Stepping Motor Driving Disturbance Test and Identification of ...Stepping Motor Driving Disturbance Test and Identification of Mathematical Disturbance Model Toshio Kamiya NEC TOSHIBA

Stepping Motor Driving Disturbance Test and

Identification of Mathematical Disturbance Model

Toshio Kamiya

NEC TOSHIBA Space Systems, Ltd., Fuchu, Tokyo, 183-8551, Japan

Abstract: Stepping motor is one of the most serious disturbance sources which generate

high-frequency vibration and deteriorate pointing stability of satellite. Those disturbance

sources need to be under control of satellite system design. To control disturbance sources

in system design and meet pointing stability requirements, we need both of a high-

frequency vibrations control method and accurate mathematical disturbance models. For

this reason, we tested a stepping motor and evaluated the data of driving disturbance vi-

brations and identified “stepping motor mathematical disturbance model”. Consequently,

we realized an accurate mathematical disturbance model of stepping motor which in-

cludes flexible structure as inertial load. This mathematical model can be applied to all

stepping motors in which key parameters like stepping motor characteristics and inertial

load’s structural characteristics are given. Keywords: Stepping Motor, Disturbance, Microvibration, Pointing Stability, Model Iden-

tification

ステッピングモータステッピングモータステッピングモータステッピングモータ駆動擾乱試験駆動擾乱試験駆動擾乱試験駆動擾乱試験とととと擾乱擾乱擾乱擾乱モデルモデルモデルモデル同定同定同定同定

摘要：衛星内部に存在する各種の振動擾乱源の中でも擾乱レベルが高く、衛星システム設計の際の擾

乱管理対象として注意が必要なステッピングモータ駆動系について、モータ駆動時に発生する擾乱の

評価試験を行い、データ評価ならびに擾乱モデル同定を行った。結果として、太陽電池パドル駆動系

のような、柔軟性構造特性を有する慣性負荷をモータ負荷として乗せたステッピングモータ駆動系に

ついて、実測結果を精度良く再現できる擾乱数学モデルを構築した。

1. Introduction

Stepping motor is one of the most serious distur-

bance sources which generate high-frequency vibra-

tion and deteriorate pointing stability of satellite.

Those disturbance sources need to be under control

of satellite system design. To control disturbance

sources in system design and meet pointing stability

requirements, we need both of a high-frequency vi-

brations control method and accurate mathematical

disturbance models. For this reason, we tested a step-

ping motor and evaluated the data of driving distur-

bance vibrations and identified “stepping motor

mathematical disturbance model”. Consequently, we

realized an accurate mathematical disturbance model

of stepping motor which includes flexible structure

as inertial load. This mathematical model can be ap-

plied to all stepping motors in which key parameters

like stepping motor characteristics and inertial load’s

structural characteristics are given.

“Microvibration management” means satellite sys-

tem design regarding satellite internal microvibration.

Microvibration management is conducted for the

purpose of realization of the pointing stability that is

required from the satellite mission. In evaluating a

satellite mission which requires a pointing stability in

a short term such as camera exposure, the microvi-

brations generated from satellite internal disturbance

sources such as reaction wheel or stepping motor

become critical factors which degrade the pointing

stability. For that reason, microvibration manage-

ment and pointing stability evaluation should be a

pair in satellite system design. In this paper, stepping

motor which is known as one of the most serious

disturbance sources is taken as an object.

2. What is a Satellite Disturbance Management ?

This section shows the fundamental policy of mi-

crovibration management, especially performed for

the SELENE satellite. In order to clarify the man-

agement factors for microvibration management, the

affecting factors on the pointing stability which exist

in each frequency range are shown in Fig.1.

