Acta Astronautica 128 (2016) 210–216

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Acta Astronautica journal homepage: www.elsevier.com/locate/aa

Nanosatellite spin-up using magnetic actuators: ESTCube-1 flight results Hendrik Ehrpais a,b,n, Johan Kütt b, Indrek Sünter a,b, Erik Kulu a,b, Andris Slavinskis a,b,c, Mart Noorma a,b a

University of Tartu, Institute of Physics, W. Ostwaldi 1-D601, 50411, Tartu, Estonia Tartu Observatory, Department of Space Technology, Observatooriumi 1, 61602, Tõravere, Estonia c Finnish Meteorological Institute, Erik Palménin aukio 1, P.O. Box 503, FI-00101, Helsinki, Finland b

art ic l e i nf o

a b s t r a c t

Article history: Received 15 November 2015 Accepted 22 July 2016 Available online 25 July 2016

This paper presents the in-orbit performance of the ESTCube-1 attitude control system that used electromagnetic actuators to achieve a high angular velocity. ESTCube-1 is a one-unit CubeSat that aimed to perform the first electric solar wind sail experiment. The attitude control system was designed to provide enough centrifugal force by spinning up the satellite to deploy a 10 m long tether. The required spin rate was a minimum of one rotation per second. The actuators used were three electromagnetic coils, each able to produce a magnetic moment of up to 0.1 A m2. In this paper, we describe the design of the attitude control system, implementation of the spin controller and the in-orbit performance of the system. In addition we describe the effect that a residual magnetic moment had on the attitude control of the satellite and the measures taken to overcome this issue. During testing of the satellite, ESTCube-1 achieved the highest known spin rate of 841°/s for small scale satellites. The satellite ended its operations on the 19th of May, 2015 after 2 years in orbit. & 2016 IAA. Published by Elsevier Ltd. All rights reserved.

Keywords: CubeSat ESTCube-1 Nanosatellite Magnetic attitude control High spin rate Flight results

1. Introduction Magnetic satellite spin and spin-axis control has been extensively analysed in the literature for specific missions and as theoretical studies [1–6]. On nano- and microsatellites magnetic attitude control has been researched, or used for different applications, such as detumbling [7], Sun-pointing [8], nadir-pointing [9], alignment with the geomagnetic field [10] and spin-stabilisation [11]. Nanosatellites and picosatellites are often influenced by residual magnetic moments that reduce the ability to perform attitude control manoeuvres [12,13]. This problem has been analysed and a method for compensation has been developed previously [14]. Problems with a residual magnetic moment were also encountered on ESTCube-1. However, for ESTCube-1 the residual magnetic moment is similar in magnitude to the magnetic torquers and therefore it is not possible to compensate for it fully. Although attitude control using magnetic torquers on nanosatellites has a long history, to the best knowledge of the authors, inorbit performance of magnetic spin control for nanosatellites at high spin rates (in the order of 100°/s and more) has not been n Corresponding author at: University of Tartu, Institute of Physics, W. Ostwaldi 1-D601, 50411, Tartu, Estonia. E-mail address: [email protected] (H. Ehrpais).

http://dx.doi.org/10.1016/j.actaastro.2016.07.032 0094-5765/& 2016 IAA. Published by Elsevier Ltd. All rights reserved.

presented. In this paper, we present the flight results of the ESTCube-1 attitude control system (ACS) which was designed to achieve an angular velocity of 360°/s. The large angular velocity was needed for the centrifugal deployment of the tether to be used for the electric solar wind sail (E-sail) mission [15]. During preparations for tether deployment a significant residual magnetic moment was identified on the satellite that had a detrimental effect on attitude control capabilities and aligned the satellite with the Earth's magnetic field vector. This problem was approached by characterising the residual magnetic moment, developing a coil correction function that would alter the coil output to counter the disturbing moment and by modifying the original spin controller to allow spinning up the satellite around an arbitrary axis. Fortunately, the uncontrolled spin axis that is influenced by the inertia tensor and the residual magnetic moment was still perpendicular to the direction of tether deployment so it was not seen as a major issue. The strong residual magnetic moment of the satellite also made it impossible to perfectly realign the spin axis with the Earth's polar axis and maintain the alignment without continuously running the spin controller. Because it was not safe to actively control the satellite's attitude during the experiment, the spin axis alignment was not used while performing the spin-up for the tether deployment experiment. The spin controller was originally described in [16] and studied

