-sium on Systems and Control in Aerospace and Astronautics(ISSCAA rsquo08) Shenzhen China December 2008

[25] J Prado G Bisiacchi L Reyes et al ldquoThree-axis air-bearingbased platform for small satellite attitude determination andcontrol simulationrdquo Journal of Applied Research and Technologyvol 3 no 3 pp 222ndash237 2005

[26] J J Kim and B N Agrawal ldquoAutomatic mass balancing of air-bearing-based three-axis rotational spacecraft simulatorrdquoAIAAJournal of Guidance Control and Dynamics vol 32 no 3 pp1005ndash1017 2009

[27] K S Kim and Y Kim ldquoRobust backstepping control for slewmaneuver using nonlinear tracking functionrdquo IEEE Transac-tions on Control Systems Technology vol 11 no 6 pp 822ndash8292003

[28] S C Lo and Y P Chen ldquoSmooth sliding mode control forspacecraft attitude tracking maneuversrdquo Journal of GuidanceControl and Dynamics vol 18 no 6 pp 1345ndash1349 1995

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of