Mitigation of Wheel Friction Torque Instabilities Final Report · Wheel Friction Torque...

Wheel Friction Torque Instabilities

RockllvellCollins

Deutschland 15. Jan. 15

Part No.: 15279-138

Rev.:

Date:

Mitigation of

Final Report

Prepared by Checked by Approved by Authorized by

EMDr. M. Ehinger

Filename: 15279-138_-.Docx

SP IP. MeI'er

J/

Continued on page 2 to page 53

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54400-732Rev.B

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Wheel Friction Torque Instabilities Rev.: -

Final Report Date: 15. Jan. 15

2 54400-732 Rev. B

Change Record

Page /

Para. Rev.

Rev.

Date Change No. Type of Change

All - 15.01.15 EC-DE0016837 First Issue

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Distribution List

RCD Quantity

External Quantity

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Table of Contents

1 Scope ......................................................................................................................6

2 Documents ...............................................................................................................7 2.1 Reference documents .................................................................................................7 2.2 Applicable documents ................................................................................................7 2.3 Abbreviations ............................................................................................................7

3 Study objectives and background ................................................................................8 3.1 Importance of torque stability .....................................................................................8 3.2 Experience in torque variations ...................................................................................8 3.3 Study logic and teaming .............................................................................................8

4 On ground test ........................................................................................................ 10 4.1 On ground test set-up .............................................................................................. 10 4.2 Wheel selection for on ground test ............................................................................. 12 4.3 On ground test evaluation ........................................................................................ 13 4.4 On ground test results ............................................................................................. 13 4.4.1 Time signals of the torque variations .................................................................... 13 4.4.2 Standard deviations of mean friction torque .......................................................... 16 4.4.3 Fluctuations ...................................................................................................... 18 4.4.4 Deviations of mean friction torque (spikes) ........................................................... 18 4.5 Extraction of data for the physical model .................................................................... 20

5 In orbit data analysis ............................................................................................... 22 5.1 In-orbit data exploitation process .............................................................................. 22 5.2 Statistical results ..................................................................................................... 23

6 Statistical model of friction torque instabilities............................................................. 27 6.1 Typical values / worst case values ............................................................................. 27 6.2 Detailed models of the distribution ............................................................................ 27 6.3 Matlab model .......................................................................................................... 31

7 Synthesis ............................................................................................................... 32

8 Assessment of impact at AOCS level .......................................................................... 33 8.1 Simulation and results ............................................................................................. 33 8.1.1 Worst case ........................................................................................................ 34 8.1.2 Statistical .......................................................................................................... 35

9 Synthesis & Recommendations .................................................................................. 37

10 Way of improvements .............................................................................................. 38 10.1 AOCS/System level ............................................................................................. 38 10.1.1 Rejection at AOCS level .................................................................................... 38 10.2 Wheel speed control ............................................................................................ 43 10.3 Consequences on RW .......................................................................................... 46 10.3.1 AOCS rejection ................................................................................................ 46 10.3.2 Wheel speed loop ............................................................................................. 46

11 Improvements on reaction wheel level ....................................................................... 49 11.1 Wheel internal speed control loop ......................................................................... 49 11.2 Decrease of wheel reaction time ........................................................................... 50 11.2.1 TACHO signal accuracy ..................................................................................... 50

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11.2.2 Response time to Torque command changes ....................................................... 51 11.3 Improvements at ball bearing unit level ................................................................. 52

12 Conclusion .............................................................................................................. 53

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1 Scope

Loss torque variations are a feature of all reaction or momentum wheels based on ball bearing

technology. Earth observation and science missions require more and more stringent stability

performances, for which the performance of the reaction wheels become the drivers.

It is important to note, that only fully operative wheels with perfect function have been ana-

lysed. The goal of the study was to identify remaining loss torque variations and to identify the

most promising way forward to improve the satellite pointing stability for future missions to

come, where extremely demanding pointing requirements are expected.

For satellites with very high pointing accuracy requirements it is essential to be able to verify

the attitude orbital control system performance by simulation on ground. Therefore a detailed

knowledge of the friction torque instabilities and a simulation model is necessary.

The scope of the ESA TRP program ‘Mitigation of wheel friction torque instabilities’ is twofold:

the measurement of those instabilities on-ground with high temporal resolution and in-orbit

using existing satellite telemetry, evaluation of this data and extraction of a model, which can

be used for satellite simulations and to propose possible ways to reduce these disturbances at

wheel level, AOCS subsystem level and system level.

The following document describes the test activities at Rockwell Collins Deutschland GmbH on

reaction wheel level, the satellite data extraction and data analysis from Airbus Defence &

Space SAS, the results of the analysis of the observed loss torque variations and summarizes

the proposed ways of improvement to reach a better pointing accuracy on satellite level.

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2 Documents

2.1 Reference documents

Document number Document title

15279-061 Test plan and test procedure for ESA TRP friction torque instabilities

15279-067 Test report about friction torque instabilities of RSI 12-75/604, SN 0034



15279-074 Test report about friction torque instabilities of RDR 57-0, SN 6117

15279-088 Torque instability characterization report

Astrium contribution to RCD proposal “Mitigation of Wheel Friction

Torque Instabilities” APB32.PC.DE.723725.12

Processing of in-orbit data from RCD reaction wheels

GNC_T.IOR.776003.ASTR – issue 02/00

Pointing stability analysis considering Euclid mission

GNC_F.TCN.777341.ASTR – issue 01/00

Improvement solutions - AOCS and system level

GNC_T. TCN.779041.ASTR – issue 01/01

Astrium contribution to the final report

GNC_T.TCN.779959.ASTR – v1.0 – Jan. 5th, 2015

2.2 Applicable documents

Document number Document title

ESTEC ITT AO/1-

7337/12/NL/MH

Appendix 1 of the contract, Statement of Work

2.3 Abbreviations

BBU Ball bearing unit

FA Fertigungsanweisung

FWHM Full width at half maximum

FM Flight model

GSEOS Ground support equipment operating system

MRB Material review board

MW Momentum wheel

PCB Printed circuit board

TOCO Torque command

UWI Universal wheel interface

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3 Study objectives and background

3.1 Importance of torque stability

The topic of friction torque instabilities is known since many years and has been observed dur-

ing ground tests before launch but also spacecraft operators sporadically report about AOCS

disturbances which can be put back to the wheel in-orbit performance. In most cases these

unwanted disturbances are considered as negligible and are compensated by the AOCS control

system with no impact to the overall spacecraft performance. However, in particular for obser-

vation missions, pointing stability becomes critical.

3.2 Experience in torque variations

Although the study is called “Mitigation of wheel friction torque instabilities”, it is more ade-

quate to talk about friction torque variations. For this study only fully functional wheels have

been taken into account. The observed friction variations are due to multibody interactions of

the different balls, their position inside the retainer pockets, the exact position of the retainer

(guided by the bord or only guided by the balls) and the distribution of the oil inside the bear-

ing unit.

As a result friction torque variations are globally considered as a complex phenomenon with the

following characteristics:

• Torque variations are wheel design specific with respect to frequency of occurrence and

waveforms of rising and falling slopes and of plateaus

• Torque variations are the result of many interacting, dynamic parameters

• Torque variations depend on the load levels the wheel was exposed to especially during

launch.

• Torque variations are difficult to measure as their occurrence and their characteristic are

of random nature and may change during wheel life.

Prior to this study there was no statistical description of friction torque variations available. If

only considering this selected point, there was a great need for this info to support the design

of future missions.

3.3 Study logic and teaming

The study is separated into three main work package.

1. Characterize in-orbit and on-ground friction instabilities.

In the first package, friction variations of reaction wheels are measured on ground with

high temporal resolution and with about 1mNm sensitivity. The wheels to be character-

ized had been selected to cover the different stages of a wheel life: brand new (includ-

ing FM vibration campaign) and after about 10 years of operation.

In parallel in orbit data was evaluated using the housekeeping data of about 34 wheels

(selected for due to known variations out of a satellite fleet carrying about 100 wheels).

This selection ratio is supported by Rockwell Collins Deutschland GmbH production ex-

perience, that about 25% of the wheels show a slightly higher friction variation.

Out of those evaluations a statistical model of the friction variations was developed.

It is important to note that due to the on-ground test with high temporal resolution the

complete range of variations (0.1 second to several hours) could be covered.

2. Characterize the impact of the wheel friction torque instabilities on the point-

ing stability.

As an example the effect of the wheel friction torque instabilities has been simulated us-

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ing the existing simulation for the demanding satellite mission EUCLID. Since this is a

satellite design optimized for stability the simulation was extended with general stability

considerations which are valid for typical satellites also

3. Propose possible solutions to reduced friction instabilities on wheel level or

improve the pointing stability and assess the impact on the pointing stability.