H. Ehrpais et al. / Acta Astronautica 128 (2016) 210–216

Fig. 1. Illustration of the satellite's spin axes and tether deployment direction [20].

for ESTCube-1 in [17]. However, that research did not include such a severe case of internal magnetic disturbances. In addition to the disturbances further alterations had to be made to the controller to account for a new magnetic coil activation timing algorithm (described in [18]). Due to these changes and the updates to the satellite's inertia matrix the simulation results presented in [17] differ significantly from the in-orbit results. The ESTCube-1 ACS was capable of spinning up the satellite around an axis that runs across the cube between opposite edges (Fig. 1) to an angular velocity of 841°/s. Such a high speed was used in an attempt to loosen the reel locking mechanism by exerting larger centrifugal forces on it.

2. System design The ESTCube-1 ACS was designed with the aim to perform a controlled spin-up to high angular velocities that would provide enough centrifugal force to deploy an up to 10 m long tether. Tether deployment set a series of requirements for the attitude determination and control system (ADCS) of the satellite [17]. Initial requirements for tether deployment.

211

tether tension to reel out the first 3 m of tether. The 3 m of the tether were reinforced and was more likely to survive the vibrations during launch. For additional testing we also wanted to spin up the satellite to very high angular velocities. This is further described in Section 5. The ESTCube-1 ACS uses magnetic torquers as its only actuators. These are three flat magnetic coils with no core, each capable of producing a maximum magnetic moment of roughly 0.1 A m2. The three coils are placed on the insides of three orthogonal sidepanels of the satellite and are aligned with the satellite body axes. The coils were built in-house to comply with the requirements and structure of ESTCube-1 [19]. Each of the coils consumes up to 0.4 W of power. The electrical power system was originally designed to produce up to 2 W of power with its solar panels. This power is used to power the coils, the on-board computer and other electronics. Unfortunately, by the time the satellite was deemed ready for the experiment (16 months after launch) the power production had decreased to roughly 1 W [20]. This meant that the experiment could still be done, but it needed longer breaks to recharge the batteries. That waiting time was reduced by implementing subsystem sleep modes in the electrical power system software and therefore reducing the power consumption for the rest of the satellite [21]. The attitude determination system was designed to calculate the attitude at high spin rates, which meant that sensors had to be chosen according to how frequently it would be possible to obtain attitude. For this reason we chose sensors with high measurement rate to be used in the design. The satellite uses six sun sensors, two magnetometers and two gyroscopic sensors to calculate and predict attitude information. Originally the system had four gyroscopic sensors, but one of them failed in the early stages of the mission, which also rendered a second one inoperational due to a simplification in the design of the low-level measurement filter. The attitude determination accuracy for ESTCube-1 is better than the required 2° [18]. The magnetic field vector is separately provided by magnetometers which have an uncertainty of 3.2°. The uncertainty for the Sun sensors is 2.5° [19]. The uncertainty that was achieved by the gyroscopes after in-orbit calibration was approximately 0.5°/s [18]. All uncertainties are given as expanded uncertainties at approximate confidence level of 95%, coverage factor k¼ 2.


Spin up the satellite to at least 360°/s to provide enough centrifugal force for the deployment of 10 m of tether.


The satellite spin axis must be perpendicular to the tether de-




ployment direction. The axis precession must be kept as small as possible. The deviation of the spin axis must not exceed 10° at any time. This is required to avoid the tether rubbing against the satellite structure when it is reeled out. The tether deployment direction is illustrated in Fig. 1. Align the satellite spin axis with the Earth's polar axis with a pointing error of less than 3° to minimise the Lorentz force acting on a charged tether.