In satellite system design, comprehensive evalua-

tion of each factor shown in Fig.1 must be carried

out. In SELENE, the system requirement (0.003

[deg/sec]) for the attitude control subsystem (ACS) is

applied only to the affecting factors whose frequency

ranges are lower than the attitude control frequency

(approximately 0.05[Hz]). Examples of such factors

are natural disturbances etc.. High frequency distur-

Disturbance

ManagementPointing Stability

Requrements

0 1 2 3 4 5 6 7 8 9 10

-30

-20

-10

0

10

20

30

Z-T

orq

ue [

Nm

]

ti me [sec]

no rmal pulserandom pulse

10-1

100

101

102

103

104

10-4

10-3

10-2

10-1

100

101

102

Frequency (Hz)

Z-T

orqu

e [

Nm

]

no rmal pulserandom pulse

100

101

102

10-2

10-1

100

101

102

Frequency [Hz]

Q

XYZ

(A) Disturbance

Mathematical Model

(B) Structural Transfer

Characteristic

(C) Pointing Stability

10-2

10-1

100

101

102

-20

-10

0

10

20

Frequency response (Rotational)

X -

gain

[dB]

10-2

10-1

100

101

102

-5

0

5

Y -

gain

[dB]

10-2

10-1

100

101

102

-10

0

10

20

Frequency [Hz]

Z -

gain

[dB]

10-3

10-2

10-1

100

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

← TOTAL

↑ SAP Peak

↑ HGA Boom-Reso

↑ HGA Ref-Reso

↑ RW Peak

↑ GRD Total

↑ UP I 80PPS

↑ UP I 800PPS

↓ IMU Dither

↑ AOCS

← LISM(TC) 2 .7e-006rad/0.0065sec

← LISM(MI) 5 .7e-006rad/0.013sec

← LISM(SP) 0 .00014rad/0.091sec

← UPI 0 .015deg/1sec

← LMAG 0.1deg/1sec

time [sec]

X -

Att

itud

e Err

or

[rad,

0-P]

Comparison of Test and Simulation (MOOG Type-3)

1.57E-05

3.29E-05

5.63E-06 5.85E-066.19E-06

1.11E-05

2.19E-05

4.96E-05

4.66E-06

3.52E-05

2.47E-05

4.66E-06

3.34E-06

4.80E-06

1.19E-05

2.15E-05

6.33E-05

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000

Drive Pulse Rate [PPS]

Poin

ting

Sta

bilit

y [r

ad/dt

1se

c, P-P]

MOOG Type-3 TestData

SimulationData

　　　　　　　　　　　　　 θ ��IQT =×

Fig. 2. Outline of Disturbance Management

System requirement for ACS

0.003 deg/s (Apply to below

attitude control frequency)

0.1Hz 1Hz 10Hz 100Hz

Disturbances

Other

influences

Frequency range of attitude control

Characterictic frequencies of flexible structure

(SAP, HGA, LRS, LMAG, Sloshing etc.）

Natural disturbances (Solar pressure, Gravity gradient etc.)

Characteristic frequencies

of satellite body 10Hz-

Microvibrations (SAP/HGA Stepping motor,

RW, GRD Compressor etc.）

DC

The target frequency range of microvibration

management is the whole frequencies!

Pointing stability

requirements

Requirements from observational equipments

(Apply to the whole frequency)

ACS subsystem

management factors Bus system management factors

Frequency rangeFrequency rangeFrequency rangeFrequency range

Factors ofFactors ofFactors ofFactors of influenceinfluenceinfluenceinfluence

Fig. 1. Frequency distribution of pointing stability requirements and affecting factors (SELENE)

bances (reaction wheel, stepping motor etc.) are in-

applicable for the ACS design. Accordingly, for the

microvibration management of a satellite system

design, it is not necessary to manage directly the

natural disturbances with a long cycle. The pointing

stability of a long cycle below the attitude control

frequency can be considered to be contained in the

system requirement for ACS (0.003[deg/sec]). The

internal disturbances and the structural characteris-

tics etc. which are indicated in Fig.1 with an asterisk

become direct targets for the SELENE system mi-

crovibration management. That is, microvibration

management of the SELENE system means compre-

hensive management of the factors indicated with an

asterisk in order to meet the pointing stability re-

quirements.