The variety of topics covered by this study directly implied, that it can only be handled in a

consistent way if a satellite manufacturer and a wheel manufacturer team to combine the spe-

cific knowledge.

The study was conducted by Rockwell Collins Deutschland GmbH and Airbus Defence & Space

SAS, both world leading manufacturers for reaction wheels (TELDIX® Space Wheels) respec-

tively satellites.

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4 On ground test

4.1 On ground test set-up

For completeness of the characterisation report, the test setup and its limitation are described

briefly. By the purpose of the research contract, the investigation has focused on torque varia-

tions with a duration of 0.1 sec to 10 seconds with the aim to characterise the slew rate and

height distribution and timespan between events. High temporal resolution of the reaction

torque measurement was required.

To evaluate this information, an internal test equipment of RCD, which is used to evaluate the

bearing quality during bearing production with a high resolution torque sensor, is slightly modi-

fied to allow the measurement of completely closed wheels. The baseline test equipment (RCD-

IP) is measuring the torque of a single bearing unit, which is mounted on a static air bearing to

minimise the influence of the test set-up to the torque sensor.

Reaction wheel

Wheel adapter plate

Air bearing adapter flange

Air bearing

Connecting shaft

Metal bellow coupling

Torque sensor

Torque sensor mounting flange

Baseplate

z

Figure 1 Fundamental mechanical setup.

When the wheel is mounted on the test rig with its additional degree of freedom (rotation

around the z-axis), this is altering the performance by introducing an additional resonance,

which had to be taken into account during data evaluation. Also the effect of the cabling and

moment of inertia, the test rig has been undergone functional tests to evaluate performance

parameters, resonance frequencies and the resolution has been adapted to this result.

The electrical setup containing all signal wiring is shown in the next figure.

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The additional features for this measurement campaign are the torque sensor of the test rig,

which was evaluated with a sampling rate of 200Hz and a reaction torque resolution of

0,1 mNm.

Figure 2 Electrical setup

The usual setup to operate a wheel with the standard Rockwell Collins ground support equip-

ment, the Universal Wheel Interface (UWI) is shown in the center. The wheel with the wheel

with power connector X1 and wheel control connector X2 is connected to the universal wheel

interface UWI. The wheel is powered by an external power supply connected also to the UWI.

As a further addition the speed signal TACHO of the wheel control connector X2 is routed to the

National Instruments Timer/Counter card NI 6608 by means of a plug adapter. This was used

for verifying the performance of the torque sensor within the test setup only. Furthermore the

ambient temperature is monitored by an iButton 1-wire temperature sensor that is also hooked

up to the UWI. The torque sensor DH-15 is controlled by an USB sensor interface, which direct-

ly connects to the Control PC. This PC also controls the UWI via RS-232 connection and the

National Instruments data acquisition rack PXI 1033 by a PCX-Express interface card.

With this setup, all measurement requirements could be fulfilled. The test setup showed high

sensitivity to thermal environment conditions, which prevents the operation at extended tem-

peratures.

The tacho signal evaluation with the NI 6608 can be used to evaluate the wheel speed with

10Hz resolution and as a result of this investigation, this resolution is sufficient to measure the

relevant torque variations of a Rockwell Collins TELDIX® reaction wheel. This allows for further

investigations over temperature in a modified test setup.

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4.2 Wheel selection for on ground test

In the scope of the ESA TRP project a total of four momentum wheel assemblies from life test

are selected for the measurements. The first pair of similar wheels is equipped with a short

bearing unit and the second pair with long ones.

Figure 3 Short and long bearing unit.

Both types of bearing units were selected as typical assemblies in TELDIX® wheels which are

integrated in satellites of relevant projects. The shorter distance between the upper bearing

and the baseplate of the bearing unit is the main difference between both bearing units which

might influence the friction torque instabilities. The wheels where selected from life test in dif-

ferent stages to provide a first insight into different stages of the wheel life.

The tested wheels are the following ones:

Momentum wheel Serial

number Part number Mass BBU type

Vibration

tested

Life test

duration

Life

test

RSI 12-75/604 SN 0034 69662-001 4,9 kg “short” yes 13,0 years ZC1

RSI 12-75/601 SN 0033 68303-001 4,9 kg “short” yes 13,3 years ZC2

RSI 25-75/60 SN 9004 72370-002 6,8 kg “long” yes 0,0 years -

RSI 25-75/60 SN 0001 72370-001 6,8 kg “long” - - -

RDR 57-0 SN 6117 68683-001 7,6 kg “long” yes 11,9 years CS

ZC1: zero crossing 2x ±600rpm/24h; ZC2: zero crossing 8x ±4500rpm/24h

CS: constant speed 5100 rpm

Table 1 Tested wheels

The wheel with SN 0001 has been selected at the start of the project as a wheel almost identi-

cal with SN 9004. Because this wheel has not been available within the schedule of this project,

it has been replaced by the RDR 57-0. This life test wheel has been available at once and has

the same type of bearing unit as the replaced wheel. Due to the relevant difference concerning

the moment of inertia, significant deviations regarding the eigenfrequency of the test set-up

occurred. In consequence, the maximum wheel speed during the measurements was limited to

approx. 5350 rpm.

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The detailed histories of the wheels are described in the Rockwell Collins test reports about the

friction torque instabilities (see Table 2).

Momentum wheel Serial number Document number of test report

RSI 12-75/604 SN 0034 15279-067

RSI 12-75/601 SN 0033 15279-071

RSI 25-75/60 SN 9004 15279-070

RDR 57-0 SN 6117 15279-074

Table 2 Detailed test reports about friction instabilities of the tested wheels

4.3 On ground test evaluation

During reviewing of the measurement data, three classes of torque variations became visible.

Clearly visible was a noise band around the mean value. In the same order of magnitude, fluc-

tuations in the mean value on a much lower time scale became visible. During first data analy-

sis experiments the small fluctuations could be identified in friction histograms as two overlap-

ping normal distributions. Another feature could be observed, which are clear spikes with a

maximum duration of 10 seconds. These three types of fluctuations should be modelled to sim-

ulate the behaviour of the bearing units.

The three components of torque variations are characterised:

- Statistical variations characterised by the FWHM of a best fitting normal distribution

- Variations between two main values characterised by the difference of the mean values

of the respective normal distribution, the mean slopes and plateau duration.

- Spikes, which means any structure in the loss torque signal observed with a duration of

below 10 seconds and a level > 2 mNm above the mean torque level will be called

torque spike and will be characterised by its height, rising slope (10% to 90% of height

divided by duration), plateau duration (90% to 110%) and decay slope (90% to 10% of

height divided by duration) and timestamp of start slope (10% value) and end of decay

slope (10% value).

4.4 On ground test results

As a general statement after reviewing the measurement data, the occurrence of friction torque

instabilities did not occur very often during the test campaign even though the test campaign

lasted approx. 10 days for each wheel.

The only exception was the wheel RDR 57-0, SN 6117. It was tested as a substitute for a fourth

RSI 12-75 wheel which was not available with respect to the program schedule. This wheel with

different moment of inertia required a modification of the data analysis by an exceeding of the

damping frequency range and different wheel speeds for data acquisition. Nevertheless, this

wheel showed a quite noisy friction torque with thousands of spikes at several test speeds.

4.4.1 Time signals of the torque variations

The following diagrams show examples of the torque variations during measurements at con-

stant 500 rpm (1100 rpm for RDR 57-0) over a time span of 1000 seconds (16 minutes). The

torque variations result from the subtraction of the friction torque mean value from the meas-

ured torque signal.

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Figure 4 Friction torque variations of RSI 12-75/604 SN 0034 at 500 rpm


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Figure 7 Friction torque variations of RDR 57-0 SN 6117 at 1100 rpm

All single peaks, indicated by the colored points in fig. 4 to fig. 7 were selected automatically by

data analysis as described in the test reports (see Table 2), section 10.

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A typical spike and the relevant points for spike analysis are shown in the following diagram.

Figure 8 Single peaks of RSI 12-75/604 SN0034 at 500 rpm

The differences in the amount of friction torque and the delay time between the occurrences of

these points were used for calculations like torque change rate or peak duration.

4.4.2 Standard deviations of mean friction torque

A mean friction torque was determined individually for each tested wheel speed of each wheel.

Based on this mean value, standard deviations of the measurements were calculated. These

deviations are shown in the following diagrams.

Figure 9 Friction torque standard deviations of tested wheel SN 0034

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The standard deviations of the three RSI wheels are very similar, amount to less than

0,52 mNm and occur below 2000 rpm whereas the RDR 57-0 shows significant increased val-

ues up to 3000 rpm. As a first assessment – after reviewing the history of the wheels - this

results most probably from the higher loads during vibrations which are generated by the ap-

plied vibration profile and the higher mass of the rotating parts of this wheel. These increased

loads can generate a small flattening or even imprint in the range of a few to hundreds of na-

nometers (inside the tolerance given by the life time requirement) in the surface of the bearing

rings and balls which result in an increased wheel noise.