The requirement to align the spin axis was relaxed because of the electrical power needed to keep continuously aligning the spin axis and because it is not possible to control the spin axis during the experiment phase after tether deployment. It is still possible to measure the E-sail effect without inertial alignment, but the results need more thorough analysis for the verification of the force acting on the tether. The tether on ESTCube-1 was manufactured so that the first 3 m of the tether was less likely to break. Because of this the experiment plan was changed and a minimum of 115° angular velocity was set as a new requirement. This would provide enough

3. Spin controller The spin controller algorithm was mostly based on the well known Euler's equation of rigid body dynamics (Eq. (1)),

→ → Td = I·ω̇d + → ωS × (I·→ ωS )·kprecession

(1)

→ where Td is the desired output torque vector, I the 3  3 inertia → matrix, ω̇d the desired angular acceleration vector, → ωS the current angular velocity vector and kprecession the precession gain (not part of the original Euler's equation). The precession gain was added for testing purposes to enable or disable the precession component, but it could also be used for scaling. Scaling is necessary when a large angular acceleration demand saturates the actuators and the output signal is scaled down to the actuator limits. To avoid the precession component being scaled down to minute levels, kprecession should be set greater than 1. The desired angular acceleration for spin-up and realignment is calculated using Eq. (2). This equation was derived from the equation given in [16].

212

→ ω̇d = k realign·(→ ωdIS − → ωS ) + kspinup·(→ ωdS − → ωS )

H. Ehrpais et al. / Acta Astronautica 128 (2016) 210–216

(2)

→ where ω̇d is the desired angular acceleration vector, krealign the gain for sizing the realignment component, ωdIS the desired inertial angular velocity vector in the spacecraft reference frame, → ωS the current angular velocity vector, kspinup the gain for sizing the spinup component, → ωdS the desired angular velocity vector aligned with body spin axis. To accommodate spin-up and alignment for any arbitrary axes the nutation damping part was removed and the rest of the equation adjusted to take a more general form. In this equation there are two competing components: spin-up and realignment. Using the controller the spin-up should be completed in three steps: (1) spin the satellite up to some velocity (approx. 50°/s for ESTCube-1) to obtain a stable spin axis and avoid spinning up around the wrong body axis (k realign ≪ kspinup ). (2) perform inertial realignment without a considerable angular velocity increase (k realign > kspinup ). (3) continue spinning up towards the desired target while maintaining inertial alignment (k realign ≈ kspinup ). As the target and current angular velocity difference is initially rather large, the actuators would saturate if the direct controller output was provided as input. To avoid this a desaturation algorithm was added that would scale the required output down while correctly taking into account the desired output vector direction, zero coil offset (residual magnetic moment) and the coil output distortion. To prevent sensor measurement and coil activation overlap, a measurement cycle that would maximise coil activation time was developed. By running attitude determination and actuators at the same time the amount of power consumed during spin-up is reduced. This results from the reduced total time the controller and necessary subsystems need to be powered on [18]. While spinning up the satellite for the experiment, angular velocity measurements and magnetic field measurements were directly provided to the spin controller, because the Unscented Kalman filter became unreliable at high angular velocities. The spin-up for experiment is further described in Section 5. Several in-orbit tests were performed and the corresponding attitude and angular velocity logged and analysed. Results were used to validate the attitude determination and control system. This resulted in the discovery of a significant residual magnetic moment, which was similar in magnitude to the maximum output of one magnetic coil. The magnetic moment of the satellite keeps itself roughly aligned with the Earths magnetic field and therefore makes pointing and inertial alignment difficult. The uncontrolled behaviour of the satellite at low spin rates is shown in Fig. 2. It can be seen in the top plot that the angle between the satellite's residual magnetic moment and the Earth's magnetic field stays mostly within the 20–30° region with occasional peaks up to 40°. In the bottom plot it can be seen that the yaxis of the satellite always points across the Earth's magnetic field lines. The most likely sources for the residual magnetic moment are the ferromagnetic materials used in both the battery casing and the stack connectors. The estimated residual magnetic moT ment vector is ⎣⎡ −0.081 − 0.035 0.039⎦⎤ Am2 (total magnitude