Fig.2 shows general image of disturbance man-

agement. Basically, disturbance management con-

sists of three parts as shown below,

• Disturbance Mathematical Modelling • Structural Transfer Modelling • Pointing Stability Analysis Fig.3 shows a disturbance modelling of HGA an-

tenna (main subject of this paper). Fig.4 shows other

disturbance sources such as reaction wheels and

equipment including compressor. Fig.5 shows a

structural transfer modelling such as transfer function

of appendage flexible structures or satellite body

panel flexible modes or damping ratio of an antenna

boom. Fig.6 shows

In this paper, we pick up disturbance mathematical

modelling. Here, we emphasize that if a equipment

which generates disturbances can be formulated ana-

lytically, and if the disturbance mathematical model

duplicate the actual disturbances, then there is no

need to test by actual equipment.

0 1 2 3 4 5 6 7 8 9 10

-30

-20

-10

0

10

20

30

Z-Tor

que [

Nm

]

time [sec]

normal pulserandom pulse

10-1

100

101

102

103

1010

-4

10-3

10-2

10-1

100

101

102

Frequency (Hz)

Z-Tor

que

[Nm

]

normal pulserandom pulse

Low Disturbance Drive Algorithm (HGA)

High Accuracy Test Based Dynamics Model


1 .57E-05

3.29E-05

5 .63E-06 5 .85E-066.19E-06

1 .11E-05

2.19E-05

4 .96E-05

4 .66E-06

3.52E-05

2.47E-05

4 .66E-06

3 .34E-06

4.80E-06

1 .19E-05

2.15E-05

6 .33E-05

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000


Poin

ting S

tabi

lity

[rad/

dt1sec, P-P]


SimulationData

High Accuracy Test Based Dynamics Model


1 .57E-05

3.29E-05

5 .63E-06 5 .85E-066.19E-06

1 .11E-05

2.19E-05

4 .96E-05

4 .66E-06

3.52E-05

2.47E-05

4 .66E-06

3 .34E-06

4.80E-06

1 .19E-05

2.15E-05

6 .33E-05

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000


Poin

ting S

tabi

lity

[rad/

dt1sec, P-P]


SimulationData

Stepper Motor in

HGA/SAP/UPI

Stepper Motor Model Identification Test

Fig. 3. Disturbance Modelling

Analysis Based Model –Reaction Wheel

Flywheel in RW/Gyro

Test Based Model –GRD Compressor

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-15

-10

-5

0

5

10

15

time [sec]

Forc

e [N

]

100

101

102

103

10-3

10-2

10-1

100

101

Frequency [H z]

Forc

e [

N]

RW Disturbance Test for Solar-B

Other Disturbance Source:

Compressor used in GRD

If RW has critical efffects on

pointing stability, you can

conduct the disturbance test,

and design accuracy will be

much better.

Fig. 4. Disturbance Modelling

Disturbance Source

Mission Equipment

Disturbance Source

Mission Equipment

100

101

102

10-2

10-1

100

101

102

Frequency [Hz]

Q

XYZ

Analysis Based –Satellite Body Modes (NASTRAN)

HGA-Boom Hammering Test

-5.00E+00

-4.00E+00

-3.00E+00

-2.00E+00

-1.00E+00

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

2040 2540 3040 3540 4040

Data No. （dt=1/2560*6）

[m/s

ec^2

]

Hammering Data

zetaA= 0.2

zetaB= 0.04

zetaC= 0.01

Test Based –Damping Ratio of HGA-Boom

10-2

10-1

100

101

102

-20

-10

0

10

20

Frequency response (Rotational)

X -

gain

[dB

]

10-2

10-1

100

101

102

-5

0

5

Y -

gain

[dB

]

10-2

10-1

100

101

102

-10

0

10

20

Frequency [Hz]

Z -

gain

[dB

]