4.4.3 Fluctuations

Only one of the tested wheels showed relevant friction torque fluctuations at the single speed

of 4200 rpm ccw with a mean duration of approx. 40 seconds. A systematic analysis is impos-

sible due to missing occurrence. The typical size of those fluctuations is around 0.7 mNm to 1

mNm. The slope is very small and hard to evaluate, because it is obscured by the normal dis-

tributed noise of the wheel. The root cause of those fluctuations is most probably the cage

movement of the bearing unit. The cage movement is influenced by the amount of oil available

at the cage land.

4.4.4 Deviations of mean friction torque (spikes)

Again the observation can be split in to two classes, where the first class with three wheels

(beside the RDR 57-0) is represented by wheel RSI 25-75/60 SN 9004.

The tested wheel did not show relevant fluctuations during the test campaigns at all. The only

deviations from the mean friction torque were spikes with an average increase between

2.2 mNm and 2.9 mNm.

As shown in the tables of the test reports of each wheel, the total number of torque instabilities

during the complete test campaign was less than 64 for the three RSI wheels. The duration

amounted to less than 10 seconds and the maximum torque change rate amounted to 2,33

mNm/s. The RSI 25-75/60, SN 9004 has had most of spikes. Beside this test campaign, the

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maximum observed value was about 4.5mNm. The typical behavior is a variation toward higher

friction. In rare cases, when a high amount of oil is available, spikes to lower friction also have

been observed, but in this case maximum value was about 3 mNm.

Figure 13 Torque spikes of RSI, SN 9004 during the complete test campaign

Once again the RDR 57-0 showed a complete different behavior. The average torque increase

amounted to approx. 2.3 mNm as well. Nevertheless, the occurrence of these spikes was much

more often than measured with the RSI wheels: several thousand of this spikes occurred dur-

ing the test campaign but with a complete different characteristic. The torque change rate did

not exceed 0,37 mNm/s and the duration was less than 2.1 seconds (see Figure 14).

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Figure 14 Torque spikes of RDR 57-0 during the complete test campaign

The different characteristics of the torque spikes might result from the higher noise level of the

wheel. Due to the remaining probability to have peaks higher than 2mNm for this wheel (about

2 sigma of distribution) and the fixed recognition limit of 2 mNm the observed peak structure

could result.

Because no data were available until this document was released, neither analysis nor compari-

son has been possible yet.

4.5 Extraction of data for the physical model

The measurements with four tested wheels on ground were performed with a special test set-

up. The recorded torque measurements have been analysed. The main kinds of instabilities

which have been detected are

- friction noise

- spikes shorter than 10 seconds.

The friction noise shown by the smaller RSI 12-75 wheels has been very similar. The standard

deviation did not exceed 0,52 mNm for these wheels. The wheel RDR 57-0 with the highest

bearing loads due to vibration showed standard deviations up to 0,92 mNm.

The occurrence of torque spikes was quite rare for the RSI wheels. During approx. 10 days of

operation only less than 64 spikes occurred. Mean reaction torque deviations during these

spikes amounted to approx. 2,3 mNm with durations less than 8,3 seconds.

The RDR 57-0 showed several thousands of torque spikes during the measurement campaign.

Nevertheless, these spikes had a lower torque change rate and much shorter durations and are

probably due to an not adopted detection limit compared to the noise level.

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The binary raw data acquired during the measurements of all four wheels were delivered to

ESA on 13th March 2014 in combination with the required MATLAB© scripts for further data

analysis.

It is chosen to use the parameters of RSI 25-75/60 SN 9004 as representative for the first

model generation.

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5 In orbit data analysis

The processing of wheel in-orbit data aims at providing complementary results to ground test

by analyzing the reaction wheel behavior in operational conditions and over larger time scales.

Telemetry from 34 wheels has been gathered from several platforms for which Airbus DS can

access to in orbit data, covering a period from 2004 to 2013.

It is important to emphasize that friction instabilities are not necessarily failures or abnormal

wheel behavior. Wheels showing friction “peaks” are operating nominally, even after several

years. Furthermore, the occurrence statistic is biased in this study, since all wheels have been

selected to maximize the chance to find (and characterize) friction instabilities.

5.1 In-orbit data exploitation process

Focusing on torque variations appearing as sudden increases, the problem is simply to detect a

step within the signal. The idea is then to use the Haar wavelet transform, since very well

adapted to solve this problem. Applying this Haar wavelet transform to the torque signal will

directly allow identifying the rising and falling edges of the torque jumps.

Figure 15 Step detection using the Haar transform

The global processing is detailed in following table, listing all steps leading to a full characteri-

zation of all friction torque instabilities to be found in the in-orbit data set.

2.844 2.846 2.848 2.85 2.852 2.854 2.856 2.858

x 105

10

11

12

13

14

15

sample

Torq

ue (

mN

m)

Detection

Raw signal

2.844 2.846 2.848 2.85 2.852 2.854 2.856 2.858

x 105

-1

-0.5

0

0.5

sample

Haar Transform

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Step Purpose / Description

0: Decimation Increase the efficiency of the Haar transform based detection: friction

torque increases spread over more than 1 sample is better detected

1: Detection Compute the Haar transform and compare to detection threshold

(equivalent to detection of torque step of ± 0.5 mNm)

2: Cleaning Remove manoeuver phases (by checking wheel speed variations) and

missing TM areas (these induce discontinuous torque estimations and

are detected by a checking of the data timestamp)

3: Characterization Extraction of parameters (amplitude, duration, etc…) for the different

types of phenomena

Table 3 Detailed processing

5.2 Statistical results

All the processed telemetries are put together to provide the richest possible statistic. In the

end, different statistics are provided for three types of detections:

- Plateaus, give the most reduced statistics. This data corresponds to a full detection of a fric-

tion torque increase and decrease, allowing identification of duration.

- Spikes, corresponding to single events not related to a change of friction level (same level

before and after the spike). Such a spike can be considered as a plateau with duration shorter

than the telemetry sampling.

- Edges, that are basically torque level changes that may lead to a plateau that the processing

failed to identify correctly, or to a plateau extraction. In the end, the plateau data is contained

within the edge results, as depicted in following figure.

Figure 16 Schematics of the extracted statistics

Spikes

?

Edges

Plateaus

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For all detected plateaus (rising edge followed by a falling one before a maneuver occurs) the

distribution of duration is be provided. Following bar-charts show (as all following figures) the

distribution among the detected plateaus, expressed as probability density estimation.

Figure 17 Plateau friction torque increase

The next data is the duration of the plateau (to be understood as the time elapsed between the

rising edge of the torque increase and the falling edge back to a lower level of friction) and the

repetition (understood as delay between two events).

Figure 18 Plateau duration

Figure 19 Repetition statistics

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

1

2

3

4x 10

-4

Plateau duration (s)

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 104

0

0.5

1

1.5

2

2.5

3

3.5

4x 10

-5

Plateau repetition (s)

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0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

Plateau level (mNm)

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25 54400-732 Rev. B

Here a distortion is induced by the precision of the plateau detection. Between two plateaus,

several single spikes may have occurred. From these plots, it appears that a typical duration

between two consecutive plateaus is around 1h.

Similar results are obtained for spikes and edges, allowing to outline a statistical model for all

kind of events (see next chapter).

While the previous figures outlined statistical distribution of wheel friction torque plateaus time

proprieties, the next plot are intended to explore potential links between the plateau occur-

rences and environment evolution (mainly wheel bearing temperature, wheel speed).

On next figure, the distribution of detected torque jumps over wheel temperature (red bars),

and the distribution of the global telemetry samples over wheel temperature (blue line) are

displayed. This will help the interpretation of the results, since the wheel temperatures are not

uniformly distributed over the samples. For each temperature range, the comparison between

the global amount of sample (blue “global” line) and the number of detections (red bars) can

provide information about sensitivity to environment.

Figure 20 Distribution of wheel temperature (all TM / plateau detections)

On this figure, the area around 23°C shows the most plateau detections (red bars), while the

global number of samples (blue line) in this range of temperature is not significantly higher

than around 10°C. Indeed, on the opposite, the range below 10°C and above 30°C represent a

rather important probability density of the global samples, while the peak detection is almost

void on this area.

The next source of influence could of course be the wheel speed. With different speeds, differ-

ent lubrication equilibriums can establish, and thus the wheel friction may show more instability

on specific speed ranges.

-10 0 10 20 30 40 500

0.02

0.04

0.06

0.08

0.1

0.12

Wheel temperature (°C)

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Torque jumps

Global

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26 54400-732 Rev. B

Figure 21 Distribution of wheel speed (all TM / plateau detections)

From previous figure it appears difficult to express a clear relation between wheel speed and

number of friction torque jumps detected.