0.096 Am2) (see Fig. 1). The residual magnetic moment was estimated using the engineering model of the satellite and some differences with the actual satellite in the direction of the vector are likely. Because of this, the residual magnetic moment was also calculated from the in-orbit magnetometer and gyroscope results. This method was based on a method described in the following paper [22]. The calculated residual magnetic moment from the orbit

measurements is ⎡⎣ −0.0986 − 0.0010 0.0953⎤⎦ Am2. These differences originate from a lack of electron emitters on the engineering model, slight differences in the materials used for rods and spacers between different printed circuit boards and the lack of side panel screws. The soft magnetic materials on-board the satellite can also be differently magnetised than the engineering model, because of different magnetic fields that have affected the hardware. In addition to creating a residual magnetic moment on the satellite, the ferromagnetic materials also had a significant effect on the output of the electromagnetic coils used for attitude control. In the controller software it was assumed that the outputs of the coils are aligned with their respective axes. However, according to laboratory measurements on the engineering model, the coils outputs were distorted. The major principal spin axis of the satellite was also different from the axis that was estimated from the inertia matrix. The uncontrolled spin axis was similar at high and low angular velocities, which means they were most likely caused by an incorrect estimation of the inertia matrix instead of only the residual magnetic moment. The inertia matrix was estimated before launch using the satellite mechanical design model. T

4. Corrective actions To remedy the problems mentioned in the previous section, additional calibration of the attitude control system was needed. This required further laboratory tests to estimate the residual magnetic moment of the satellite and the actual output vectors of the coils. Simulation data and telemetry data were compared and the simulation data was iteratively adjusted by changing the inertia matrix. This resulted in an inertia matrix that better explained the situation in orbit. For magnetic measurements one-axis Helmholtz coils, which were able to produce a magnetic field of 3 Gauss, were set up so that the engineering model of the satellite could be hung on a long string inside an anechoic chamber. This allowed the satellite to rotate around one axis inside the controlled external magnetic field. Completely unrestricted rotation was not achievable due to lack of equipment. Four measurements were performed for each axis—one with no magnetic coils active and one for each powered on coil. During each test the stable angle between the external magnetic field and the satellite reference frame was measured. These angles were combined into a linear equation system which provided the direction of the magnetic moment vector as its solution. This system is shown in Eq. (3), where x, y, z are the components of the magnetic moment vector, angles α , β , γ are the measured stable angles and M is the estimated magnitude of the magnetic moment vector. The magnitude of the vector was estimated from the angular acceleration of the satellite observed shortly after enabling the external magnetic field. This system was an overdetermined system and the results using different axes had a significant variance. Because of this, it is likely that there is some added uncertainty in these measurements because of the test setup. The results of the measurements are shown in Table 1. Significant differences can be seen between the positive and negative activations of the coils. This is due to the way the ferromagnetic materials present in the satellite distort magnetic fields with different polarities.

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213

60

Angle [deg]

50 40 30 20 10 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Magnetic Field [uT]

50 Total 25 Z−axis 0 Y−axis −25 X−axis −50

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Time [orbits] Fig. 2. ESTCube-1 unactuated behaviour at an angular velocity of 3°/s. Top plot shows the angle between the satellite's residual magnetic moment vector and the Earth's magnetic field. The bottom plot shows the Earth's magnetic field in the satellite's body axes.

Table 1 Actual coil output direction and magnitude. Unit coil output vectors are given in columns. The rows X, Y, Z give the components aligned with the respective satellite axis. The angle (Ang.) below the line is in degrees and magnitude (Mag.) in Am2. To obtain the total effect of a coil the respective coil output should be added to the zero offset given in the first column.

Table 2 Estimated inertia matrix. 0.001813 0.000024 0.000042

0.000024 0.001963 0.000029

0

þX

X

þY

Y

þZ

Z

X Y Z

 0.84  0.36 0.41

0.97 0.25  0.06

 0.93 0.35  0.09

 0.07 1.00  0.04

0.13  0.93  0.35

 0.01  0.01 1.00

 0.16 0.19  0.97

presented in Table 2.

Ang. Mag.