Analysis Based –Flexible Appendages Modes

Fig.5. Structural Transfer

Auto spectrum

1.00E-14

1.00E-07

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

0 1600 500 1000Frequency (Hz) 5Z+

34 : 5Z+ 1test13_6

Auto spectrum

1.00E-12

1.00E-05

1.00E-11

1.00E-10

1.00E-09

1.00E-08

1.00E-07

1.00E-06

0 1600 500 1000Frequency (Hz) 5X+

35 : 5X+ 1test13_6

Auto spectrum

1.00E-14

1.00E-07

1.00E-13

1.00E-12

1.00E-11

1.00E-10

1.00E-09

1.00E-08

0 1600 500 1000Frequency (Hz) 5Y+

36 : 5Y+ 1test13_6

Campbell Diagram

0.00

1600.00

500.00

1000.00

1500.00

500.00 6000.00 2000.00 4000.00RPM

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

0.858

0.665

0.472

0.279

LinearAcceleration

25011 :24Z+ 1Z+ 626

13-Feb-04 16:21:15

Test Based –Satellite Body Transfer Characteristics (Under Evaluation)

100

101

102

103

104

10-1

100

101

102

103

F requ ency [H z]

Q [

]

Fig.6. Structural Transfer

3. Outline of Stepping Motor Driving Disturbance

Test

Fig.7 shows a test configuration of stepping motor

driving disturbance test. This configuration includes

rigid mass as an inertial load on the motor, and rigid

plate as a motor attachment to the 3-axis torquemeter.

Torquemeter is fixed on air-suspension table to re-

duce a transmission of ground vibration. Fig.8 shows

schematic diagram of test configuration. Fig.9 shows

other test configurations. Rigid inertial load is re-

placeable to flexible inertia. Rigid attachment is re-

placeable to flexible attachment either.

Fig.10 shows the internal structure of stepping mo-

tor. Stepping motor can be divided into three parts.

Rotor side and stator side, rotor side consists of out-

put axis and input axis through contact with har-

monic drive (hereinafter called H/D). The H/D is a

compact, light weight and high ratio torque transmis-

sion device which is used in many electrically actu-

ated antenna. The H/D is a special gear-drive speed

reduction system whose operation principle is based

on elastic deformation rather than rigid-body motion

of the general gearing system. Table 1 shows a

specification of test system.

Rigid Inertia

Stepping Motor

Rigid Attachment

Three-Axis Torquemeter

Air-Suspension Table

Fig.7. Test Configuration (Rigid Inertia)

慣性負荷（円柱形）

モータ

モータ固定治具

キスラーテーブル

エアサステーブル

加速度計（感度軸：円の接線方向）

ＡＭＰ

チャージＡＭＰ

ＰＣＡ／Ｄボード

ＢＮＣ端子パネル

オシロスコープ

オシロスコープ

モータ駆動回路

OSC

BNC Port

OSC

Charge AMP

Charge AMP

A/D board

Air-suspension Table

Inertial Load

Stepping Motor

Stepping Attach.

Torquemeter

Accel. Pick-up Sensing Axis: tangential

Motor Driver Elec.

Fig.8 Test Configuration

Flexible

Inertial Load

Flexible

Attachment

Flexible

Attachment Fig.9. Other Test Configuration

Harmonic Drive Harmonic Drive

Input Axis Output Axis

GearRatio : 160 : 1

: Harmonic Drive (Output Axis) and

Output I/F

: Harmonic Drive (Input Axis) and

MotorRotorAxis

: Actuator andMotorHousing and Other Parts

(That is All of the MotorUnit except Upper 2 Parts)

Rotor Side

Stator Side

①①①①：：：：

②②②②：：：：

③③③③：：：：

MotorHousing

Actuator

MotorRotorAxis

Output I/F

Fig.10. Internal Structure of Stepping Motor

Table 1. Specification of Test System

Torquemeter

output 3-axis torque / force

frequency 5[Hz]～1.7[kHz] resolution Not greater than 0.01[N]

Data Recorder

sampling rate 2048[Hz]

measurement time below approximately 30[s]

4. Test Data

In this chapter, test data is shown. Each figure

shows time-based disturbance torque profile and fre-

quency characteristic of the same data.