As a result, following synthesis can be drawn on the plateau statistics:

- The time data (repetition and duration) should be handled with care. In particular, only short

duration should be considered as valid results, knowing that there are potentially biases intro-

duced by false detections or missing edges.

- The torque increase level is valid, and does not call for any precaution

- The resulting statistic may be a little poor, since plenty of single edges and spikes are dis-

carded during this “plateau” processing.

- No clear relation between wheel speed and occurrences of wheel friction torque instabilities is

identified.

- A slight influence of temperature seems to appear, in line with experience from RCD that

higher oil viscosity (= lower temperatures) may limit occurrences of wheel friction torque in-

stabilities.

-600 -400 -200 0 200 400 6000

1

2

3

4

5

6

7x 10

-3

Wheel speed (rad/s)

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Torque jumps

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6 Statistical model of friction torque instabilities

After having presented all detailed statistical curves, a mathematical model should be set up, in

order to be able to inject all this data in predesign or development activities.

6.1 Typical values / worst case values

The first extraction will be rather simple, and propose “typical values” to consider in order to

establish rough order of magnitude or first order sensitivities. Here no specific model is consid-

ered, only a purely deterministic approach, that can be used for analytical budgets

Characteristics Plateau Edges Spikes

Duration 1200 s N/A N/A

Level of torque increase 0.6 mNm 0.7 mNm 0.7 mNm

Repetition 1 h 300 s 200 s

Table 4 Typical values

To complete the previous data set, worst-case values should also be provided, allowing as-

sessing the design robustness to some higher instability. Without any hypothesis on the distri-

bution, a 99% value is given for each parameter. On time characteristics, the expression of a

worst-case may be a bit different; since it is not obvious whether a short duration or a long

duration (same for repetition) is the most detrimental to the mission performance. Thus, two

values are given (minimum and maximum time).

99% values Plateau Edges Spikes

Level of torque

increase 2.40 mNm 2.06 mNm 2.93 mNm

Duration

(mini./maxi.)

300 s

> 10 000 s N/A N/A

Repetition

(mini./maxi.)

2200 s

> 10 000 s

200 s

> 10 000 s

200 s

> 10 000 s

Table 5 Worst-case values (99%)

6.2 Detailed models of the distribution

Friction variation level

Looking at the shape of torque level distribution, with a more detailed sampling, it appears that

the statistics is related to a Gamma distribution, with a decreasing occurrence rather than a

straight evolution (like for an exponential distribution) close to 0 mNm.

For the sake of simplifying the implementation in a further simulation model, the goal is to fit

an Erlang distribution, a special case of Gamma distribution with integer shape parameter.

Such a probability distribution is expressed using the Gamma function:

𝑓(𝑥, 𝑘, 𝜆) =𝜆𝑘 . 𝑥𝑘−1𝑒−𝜆𝑥

Γ(𝑘)

with k the shape parameter being an

integer and λ being the rate parameter.

For both kind of models (Exponential and Erlang) a set of 100 000 samples is generated, to

compare the resulting distributions to in-orbit data distribution

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Figure 22 Fitting of the distributions

The Erlang distribution is perfectly fitting the in orbit data, although bringing some slight over-

representation of lower level events. Here a shape parameter k=2 is chosen, with a rate pa-

rameter λ = 4.8. Thus, the random variables can be generated with two independent uniform

random variables (Ui). The additional bias of 0.63 reflects the fact that the natural Erlang dis-

tribution starts from 0, what is not the case in our case.

𝑇𝑞𝑙𝑒𝑣𝑒𝑙(𝑠𝑝𝑖𝑘𝑒𝑠) → 0.63 −1

4.8𝑙𝑛(𝑈1. 𝑈2)

with Ui uniform distributed random variables.

If focusing on edge detections, the same model fitting can be proposed. It appears that the

exponential model is the best model to be used. Besides, as handling rising and falling edges,

two separate but symmetrical distributions are at stake.

𝑇𝑞𝑙𝑒𝑣𝑒𝑙(𝑒𝑑𝑔𝑒𝑠) → {0.5 −

1

3𝑙𝑛(𝑈1)

−0.5 +1

3𝑙𝑛(𝑈2)


The same distribution also applies for plateaus since the statistics on edges includes the plat-

eaus.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Spike level (mNm)

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In orbit data

Exp. = 2

Erlang = 4.8 k=2

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Figure 23 Plateau level distribution

Instability repetition

Here due to low sampling rate of the data and further processing, the lowest time bin is around

100 s, while the peak noticed for spikes is located around 300 s to 400 s. Under these circum-

stances, the modeling of the distribution is less precise, since focused on the first bins. As pre-

viously presented, the time statistics are limited to repetition shorter than 10 000 s. An expo-

nential distribution can be proposed as an approximation since some single peaks (like for in-

stance around 2000 s are not covered with such a model.

Figure 24 Repetition of wheel friction torque spikes

The distribution of the edge repetition is rather close to the distribution of spike repetition. The

plateau repetition statistics is left aside, since the statistic seems too reduced, and too much

influenced by external elements (disturbed detection, maneuvers, etc…) to be significant. The

edge statistics should be used as a basis to model the plateau repetition.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

Plateau level (mNm)

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In orbit data

Exp. = 3

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

1

2

3

4

5

6

7

8x 10

-4

Spike repetition (s)

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In orbit data

Exp. = 0.0008

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30 54400-732 Rev. B

Plateau duration

The duration of detected plateau phases is the most uncertain parameter. As previously men-

tioned, various issues arise: wrong detections (missing of the plateau end for instance) but also

anticipated end due to a maneuver, etc… Nevertheless, in addition to the typical duration of

1200 s announced, a distribution is proposed in order to prove an envelope of the behaviour.

Figure 25 Plateau duration distribution

The Erlang distribution is selected, once again because it appears as the best compromise be-

tween fitting and possibility to generate variables easily in further steps of the study.

𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 → 600 −1

0.002𝑙𝑛(𝑈1. 𝑈2)


The different models introduced in previous sections are reported in following table. All the lev-

els are expressed as milli-Newton-meter and time values in seconds

Level (mNm) Repetition (s) Duration (s)

Spike 0.63 −

1

4.8𝑙𝑛(𝑈1. 𝑈2) 125 −

1

0.0008𝑙𝑛(𝑈1) N/A

Edge

{0.5 −

1

3𝑙𝑛(𝑈1)

−0.5 +1

3𝑙𝑛(𝑈2)

125 −1

0.0008𝑙𝑛(𝑈1) N/A

Plateau 0.5 −

1

3𝑙𝑛(𝑈1) N/A 600 −

1

0.002𝑙𝑛(𝑈1. 𝑈2)

Table 6 Synthesis of the distributions

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1x 10

-3

Plateau duration (s)

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In orbit data

Erlang k = 2 - = 0.002

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6.3 Matlab model

The previously introduced mathematical description is to be transferred into a Matlab-Simulink

model that can be used in further steps of the study. The principle of modeling the friction

torque instabilities relies on two steps:

- generate an instability (spike or plateau), along with time data (repetition, duration)

- wait for the needed time (repetition, duration) and generate a new event

Figure 26 Modeling spike events

To generate the random values during the simulation, the approximation of Erlang and expo-

nential distributions provided in synthesis of the distributions

are directly implemented in the Simulink model. As soon the time since previous event is

elapsed, a new one is generated by the re-activation of the “SPIKE_GENERATION” block.

The torque instability generated by this model is only a single square impulse. Nevertheless,

any convenient shape could be implemented, like for instance the shape characterized during

RCD ground tests (friction evolution according to a specific slope).

The model is then used to simulate wheel friction torque instabilities, and then the same pro-

cessing than for the in orbit data is used to check the statistics. Unlike for orbit data, the simu-

lation is sampled at 10 s, and no decimation is used in the post-processing. Purpose of chang-

ing the sampling rate with respect to in orbit data is also to confirm that the model of repetition

and its distribution are well defined and independent from sampling rate. This eventually vali-

dates the correct behavior of the simulation model.

Figure 27 Comparing model and in orbit data - spike level and repetition

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Spike level (mNm)

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In orbit data

Simulation

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

1

2

3

4

5

6

7

8x 10

-4

Spike repetition (s)

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In orbit data

Simulation

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7 Synthesis

Among the 34 wheels considered, a fair amount of friction torque instabilities could be detect-

ed: plateaus, edges or single spikes. This has allowed drawing some trends, with statistical

models that are well correlated between simulation and orbit data.

A correlation with wheel temperature and wheel speed could not clearly be outlined, and would

be difficult to justify since all wheels are not operating in the same conditions. It could be of

interest to investigate the root cause of the differences displayed (intrinsic behavior of one spe-

cific wheel, specific operations, etc…).