– 0.096

15.2 0.156

21.4 0.074

4.9 0.115

21.9 0.107

0.99 0.110

14.4 0.125

5. Spin controller performance

⎧ x/y = tan (α ) ⎪ ⎪ x/z = tan (β ) ⎨ ⎪ y /z = tan (γ ) ⎪ 2 ⎩ x + y2 + z2 = M 2

(3)

The initial inertia matrix was based on the computer-aided design model of the satellite. A different approach was needed as adding more details to the model did not produce the desired results. Some improvement was achieved by analysing the angular velocity of the satellite after removing the influence of the residual magnetic moment. The inertia matrix was iteratively changed to match the simulation results with in-orbit results. By analysing different datasets and stable angular velocities of the satellite over different orbits, we were able to find an inertia matrix, that was able to predict these stable angular velocities. However, with this method we are not able to estimate the magnitude of the matrix, because multiplying the inertia matrix with a constant would create similar equilibria. By analysing the torques acting on the satellite together with the residual magnetic moment, we were able to find the inertia matrix used on the satellite. This approach was further verified when the change in the inertia matrix improved our attitude determination results at higher angular velocities. The attitude determination process involves a step where the rotation of the satellite is propagated using torques calculated from Euler's equation of rigid body dynamics (see Eq. (1)). Because the resulting attitude quaternion from the attitude determination was smoother with the new matrix, then the torques resulting from the inertia matrix were a better match to the behaviour in orbit. The resulting matrix is

0.000042 0.000029 0.001796

While estimating the spin controller performance and also while performing the experiment, the satellite encountered problems with magnetometer measurement filtering. The filter was removed, which caused around 10% of the resulting magnetic vectors to be in an unknown direction. It was removed because at high angular velocities the magnetometer filter that was based on the difference between two consecutive measurements did not work properly. Also averaging was not useful because of the phase shift that would be created by taking measurement samples at different times. This measurement error affected both the controller performance and the data analysis of various spin control results. In order to estimate the performance of the spin controller after corrective actions, additional spin-up tests were performed with and without coil output correction. Tests were run with the target angular velocity set to 50°/s. By comparing the two plots in Fig. 3 one can see that with coil correction the satellite behaviour during spin-up is less variable. However, there is no significant difference in the angular acceleration of the satellite. This lack of difference can most likely be attributed to the differences between the engineering model that the coil output measurements were performed on and the satellite in orbit, because there was a noticeable difference when performing a static attitude comparison in the laboratory. Because of this difference, it is important to test the flight model of the satellite for magnetic influence instead of using an engineering model. The improvements to the inertia matrix and the attitude control software led to a reduction in the precession of the satellite while spinning up. Various improvements in the attitude determination and sensor filtering also helped the spin controller to perform better [17].

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Angular Velocity [deg/s]

Without Coil Correction 60

40

20

0

0

5

10

15

20

25

30

35

Angular Velocity [deg/s]

With Coil Correction 60

40

Test 1 Test 2 Test 3

20

0

0

5

10

15

20

25

30

35

Time [min] Fig. 3. Effect of coil correction on total angular velocity during spin-up. There are six separate tests shown, three with coil correction disabled and three with it enabled. The target angular velocity was set to 50°/s.

Although there is no significant difference in the angular acceleration of the satellite, the coil correction enabled us to perform limited inertial alignment with the Earth's polar axis. We were able to achieve inertial alignment, but once the controller was turned off the residual magnetic moment caused the alignment to deteriorate rapidly. At 50°/s we were unable to detect any inertial alignment when logging data on the next day. A higher spin rate would have increased the gyroscopic stability of the satellite, but the resulting perturbations of the spin plane would have posed a high risk for the experiment—should the tether rub against the metal edge of the side panel it may easily break. For this reason and because of the requirement not to control the satellite after deployment, inertial alignment was not considered to be a safe option for the ESTCube-1 tether deployment experiment. The results from an inertial alignment test are presented in Fig. 4. This was carried out at the desired angular velocity of 50°, which, according to simulations, was the optimal speed for realigning the spin axis in the inertial reference frame while maintaining spin stability in the satellite body reference frame. Actively performing alignment with the Earth's polar axis during an eclipse is not possible for ESTCube-1 as the attitude determination

system, relying heavily on accurate sun sensor readings, has an uncertainty an order of magnitude higher during an eclipse. The apparent noise in the resulting angular velocity is caused by a magnetometer filtering problem, because it caused an error in the attitude determination output. The magnetic field measurement issue also affected the attitude knowledge and magnetic field measurements that are input to the spin controller. Having been unable to deploy the tether because of a deployment hardware malfunction, an additional test was performed to try to dislodge the tether reel lock or the tether reel motor. The angular velocity of the satellite was increased to exert more centrifugal force on those objects. Because we had already achieved the one revolution per second requirement, the target angular velocity was set to three revolutions per second. During this test the spin axis was set in exactly the opposite direction. Fig. 5 describes the angular velocity changes during spin-up, which was performed in steps over a period of one month. Starting from an angular velocity of a few deg/s a maximum of 841°/s was reached. At higher velocities the performance of the controller declined, but an even higher spin rate could be achieved with a similar attitude control system by running the controller for a