Fig.11 shows 1PPS (PPS: pulse per second) driv-

ing disturbance torque in the configuration of rigid

inertia and rigid attachment. As shown in this figure,

we can see the characteristic mode (69Hz) which is

characterized by the rigid inertia and the H/D stiff-

ness.

Fig.12 shows 69PPS driving disturbance torque in

the configuration of rigid inertia and rigid attachment.

As shown in this figure, we can see a mechanical

resonance which is caused by the correspondence

between characteristic mode (69Hz) and driving

pulse rate.


the configuration of flex1 inertia (3.3Hz) and rigid

attachment. As shown in this figure, we can see the

characteristic mode (3.3Hz) which is characterized

by the flex1 inertia and the H/D stiffness. Higher

structural modes also can be seen in the diagram.

Fig.14 shows 3.3PPS driving disturbance torque in

the configuration of flex1 inertia and rigid attach-

ment. As shown in this figure, we can see a mechani-

cal resonance which is caused by the correspondence

between characteristic mode (3.3Hz) and driving

pulse rate.


the configuration of flex2 inertia (6.1Hz) and rigid

attachment. As shown in this figure, we can see the

characteristic mode (6.1Hz) which is characterized

by the flex2 inertia and the H/D stiffness. Higher

structural modes also can be seen in the diagram.

Fig.16 shows 6.1PPS driving disturbance torque in

the configuration of flex2 inertia and rigid attach-

ment. As shown in this figure, we can see a mechani-

cal resonance which is caused by the correspondence

between characteristic mode (6.1Hz) and driving

pulse rate.


the configuration of rigid inertia and flexB1 attach-

ment. As shown in this figure, we can see the charac-

teristic mode (13.4Hz) which is characterized by the

rigid inertia / stepping motor and flexB1 attachment.

Fig.18 shows 13.4PPS driving disturbance torque

in the configuration of rigid inertia and flexB1 at-

tachment. As shown in this figure, we can see a me-

chanical resonance which is caused by the corre-

spondence between characteristic mode (13.4Hz) and

driving pulse rate.

Table2 shows the characteristic frequency and Q-

factor of each configuration. As shown in this table,

we can see the followings,

• Q-factor of the resonance between inertial load and driving pulse rate: 2 – 6 times

• Q-factor of the resonance between motor attach-ment and driving pulse rate: 9.5 – 30 times

Fig.11. Rigid Inertia/Rigid Attach./1PPS

Fig.12. Rigid Inertia/Rigid Attach./69PPS

Fig.13. Flex1 Inertia/Rigid Attach./1PPS

Fig.14. Flex1 Inertia/Rigid Attach./3.3PPS

Fig.15. Flex2 Inertia/Rigid Attach./1PPS

Fig.16. Flex2 Inertia/Rigid Attach./6.1PPS

Fig.17. Rigid Inertia/FlexB1 Attach./1PPS

Fig.18. Rigid Inertia/FlexB1 Attach./13.4PPS

0 5 10 15

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Z-T

orq

ue [

Nm

]

time [sec]

10-1

100

101

102

103

104

10-4

10-3

10-2

10-1

100

Frequency (Hz)

Z-Tor

que

[Nm

]

0 1 2 3 4 5 6 7 8 9

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Z-T

orqu

e [N

m]

time [sec]

10-1

100

101

102

103

104

10-5

10-4

10-3

10-2

10-1

Frequency (Hz)

Z-T

orqu

e [N

m]

0 5 10 15-1.5

-1

-0.5

0

0.5

1

Z-T

orq

ue [

Nm

]

time [sec]

10-1

100

101

102

103

104

10-5

10-4

10-3

10-2

10-1

100

Frequency (Hz)

Z-Tor

que

[Nm

]

0 1 2 3 4 5 6 7 8 9

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Z-T

orq

ue [

Nm

]

time [sec]