Although models are proposed, it should be kept in mind that these are only reflecting in-orbit

data distorted by a specific processing. Due to the complexity of the processing, various exter-

nal influences like signal noise, consequences of a threshold on the detection, have a direct

impact on the results that could not clearly be assessed. This point is obviously to be consoli-

dated in order to improve the confidence put in the models. In the same way, the correlation

between the ground test results and the in-orbit data may help to do so.

The last point to recall is the global question of probability of “friction torque instabilities“.

While the wheel selection considered here has been made in order to maximize chances to de-

tect friction torque jumps, one can wonder what the real probability to get friction torque insta-

bilities are.

To put it clear: the idea along this document is to describe as good as possible the situation of

a wheel showing friction torque instabilities: what will be the repetition, the amplitude, etc…).

Thus, in the end the conclusion is black or white: either the wheel shows torque jumps accord-

ing to previously detailed models, or the wheel doesn’t show any variation of friction torque.

This statement is a first tool in order to assess the robustness of a design to wheels with

spikes, but not to extract the final performance taking into account the probability to get a

wheel with spikes.

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8 Assessment of impact at AOCS level

Objective of this study is to perform a pointing stability analysis considering friction torque in-

stabilities on the Euclid mission example. This European scientific high-precision pointing mis-

sion was selected due to its stringent relative pointing error requirement of ≤ 25 mas (1σ) over

700 s time window. For the purpose of this study, Euclid is equipped with a four-wheel array.

The friction torque instabilities in focus are torque spikes and plateaus. Statistical and worst

case occurrence in form of torque level, duration and repetition are studied.

Figure 28 Figure 8-1 : Wheel array in Euclid spacecraft frame

In the simulator (Euclid phase A/B1 and B2/C/D prime proposal preparation) the dynamics

model is of particular interest. The rigid spacecraft body of about 2000 kg mass is combined

with a pendulum sloshing model of 0.86 Hz natural frequency and 0.01 damping ratio. Sensor

and actuator detailed models are used, along with a model of external disturbances.

8.1 Simulation and results

The test cases analyzed are summarized in following table.

Case Sens. noise

Ext. dist.

RW friction torque instability

Type Level Slope Duration Repetition

Ref. 1

2

Worst Case

3 Spike 2.9 mNm Infinite* 20 s 200 s

4 Plateau 2.4 mNm Infinite* 300 s 2000 s

5 Spike 2.9 mNm Infinite* 20 s 200 s

6 Plateau 2.4 mNm Infinite* 300 s 2000 s

Statistical Case

7 Spike 0.63 −ln(𝑈1𝑈2)

4.8 3.8 mNm/s 20 s 125 −

ln(𝑈1)

0.0008

8 Plateau 0.5 −ln(𝑈1)

3 3.8 mNm/s 600 −

ln(𝑈1. 𝑈2)

0.002 125 −

ln(𝑈1)

0.0008

9 Spike 0.63 −ln(𝑈1𝑈2)

4.8 3.8 mNm/s 20 s 125 −

ln(𝑈1)

0.0008

10 Plateau 0.5 −ln(𝑈1)

3 3.8 mNm/s 600 −

ln(𝑈1. 𝑈2)

0.002 125 −

ln(𝑈1)

0.0008

Table 7 Simulation plan & hypothesis

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With the reference test cases, first the error-free simulator shall be characterized before only

the impact of attitude knowledge errors and external disturbances is studied.

After considering worst case spikes and plateaus without (test cases 3 and 4) and with attitude

knowledge errors and external disturbances (test cases 5 and 6), statistical spikes and plateaus

are used in test cases 7 to 10. Torque noise is not considered in this study, since no consolidat-

ed data could be provided during ground tests. However, its impact can be easily anticipated

using classical noise transmission analysis.

For the statistical simulations, the wheel friction torque instabilities (spikes and plateaus) are

modelled with a finite slope value, derived from the ground tests done by RCD while for worse

case simulations, an infinite slope (ie. torque step) is simulated.

Figure 29 RPE (inst. And PSD) for the case 2 – reference with noise

This first set of figure show the RPE (1σ – 700 s) related only to sensor noise and external dis-

turbances. This plot is a main importance, and to be compared to all further plots to assess the

impact of wheel friction torque instabilities.

8.1.1 Worst case

Considering the worst-case disturbance introduced previously (see Fehler! Verweisquelle

konnte nicht gefunden werden.) the comparison with the impact of sensor noise and exter-

nal disturbances seems to indicate a low impact. Only the harmonic content induced by a con-

stant repetition allows identifying the friction torque instability on the RPE PSD.

Figure 30 Worst-case spikes – with noise

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Considering the worst case plateaus, the impact is even lower, mainly related to the longer

repetition time.

Figure 31 Worst-case plateaus – with noise

8.1.2 Statistical

As soon statistical models are considered, the impact is almost invisible compared to the other

contributions (sensor noise, etc…) Here, unlike for worst-case, the energy is no longer concen-

trated on specific frequencies, and no trace can be found on the PSD plots.

Figure 32 Statistical spikes – with noise

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Figure 33 Figure 8-2 : Statistical plateaus – with noise

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9 Synthesis & Recommendations

The overall results confirm previous observed conclusion: for the Euclid reference mission, the

main contributions are the sensor noise and external disturbances. Worst case hypothesis have

little impact (+10% on RPE) and considering statistical models, no visible impact at all can be

characterized on the RPE.

Case Sens. noise

Ext. dist.

RW friction torque instability

Type x-y-z RPE (1σ - 700s) [mas]

Ref. 1 0.1 0.2 0.3

2 20.0 20.3 74.2

Worst Case

3 Spike 10.2 14.1 1.4

4 Plateau 2.6 3.6 0.4

5 Spike 22.5 24.7 74.3

6 Plateau 20.1 20.6 74.3

Statistical Case

7 Spike 1.5 2.1 0.3

8 Plateau 0.8 1.2 0.4

9 Spike 20.0 20.4 74.2

10 Plateau 20.0 20.3 74.2

Table 8 All simulation results

The worst case friction torque instabilities induce torque disturbances and, thus, pointing errors

at distinct frequencies while the statistical ones randomly distribute their impact over frequen-

cies. As consequence, a mission might not be feasible for the worst but for the statistical (real-

istic) cases. Since, as for Euclid, friction torque instabilities can drive the AOCS design (mass,

costs etc.), it must be carefully evaluated by the project and the customer if such worst case

assumptions shall be really taken into account.

Some recommendations shall be given on how to handle friction torque instabilities on AOCS

level:

- Use fast AOCS loop to quickly recover the pointing before the next friction torque jump oc-

curs. Target: > 0.5 Hz closed-loop bandwidth should allow being robust against 99% of the

cases

- It is very important to master the friction torque instability inputs to be used. The statistical

distribution is more realistic and its impact on the pointing is far lower than for the worst case

assumptions.

- It must be taken care about all potential interaction with the platform. Especially flexible

modes and sloshing that could be excited by torque jumps should be minimized or even avoid-

ed.

All these recommendations were successfully applied to the Euclid spacecraft and proven to be

efficient as seen in the simulation results.

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10 Way of improvements

10.1 AOCS/System level

As shown previously, Euclid AOCS sensitivity to friction torque instabilities is rather low. Thus,

in order to assess potential improvements, the Euclid reference case will be used again, with

variations of the tuning to assess the efficiency of the presented solutions.

Several simulations will be done, with a reference simulation being the “worst case torque plat-

eau”: a 2.4 mNm step lasting 300 s. Of course, all results also apply in the case of different

disturbances as those identified during the in orbit data analysis Fehler! Verweisquelle

konnte nicht gefunden werden..

In order to simplify the analysis of potential improvements, a lighter simulation environment is

used. Since the detailed analysis established a low impact of flexible modes, and since sensor

noise is not considered in this part of the study, a single axis simulation is selected.

10.1.1 Rejection at AOCS level

Impact of bandwidth

During the WP2 studies, focused on the Euclid reference mission, the obvious benefit of an in-

creased bandwidth was shown. Impact of wheel friction torque instabilities was rather low, in

any case compliant with the stability requirements of the mission.

Considering a simple PD control (no integral term), the impact of a friction torque step corre-

sponds to the static error induced.

Using 𝜔𝐶𝐿 = √2𝐾𝑝/𝐼𝑠𝑎𝑡, the relation with the closed loop bandwidth expresses as:

𝛿𝜃 =2𝛿𝑇

𝜔𝐶𝐿2 𝐼𝑠𝑎𝑡

This expression will allow for a simple evaluation of the impact of wheel friction torque instabili-

ties, in particular torque steps.