Alignment Error [deg]

200 150 100 50

Angular Velocity [deg/s]

0

0

5

10

15

20

50

X−axis Y−axis

0

−50

25 Total Z−axis

0

5

10

15

20

25

Time [min] Fig. 4. Effect of inertial alignment. It is possible to see the angular error between the Earth's polar axis and satellite spin axis is declining while the controller is active.

H. Ehrpais et al. / Acta Astronautica 128 (2016) 210–216

215

1000 Total

800

Angular Velocity [deg/s]

600

X−axis

400 200 Y−axis

0 −200 −400 −600 −800

Z−axis 0

5

10

15

20

25

30

Controller Work Time [h] Fig. 5. Controller spin-up performance. Two missing logs indicated by dotted lines. Pauses for battery charging and other activities indicated by vertical lines. Average time per pause is 22.2 h.

longer time. The deterioration of the spin controller at higher angular velocities is mainly caused by the uncertainty of the measurement timing (5 ms), long coil activation time (80 ms) and the error from extrapolation to the next iteration of coil activation (100 ms). Because of our limited power production, the controller ran for approximately one orbit at a time before the batteries needed recharging for a day. Spin-up slows down because higher angular velocities also cause the satellite to slow down more between controller activations. Slowing down is caused by the increase in air drag and hysteresis of the ferromagnetic components that are also thought to have created the unwanted residual magnetic moment on-board the satellite [23].

6. Discussion and conclusions The ESTCube-1 attitude control system was designed to work at high angular velocities. Stable rotation around a specified axis was needed to generate a centrifugal force to safely deploy the tether. This paper presented the in-orbit characterisation of such an attitude control system. Electromagnetic coils were used for the attitude control of the satellite because of the necessity to achieve high angular velocities. Because of the ferromagnetic materials used on the satellite, the characterisation of the magnetic field was necessary to compensate for the influence of the ferromagnetic materials in the spin controller, coil outputs and also attitude determination. However it is strongly recommended that the estimation of any magnetic influences are performed before launch on the flight model of the satellite as the estimation based on the engineering model might not perform as well as expected. In addition, the uncontrolled behaviour of the satellite was observed and due to the mismatch with initial simulations, the inertia matrix was changed to match the behaviour of the satellite. The performance of the resulting spin controller is demonstrated by showing its ability to perform different attitude control manoeuvres. Aligning the satellite body axis with the Earth's polar axis is limited by the large residual magnetic moment of the satellite caused by ferromagnetic materials. Although inertial alignment was achieved, it rapidly deteriorates even at high angular velocities. This cannot be compensated for due to limitations in power production, and the magnetic moment of the magnetic coils relative to the residual magnetic moment. Because of this the spin-

up for the experiment was performed without aligning the satellite spin axis with the Earth's polar axis. An angular velocity record of 841°/s was achieved by spinning up the satellite in steps over a period of 20 days while trying to troubleshoot the tether deployment system.

Acknowledgements The authors would like to thank everybody who has contributed to the development of ESTCube-1 and its attitude determination and control system. The European Space Agency and the Estonian Ministry of Economic Affairs and Communications have supported ESTCube-1 via the European Space Agency's Plan for European Cooperating States (PECS) project “Technology demonstration for space debris mitigation and electric propulsion on ESTCube-1 student satellite”. Research by Andris Slavinskis was supported by the European Social Fund's Doctoral Studies, the Internationalization Program DoRa and Erasmus þ. The authors would also like to thank the AAUSAT-3 team for providing a simulation environment that the ESTCube-1 attitude control simulation environment was based on.

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