10-1

100

101

102

103

104

10-5

10-4

10-3

10-2

10-1

Frequency (Hz)

Z-Tor

que

[Nm

]

0 5 10 15

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Z-Torq

ue [

Nm

]

time [sec]

10-1

100

101

102

103

104

10-5

10-4

10-3

10-2

10-1

100

Frequency (Hz)

Z-T

orqu

e [N

m]

0 1 2 3 4 5 6 7 8 9 10

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Z-T

orqu

e [N

m]

time [sec]

10-1

100

101

102

103

104

10-5

10-4

10-3

10-2

10-1

100

Frequency (Hz)

Z-T

orqu

e [N

m]

0 5 10 15

-10

-8

-6

-4

-2

0

2

4

6

8

10

Z-Torq

ue [

Nm

]

time [sec]

10-1

100

101

102

103

104

10-4

10-3

10-2

10-1

100

101

Frequency (Hz)

Z-Torq

ue [

Nm

]

0 1 2 3 4 5 6 7 8 9 10

-3

-2

-1

0

1

2

3

Z-T

orqu

e [N

m]

time [sec]

10-1

100

101

102

103

104

10-5

10-4

10-3

10-2

10-1

Frequency (Hz)

Z-T

orqu

e [N

m]

Table 2 Characteristic Frequency and Q-Factor

T_FB3_W0.001T_FB3_W0.031

6.6/0.5= 13

31.5(FlexB3 Attachment Mode)

RigidFlexB3

T_FB2_W0.001T_FB2_W0.019

3.8/0.4= 9.5


RigidFlexB2

T_FB1_W0.001T_FB1_W0.013

2.4/0.08= 30


RigidFlexB1

T_RGD_W3.001T_RGD_W3.7_7

2.7/0.45= 6

7.7(Flex3 Inertia Mode)

Flex3Rigid


1.5/0.4= 3.8


Flex2Rigid


1/0.5= 2


Flex1Rigid

T_RGD_W0.001T_RGD_W0.069

12/3= 4

69(Rigid Inertia Mode)

RigidRigid

Data FileQ Factor (Resonance Amplitude Ratio)*

Driving Pulse Rate [PPS]= Characteristic Frequency [Hz]

Inertial Load

Attachment

T_FB3_W0.001T_FB3_W0.031

6.6/0.5= 13


RigidFlexB3

T_FB2_W0.001T_FB2_W0.019

3.8/0.4= 9.5


RigidFlexB2

T_FB1_W0.001T_FB1_W0.013

2.4/0.08= 30


RigidFlexB1


2.7/0.45= 6


Flex3Rigid


1.5/0.4= 3.8


Flex2Rigid


1/0.5= 2


Flex1Rigid

T_RGD_W0.001T_RGD_W0.069

12/3= 4

69(Rigid Inertia Mode)

RigidRigid

Data FileQ Factor (Resonance Amplitude Ratio)*

Driving Pulse Rate [PPS]= Characteristic Frequency [Hz]

Inertial Load

Attachment

*: The denominator of the Q-factor is the average peak torque of 1PPS driving. The numerator is the peak torque of each resonance. The reason being that the peak torque has steady value when it is resonated, but less steady in case of 1PPS.

5. Effectiveness of Isolation

In this chapter, we examine the pointing stability

in case that a rigid satellite (MOI=1[kgm2]) is subject

to the disturbance of stepping motor in each test case.

Pointing stability can be characterized by ‘Amplitude

of disturbance torque’ and ‘Frequency of distur-

bance’ and ‘Time span in which pointing stability is

required’. Therefore, for the purpose of general

comparison of disturbances, we evaluate the distur-

bances using the conversion data to pointing stability.

Damping (or isolation) effect by the flexibility of

motor stator side can be summarized as follows,

• Pointing stability (Short term / middle term) � Pointing stabilities are the same level in

each case, the reason can be supposed that

main factor of disturbance is H/D charac-

teristic mode (in case of flex inertia, it will

be flex inertia mode) and it doesn’t depend

on driving pulse rate.