If considering an integral term, the maximum impact can be bounded using the same ap-

proach. Only with faster reaction times of the integral term, the global impact may be reduced,

although the global bandwidth remains unchanged. In this case, the maximum value of the

time response cannot be easily expressed. Under some restrictions an analytical approximation

could be expressed, but no general expression (valid over the full range of possible tunings)

can be easily defined.

In order to provide sensitivity to bandwidth, the Euclid reference simulation will be repeated

with different values of bandwidth. In order to keep constant stability margins, the tuning mod-

ifications will be applied on the global PID controller, ensuring a constant gain margin.

While the reference case fits to the simulation showing ~1 Hz bandwidth, this also illustrates

the behavior of a more usual bandwidth: with 0.3 Hz (which is in most cases already consid-

ered as a « fast » AOCS tuning. It can be seen that with the hypothesis taken (2.4 mNm torque

plateau), a bandwidth of 0.5 Hz (-3dB closed loop) would have been sufficient to guarantee the

25 mas RPE requirement.

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39 54400-732 Rev. B

Figure 34 Step response (2.4 mNm torque step) – 1σ RPE

Another option would also be to consider a fixed bandwidth, and to modify the integral contri-

bution. This would be for instance the case if the integral part is modelling an external friction

compensation loop. Here the gain margin will be impacted, although the high frequency behav-

iour (and thus the bandwidth) remains unchanged. In the end, this corresponds to a modifica-

tion of the system resonance. The time responses to a torque step (2.4 mNm plateau) are also

well illustrating this, with a slight underdamped reaction for the last simulated case, showing

the highest integral effect.

Figure 35 Step response and integral action

A discussed previously, it appears that the impact on peak level is rather low, since a very im-

portant increase of the integral term would be needed to reduce the peak. On the other hand,

the impact on the transient phase is obvious, and will directly affect all time related metrics,

like for instance the instantaneous RPE.

Friction estimation

Along with an additional integral action, a friction compensation algorithm can also be consid-

ered. Relying on the wheel speed information along with the commanded torque, the estima-

0 2 4 6 8 10 12 14 16 18 200

50

100

150

200

250

300

350

400

450

Time (s)

Poin

ting (

mas)

Euclid Reference simulation

Fc = 0.3 Hz

Fc = 0.5 Hz

Fc = 0.6 Hz

Fc = 1.0 Hz

Fc = 1.3 Hz

500 1000 1500 20000

10

20

30

40

50

60

70

80Instantaneous RPE (1 700s)

Time (s)

1

RP

E (

mas)

Fc = 0.3 Hz

Fc = 0.5 Hz

Fc = 0.6 Hz

Fc = 1.0 Hz

Fc = 1.3 Hz

0 2 4 6 8 10 12 14 16 18 20-40

-20

0

20

40

60

80

100

120

140

160

Time (s)

Poin

ting (

mas)

Fi = 0.005 Hz

Fi = 0.010 Hz

Fi = 0.020 Hz

Fi = 0.050 Hz

Fi = 0.100 Hz

500 1000 1500 20000

5

10

15

20

25

30


Time (s)

1

RP

E (

mas)

Fi = 0.005 Hz

Fi = 0.010 Hz

Fi = 0.020 Hz

Fi = 0.050 Hz

Fi = 0.100 Hz

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40 54400-732 Rev. B

tion of the friction torque allows a finer attitude control, especially by cancelling the torque bias

induced by the friction.

The usual reaction wheel friction torque estimation is based on a Kalman filtering with constant

gains. The wheel speed measure is used along with the commanded torque to estimate the loss

torque (= wheel friction).

Previous simulations of the Euclid reference case showed that a bandwidth of 1 Hz allowed

achieving around 5 mas RPE (1σ – 700s). A close result can also be achieved considering a

friction torque estimation and compensation loop. Here again, the idea is to keep a reduced

bandwidth for the PD AOCS control (around 0.1 Hz) and to improve the figures thanks to the

friction estimation algorithm.

Figure 36 Reduced AOCS bandwidth and friction compensation

Details around the noise transmission

Previous introduced models are focused on the friction torque rejection. The final implementa-

tion of the friction torque estimation is using different measurements than the AOCS loop, thus

inducing very different noise propagation compared to a PID loop.

With a friction torque rejection based only on the AOCS controller, the wheel sensor noise (eg.

Tacho jitter) is not injected in the loop. But the AOCS sensor noise is directly transmitted to the

pointing via the closed loop. The higher the global bandwidth, the worst the impact.

Following figures offers a comparison between different tuning possibilities, compared to the

Euclid reference case: friction estimation with high AOCS bandwidth, reduced friction estima-

tion authority and eventually, a typical case of reduced AOCS bandwidth with increased friction

estimation action.

500 1000 1500 20000

5

10

15

20

25


Time (s)

1

RP

E (

mas)

K1 = 0.2 / K

2 = 1.0

K1 = 0.2 / K

2 = 2.0

K1 = 0.2 / K

2 = 6.0

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41 54400-732 Rev. B

Figure 37 Friction torque estimation – different tunings and noise rejection

The trade-off between AOCS bandwidth and friction compensation action is always deeply re-

lated to the noise transmission: AOCS sensor noise, but also wheel speed sensor noise. Here,

for the sake of illustrating the study, exaggerated tunings are considered, with a very low

AOCS bandwidth and a high reaction of the friction estimation.

On the other hand, with a friction estimation loop, the wheel sensor noise is now also injected

in the feedback loop. Thus, an estimation of its impact has to be done, in relation with the con-

sidered tunings. The wheel sensor noise transmission writes:

Figure 38 RW sensor noise transmission and different tunings

10-3

10-2

10-1

100

101

-60

-50

-40

-30

-20

-10

0

10

Magnitu

de (

dB

)

Bode Diagram

Frequency (Hz)

Euclid ref.

High AOCS BW / high estimation - Euclid tuning

High AOCS BW / low estimation

Low AOCS BW / high estimation

10-3

10-2

10-1

100

101

-180

-160

-140

-120

-100

-80

-60

-40

Magnitu

de (

dB

)

Bode Diagram

Frequency (Hz)




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42 54400-732 Rev. B

Synthesis

It has been shown that the friction torque compensation can be considered as a simple integral

action. This will ease the analysis, as a PID controller can be considered at first glance.

Figure 39 RPE performance compared

The step response plots show the main issue when considering the PID: to keep the bandwidth

constant, only the integral action was tuned, leading thus to increase the overshoot of the con-

trol (and decreasing the stability margins). On the other hand, the friction compensation tends

to reduce the step response level, while the reduced AOCS bandwidth induces a longer tranqui-

lization. Here again, an external loop relying on higher sampling rates, along with wheel speed

information will allow much higher reactions.

With similar performances compared to the Euclid reference, the question of sensor noise

transmission is then obvious: the friction estimation offers the best performances with a lower

noise transmission, while the PID approach may be questionable: although the bandwidth is

reduced, the increased gain may ruin the expected reducing of noise transmission.

1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100-40

-20

0

20

40

60

80

100

120Response to torque plateau

Time (s)

Poin

ting (

mas)

PID tuning

Euclid reference

High bw AOCS + estimation

Low bw AOCS + estimation

500 1000 1500 20000

1

2

3

4

5

6

7

8


Time (s)

1

RP

E (

mas)

Euclid reference (1Hz AOCS)

PID tuning

High BW AOCS + reactive estimation

Low BW AOCS (0.1 Hz) + reactive estimation

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43 54400-732 Rev. B

Figure 40 AOCS sensor noise transmission

A more general remark still is that the differences are rather low. Indeed, the friction compen-

sation algorithm is mainly intended to cope with low frequency friction variations such as the

ones induced by a regime change, etc… The design was not really intended to compensate for

fast variations, like the ones induced by a torque plateau or spike. This was also one of the

conclusions stated during WP1: the in flight data provided by a friction torque estimation loop

doesn’t allow for identifying quick torque variations and local events like torque spikes.

By its structure, parts of the AOCS sensor noise are still included in the transmission loop, and

besides, the friction torques estimation can be considered as part of the global AOCS control

loop (thus also participates to the bandwidth). Thus a very reactive tuning, like the one needed

for the Euclid reference case, also induces an increase in the sensor noise transmission.

One promising way of improvement seems to be a reaction wheel local control loop, not relying

on AOCS sensor, to cope with friction torque instabilities in an independent way.

10.2 Wheel speed control

As the torque disturbance originates from the bearing, the first impacted physical parameter

will be the wheel speed, as a result of a difference between commanded and realized torque.

Details & implementation

The friction torque mitigation is achieved through torque rejection by a wheel speed control

loop. Considering a PI wheel speed control, the transfer function easily expresses as:

𝑇𝑟𝑒𝑎𝑙

𝑇𝑓𝑟𝑖𝑐

=𝑠2

𝑠2 + 𝐾𝑝𝑠 + 𝐾𝑖

Thus the rejection of wheel friction instabilities is fully efficient, with a full compensation after

convergence.

10-3

10-2

10-1

100

101

-60

-50

-40

-30

-20

-10

0

10

Magnitu

de (

dB

)

Bode Diagram

Frequency (Hz)

Euclid ref.




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44 54400-732 Rev. B

Interaction with AOCS

Considering an AOCS bandwidth one order of magnitude lower than the wheel loop, the latter

showing a unitary gain in the AOCS bandwidth range, the wheel loop doesn’t interfere with the

AOCS loop, and both the external torque rejections and noise transmission performances are

the same for both implementations (at least at first order).

𝜃𝑟

𝑇𝑒𝑥𝑡

=𝐷𝑆𝐿

1 + 𝐷𝑆𝐿𝐾𝑃𝐷

With a wheel speed loop, the friction torque is rejected internally, what is not the case when

considering a PID or even friction compensation AOCS where the friction torque is rejected at

the same level than any external disturbing torque.

𝜃𝑟

𝐹=

𝑠𝐷𝑆𝐿

𝑠 + 𝑠𝐾𝑅𝑊𝐷𝑅𝑊 + 𝐷𝑆𝐿𝐾𝑅𝑊𝐾𝐴𝑂𝐶𝑆

Figure 41 Friction torque rejection

Seen from the AOCS loop, an additional integration stage is applied, inducing a second order

slope for the low frequencies. In comparison, the PID AOCS loop rejects the external torques

with a single integration stage. This is obviously related to the considered wheel speed loop

control: with a PD rather than PI control, the results would have been different.

In the same way, the wheel measurement noise injection in the AOCS loop has to be assessed,

since it will also affect the final pointing performance. Here again, the wheel closed loop is no

longer considered as a unitary gain.

𝜃𝑟

𝑁𝑟𝑤

= −𝑠𝐾𝑅𝑊

𝐼𝑆𝐿𝑠2(𝑠 + 𝐾𝑅𝑊) + 𝐾𝑅𝑊𝐾𝑆𝐶𝐴𝑂

Here again, it should be paid attention to the fact that the reaction wheel noise is expressed as

angular momentum noise.

10-4

10-3

10-2

10-1

100

101

-200

-180

-160

-140

-120

-100

-80

-60

Magnitu

de (

dB

)

Bode Diagram

Frequency (Hz)

PID

Estimator

RW loop

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45 54400-732 Rev. B

Figure 42 Wheel measurement noise transmission to attitude

The much lower AOCS bandwidth allows reducing the impact of the AOCS sensor noise, which

was the major drawback of the mitigation based on increased AOCS bandwidth. Here the

bandwidth considered for the AOCS+RW loop design is as low as 0.05 Hz.

The wheel speed loop has a bandwidth of around 1.1 Hz, allowing a reactive rejection of wheel

friction torque instabilities. With a worst case torque jumps as a reference case, the perfor-

mances simulated can be compared to the Euclid reference case, based on a high bandwidth

PID AOCS loop.

Figure 43 Torque plateau - Euclid reference and RW loop

Eventually, the performances obtained with a low bandwidth AOCS (0.05 Hz) and a local speed

control loop at RW level are even better than the Euclid reference case. This solution offers also

a major advantage by decoupling the AOCS sensor noise (global system topic) from the wheel

friction torque instabilities mitigation (local actuator issue).

10-4

10-3

10-2

10-1

100

101

-130

-120

-110

-100

-90

-80

-70

-60

-50

Magnitu

de (

dB

)

Bode Diagram

Frequency (Hz)

1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100-5

0

5

10

15

20

25

30

35

40

45Response to torque plateau

Time (s)

Poin

ting (

mas)

Euclid reference

AOCS + RW loop

500 1000 1500 20000

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Time (s)

1

RP

E (

mas)

Euclid reference

AOCS + RW loop

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46 54400-732 Rev. B

10.3 Consequences on RW

10.3.1 AOCS rejection

With an improvement relying only on an increased AOCS bandwidth, the only consequence at

RW level is a required fast reaction, with a low time constant. Since the main limitation remains

the AOCS sampling rate, it is not expected that the wheel reaction time or sampling rate will

become a driver. One point of improvement still may be the wheel sensor noise, since the fric-

tion compensation also relies on the wheel speed information.

Referring to the noise transmission detailed in previous sections, and considering a target of

0.1 µrad (3σ) pointing noise induced by wheel sensor following figures can be derived.

Tuning Integrated transmis-

sion √∫ (|𝑮𝒕𝒓𝒂𝒏𝒔|𝟐)𝒅𝒇

Attitude noise target (3σ)

RW sensor precision target (3σ)

High AOCS BW / high estimation BW (Euclid fitting)

8x10-5

0.1 µrad

1.2 mNms 62.5 mrad/s

High AOCS BW / low estimation BW

1x10-4 1 mNms

50 mrad/s

Low AOCS BW / high estimation BW

5x10-4 0.2 mNms 10 mrad/s

Table 9 Sizing of the wheel speed sensor noise

Caution has to be taken that this wheel sensor noise is expressed as angular momentum noise

in the proposed implementation. Speed values are given for an inertia of 0.02 kg/m² (typical

wheels used on LEO applications and medium sized spacecraft, eg. RCD RSI12 / RSI20). The

bigger wheels from RCD have an inertia close to 0.1 kg.m², representing a worst-case. Eventu-

ally, the relevant value for AOCS performance is the angular momentum noise, although the

physical measure at wheel level is the speed.

With the previously defined target of 0.1 µrad (3σ) noise transmitted to platform pointing, the

allocation for reaction wheel speed measure noise becomes:

Wheel speed measurement noise : < 10 mrad/s (~0.1 RPM) – 3σ

10.3.2 Wheel speed loop

Wheel speed measure

In order to have a sufficient sampling time for the wheel loop, and in order to provide some

room for improvement, a wheel speed measurement should be available at refreshment rates

higher than 20 Hz.

Wheel speed measurement sampling rate : > 20 Hz

Combining an analytical noise transmission analysis with the previously defined target of 0.1

µrad (3σ) noise transmitted to platform pointing, the allocation for reaction wheel speed meas-

ure noise becomes 0.2 mNms (3σ). Considering an usual wheel inertia of 0.02 kg.m², this be-

comes :

Wheel speed measurement noise : < 10 mrad/s (~0.1 RPM) – 3σ

Wheel time constant

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47 54400-732 Rev. B

As for the wheel speed information sampling, a higher frequency wheel speed control loop calls

for reactive wheel dynamics. In order to reduce the delay in the loop, a reaction time of around

10 ms seems a reasonable target.

Here the rational is once again to decouple the topics: with a speed control loop bandwidth of

around 1 Hz and a sampling of 10 Hz, a wheel reaction time equivalent to 100 Hz seems a good

approach. On the other hand, a higher reaction may induce additional disturbances, due to the

quantization of the torque command. Here, the 10 ms reaction time offers still a sufficient av-

eraging of the commands.

Wheel time constant: < 10 ms

Wheel measurement at low rates

Since all previous requirements (about sensor precision or rising time) seem achievable without

deep modification of the wheel design, the main issue remains the wheel speed measure at low

rates. Based on the hall sensor information, a periodmeter principle offers the lowest noise,

provided a high accuracy and high frequency counter is available, and always the same tacho

pulse is used. But at low wheel speeds, the refreshment is also reduced, causing trouble to en-

sure a sufficient reaction of the loop.

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48 54400-732 Rev. B

Solution RW impact AOCS/System impact Expected benefit Drawback

Speed control loop – RW level

- Reaction time improve-ment

- Speed sensing improve-ment

- Local control electronics

- AOCS wheel moment com-mand

- Rejection of friction variation via speed control loop.

- Local electronics allow higher efficiency (sampling, interface, etc...)

- Additional RW electronics

Speed control loop – AOCS level


- Speed sensing improve-ment

- AOCS wheel moment com-mand - High sampling rate interface for RW TM/TC

- Rejection of friction variation via speed control loop

- New interface vs. AOCS: H command, high rate

- Limited by AOCS computation load & interfaces

AOCS rejection – friction compensation


- Global optimization vs. sen-sor noise

- Control of friction instabilities, reducing pointing error

- Sensor noise transmission increase

AOCS loop rejection – bandwidth increase


- Global optimization vs. sen-sor noise

- Control of friction instabilities, reducing pointing error

- Sensor noise transmission increase

Table 10 Synthesis of the proposed improvement solutions

All methods developed and detailed in this document of course apply on all kind of wheel generated torque variations. Since no solution is model

based, every torque variation (plateau, spike, or even noise) will have its impact on pointing mitigated. Here the worst case friction torque instability

has been considered for the purpose of illustrating the various approaches, thus all other models (like the statistical friction torque instability with a

finite slope for instance) will end up with lower influence on pointing.