• Short term pointing stability � Pointing stabilities can be decreased in

flex attachment compared to rigid attach-

ment.

� Resonance frequency depends on the flexi-bility of each attachment, however point-

ing stabilities are the same level in each

case.

• Middle term pointing stability � Pointing stabilities are the same level in

each case.

� Resonance frequency depends on the flexi-bility of each attachment, and pointing sta-

bilities will be increased in flex attachment.

7.89E-06 8.26E-069.53E-06

2.51E-06

1.13E-05

2.64E-05

3.71E-06

5.75E-06

1.53E-06

1.02E-06

2.85E-05

1.07E-06 1.06E-06

1.53E-06

4.10E-06

3.16E-06

1.33E-05

3.93E-06

3.04E-05

5.29E-06

2.20E-06

1.51E-06

5.25E-06

3.01E-06

3.92E-06 4.16E-06

2.63E-06

3.37E-05

2.50E-06

6.66E-06

4.49E-06

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000

Driving Pulse Rate [PPS]

Short

Term

Poin

ting

Sta

bility

[ra

d]

Rigid

FlexB1

FlexB2

FlexB3

Fig.19. Effectiveness of Isolation by short term sta-

bility (dt=1ms)

3.77E-05 3.79E-05

4.49E-05

1.74E-05

5.64E-05

1.26E-04

2.11E-05

4.80E-05

1.89E-05

3.67E-05

1.91E-05

6.66E-04

1.98E-051.78E-05

3.36E-05

1.04E-04

5.43E-05

2.21E-04

6.58E-05

5.03E-04

8.50E-05

3.31E-052.89E-05

9.73E-05

3.19E-05

4.00E-054.64E-05

2.61E-05

3.42E-04

1.97E-05

6.09E-05 6.47E-05

1.00E-05

1.00E-04

1.00E-03

1 10 100 1000


Mid

dle

Term

Poin

ting

Sta

bility

[ra

d]

Rigid

FlexB1

FlexB2

FlexB3

Fig.20. Effectiveness of Isolation by middle term

stability (dt=37ms)

6. Identified Model

In this chapter, we propose a stepping motor

mathematical disturbance model which can be used

for system design of satellite.

As shown in the following equations and Fig.21,

mathematical model can be realized by a simple

1DOF mass-spring system.

In case of a high driving pulse rate like over

100PPS, there could be a lot of high-order flexible

modes of inertial load in general. We hereby have to

consider that this mathematical model will be inaccu-

rate when we handle the stepping motor driving dis-

turbance in condition of a high driving pulse rate.

Coupling torque to the vertical axis from the rotation

axis (Z axis) is about 3 to 7 % in many cases (single /

1 / 5 / 10 / 50PPS). However, in some high-rate

cases (20 / 100 / 256PPS), coupling torque is maxi-

mum 50 %. The reason being that a torsional mode

or a rotational axis parallel mode might be excited

and coupling torque around the other axes was in-

creased. Actually high-order flexible modes are ex-

cited in those cases. Fig.22 shows a transfer charac-

teristic of the mathematical model.

(1) Equations of inertial load

{ }

1 1 1 1 1 2 1

1 1

1

1

1 1 2 1 1 1

( ) 1,2,....

( )

i i i i i i

i i

i

i

i

i i i i

i

I D K i

I

I

T K D

θ θ θ θθ

θ

θ θ θ

+ = − =

=

= − − −

∑∑∑

��

�

Mode No. of Inertial Load

Pointing Error of Inertia C.M.

Reaction Torque from Inertia to H/D

(2) Equations of H/D mechanism

{ }2 2 2 2 2 3 2 1

2 2 3 2 2 2 Reaction Torque from H/D to Attachment

ˆ( )

ˆ( )

I D K T

T K D

θ θ θ θ θ

θ θ θ θ

+ = + − + = − + − −

��

�

(3) Equations of motor attachment

( )

3 3 3 3 3 3 2

3 3

3

3

3

2 2

3

3 3 3 3 3

1,2,....