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49 54400-732 Rev. B

11 Improvements on reaction wheel level

This part describes the improvement possibilities identified at RCD. In the last section a com-

parison will be given with the improvements deduced from the AOCS chapter before.

11.1 Wheel internal speed control loop

A speed control system implementation on wheel level would establish an independent control-

ler system in the higher level AOCS controller framework. It is essential that the bandwidths

have to be correlated with the one inside the wheel being about ten times faster than the one

of the AOCS system in order to avoid interference. In addition an internal speed controller at

wheel level will change the wheel commanding, introduce distortions at the speed control

bandwidth and will add a new source of attitude errors, since the corrective action of the speed

control loop will cause an offset in the attitude.

Accelerator

Decelerator

Commutation Logic

Torque CommandLimiter

CommutationSwitches

CurrentController

TorqueDirectionChangeLogic

BrushlessDC Motor/Sensors

PrecedingStage

DoubleForwardConverter

Primary Supply

On Command

Off Command

Primary Return

On/Off Status

Thermistor

Torque Command

Torque Direction

Tacho

Speed Direction

Motor Current

BearingThermistor

Shunt

Motor Line

Motor Line Return

Un

de

r- / O

ve

r- V

olta

ge

SensorOutput

MotorPhases (3)

Torque Command (Clamped)

Dec

AccSecondaryGround

AuxiliaryVoltages

12V LinearRegulator

Pri

ma

ry S

up

ply

+ 42 V

Sync.

TDC

CW/CCW

Under- / Over-voltage Sense

Figure 44 Block diagram of analogue wheel drive electronic

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50 54400-732 Rev. B

The wheel drive electronics of TELDIX wheels with > 1 Nms are characterized by an analogue

design, see Figure 44. A wheel internal speed controller would need a technology change to-

wards a digital design requiring a processor and its dedicated firmware.

With its RSI01-5/18 wheel type (< 0,2 Nms) RCD has experience with a digital wheel drive

electronics which can be operated in torque mode or in speed mode. The internal software

compensates automatically the friction torque by its controller algorithm, so a net reaction

torque is commanded instead of a motor torque.

To reach this effect, a perfect wheel is simulated and the speed output of this perfect wheel is

taken as the control input. The speed change can be commanded as a speed or as a reaction

torque value which is than driving the speed change of the simulated wheel. For the internal

wheel speed controller no friction estimator is implemented. During the acceptance testing it is

verified, that the maximum speed deviation under any condition at speeds above 20 RPM is

below 1 RPM. The actual wheel speed is measured using calibrated hall sensor positions and a

timer resolution in the range of micro seconds. Friction is calculated using double differentia-

tion.

11.2 Decrease of wheel reaction time

A change in the wheel reaction will requires two improvements at the same time:

1.) Improved speed measurement both in time and special accuracy

2.) Improved motor current control reaction time

According to the improvement report from Airbus DS on AOCS and system level, an improve-

ment only relying on an increased AOCS bandwidth would require a fast signal processing with-

in the wheel electronics. The main aspects are in this context a faster determination of the

wheel speed and a faster reaction to torque command changes initiated by the AOCS system.

Any friction torque variations due to instabilities are detected by a speed deviation. The speed

variation has to be detected and processed by the system controller which will react with a

torque command change. Hence a fast and precise speed information and a fast reaction to

torque command initiated by the AOCS system is essential for a better friction torque instability

rejection.

11.2.1 TACHO signal accuracy

The tacho output signal, seen by the AOCS system, is generated from the exclusive-or wired

signals of the 3 Hall Effect sensors embedded in the stator coils; it is a pulse train with constant

amplitude - independent of the speed - with 24 pulses per revolution; hence the number of

pulses per second is proportional to the speed.

The more precise way to measure the wheel speed is to measure the time needed for one revo-

lution using each 24th tacho edge of the tacho pulse train. This implies that the same magnet

and the same hall sensor is used to derive the speed information and hence the speed meas-

urement error is minimised. The tacho jitter, observed from revolution to revolution, i.e. be-

tween each 24th pulse, is typically ~ 1 µsec; at the nominal speed of 4000 rpm this yields to a

tolerance of 0.1%. Taking worst case internal distortions into account a value of < 15 µsec has

to be assumed for the tacho jitter from revolution to revolution.

With a design change of the wheel drive electronics with respect to the glue logic around the

hall sensor signal processing this worst case tacho jitter could be reduced to < 250ns for the

falling edge of the tacho signal. Such a design change is limited to some resistors and/or ca-

pacitors values and can be considered as minor, not requiring a full qualification campaign.

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51 54400-732 Rev. B

With a tacho pulse jitter < 250 ns for the falling edges between each 24th pulse, a speed evalu-

ation to better 0.1 RPM based on a 100ms speed update rate becomes possible. This speed

accuracy is reached within the speed range above 300 RPM (up to 6000 RPM) by taking at

higher speed several rotations into account. With additional calibration of the hall sensor posi-

tion it is possible to reach the 0.1 RPM accuracy down to 30 RPM (using the falling edges of the

tacho signal only) and down to 15 RPM using both edges of the tacho signal.

A local speed control loop would allow guaranteeing a maximum speed deviation below 0.5 RPM

for a given commanded speed. With this information the maximum pointing error can be calcu-

lated. An operation of any wheel for longer terms in speed mode below 20 RPM is not recom-

mended due to speed variations generated by the friction to stiction crossover caused by the

physics of the bearing unit.

11.2.2 Response time to Torque command changes

The torque response time is defined as the time delay when applying a change to the input sig-

nal “ToCo” until the torque is generated inside the motor. The motor current is considered to be

instantaneous proportional to the motor torque; it can be measured for instance on a RWA set

between the WDE and the RDR. The WDE also provides the output signal “TMC” to the AOCS

system; this signal is of course delayed due to the WDE internal time constants.

In order to provide more accurate information about the internal time delays, the results of

measurements are outlined below:

Blue: ToCo (Torque command)

Red: Motor current (measured between RDR and WDE)

Green: TMC (Motor current, as signaled on the interface pin)

In the chart above the torque command “ToCo” is raised at t=5ms from 1% torque to max

torque. The motor current (motor torque) has reached 95% (3τ) of the commanded torque

within 3ms. If the wheel drive electronics could be modified to further decrease the dead time

of 3ms, this would improve the higher level controller system.

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52 54400-732 Rev. B

The output signal “TMC” (Telemetry Motor Current) has a delay time of about 18ms; this value

is of less importance because it shall not be used as a controlling parameter of the AOCS sys-

tem.

11.3 Improvements at ball bearing unit level

For Rockwell Collins ball bearing units exhibit only minimal variations in friction. Those varia-

tions are inhearant to the working principles of the bearing units with ball having the freedom

to move inside their pockets, the guidance principle of the cage and the working principle of the

resupply system. Without changing the base principle of the bearing unit, only minor improve-

ments can be reached.

Comparing the effectivity of design changes to the bearing unit with the effect of a direct speed

control the last is by far the most efficient improvement, as could be seen in chapter 10.

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53 54400-732 Rev. B

12 Conclusion

A reaction wheel is an actuator in a higher level AOCS system for a spacecraft. It provides a

torque to the supporting structure when accelerating or decelerating of the wheels internal fly-

wheel mass. Nominally a torque is commanded by the controlling system in order to perform

specific maneuvers. Unfortunately, due to the principal design of a ball bearing unit the reac-

tion wheel generates un-commanded torque changes which may show up on a random basis

with amplitude and profile described in this report.

Depending on the pointing stability requirements the spacecraft’s AOCS system does provide

concepts to mitigate unwanted torque variations generated by the wheel itself. In the frame of

this ESA-TRP study different mitigation scenarios have been described and their effectivity has

been assessed.

1.) Speed control loop – RW level

2.) Speed control loop – AOCS level

3.) AOCS rejection – friction compensation

4.) AOCS loop rejection – bandwidth increase

Torque instability mitigation techniques on wheel level are addressed in this report, the most

effective one being most likely a speed control loop on wheel level, which is also the most ex-

pensive solution. RCD standard electronics is based on an analogue design, so detailed design

concepts for a digital electronics with an implemented speed control loop cannot be given in the

frame of this ESA TRP study. A cost-effective solution is needed which should not only focus on

the speed control loop itself but also to the wheel command interface.

The second best approach, mitigation of friction torque instabilities on AOCS level, i.e. by

adapting the reaction wheel design to improve the torque response time and to have a more

accurate speed sensing seems feasible and affordable.

As a result of this study a model for the friction variations of the Rockwell Collins TELDIX®

space wheels is available which allows the simulation of the satellite performance and a deci-

sion on the measures to be taken to reach the required pointing accuracy.

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