1,2,....

j j j j j j j

j j

j

j

j

j

j

k

k

j j j j

j

I D K T j

I

I

IT T k

I

T K D

θ θ θθ

θ

θ θ

+ = − + =

=

= =

= − − −

∑

∑

∑∑

��

�

Mode No. of Attachment

Pointing Error of Attachment C.M.

Mode No. of Attachment

Reaction T

orque from Attachment to Stator Side

where,

1 2 3, ,

ˆ

2

1, 2,3

1, 2,....

i i

mn m mn mnD I K

m

n

θ θ θθ

ζ===

No. of the Object

Mode No. of the Object

：Angle at Inertial Cordinate System

：Quantized Input Angle

I11 I12 I13

K11 K12 K13D11 D12 D13

I2 H/D Output Axis

K2 D2

I31I32

I33

K31

K32

K33

D31

D32

D33

C.M.

θ1

C.M.

θ3

θ2

C.M.θ̂

Input Angle（Quantized Input）

Inertial L

oad

（Fle

x）H

/D

Attac

hm

ent （

Fle

x）

Fig.21. Mathematical Disturbance Model Schematic

Fig.22. Transfer Characteristic of Stepping Motor

Mathematical Disturbance Model

7. Comparison between Identified Model and Test

To confirm the effectiveness of the proposed

mathematical model, we show Fig.23 and Fig.24 in

which pointing stabilities calculated by test data and

model simulation are shown. The pointing stabilities

are calculated in case of a rigid satellite (MOI = 1

[kgm2]).

We confirmed that the mathematical model can be

well identified to the test data when the damping

ratio of inertial load and H/D are both set to 0.02.

Comparison between Type-3 Test Data and Identified Mathematical ModelShort Term Pointing Stability

1.57E-05

3.29E-05

5.63E-06 5.85E-06 6.19E-06

1.11E-05

2.19E-05

4.96E-05

4.66E-06

3.52E-05

2.47E-05

4.66E-06

3.34E-06

4.80E-06

1.19E-05

2.15E-05

6.33E-05

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1 10 100 1000


Short

Term

Poin

ting

Sta

bilit

y [r

ad/dt

1 s

ec, P

-P]

MOOG Type-3

Identified Model

Fig.23. Comparison between Type-3 Test Data and

Identified Mathematical Model

(Short Term Pointing Stability)

Comparison between Type-3 Test Data and Identified Mathematical Model

Middle Term Pointing Stability

1.43E-03

2.95E-03

7.96E-04 8.62E-04 8.16E-04

1.13E-03

2.47E-03

5.13E-03

4.24E-04

3.09E-03

2.16E-03

3.84E-04

2.90E-04

5.61E-04

1.40E-03

2.86E-03

6.96E-03

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1 10 100 1000


Mid

dle

Ter

m P

ointing

Sta

bilit

y [r

ad/dt

2 se

c, P

-P]

MOOG Type-3

Identified Model

Fig.24. Comparison between Type-3 Test Data and

Identified Mathematical Model

(Middle Term Pointing Stability)

7. CONCLUSION

A stepping motor mathematical disturbance model

was proposed. The effectiveness of the mathematical

model was confirmed by the comparison between

test data and model simulation on pointing stability

basis. The mathematical model is constructed only

by identification of some representative parameters

such as H/D torsional stiffness and flexibility of iner-

tial load.

REFERENCES Kamiya, T., Kurii, T. and Kawakatsu, Y.: On the

Internal Disturbance Control and Pointing Accu-

racy of SELENE Satellite, Proceedings of the

45th Space Sciences and Technology Conference.

JSASS, 2001

Kamiya, T., Kurii, T., Kawakatsu, Y.: Microvibration

Management and Pointing Stability Analysis of

SELENE Satellite, Proceedings of the 16th

IFAC Symposium, Saint-Petersburg, Russia,

Volume 1, P.143-148., 14-18 June, 2004

10-1

100

101

102

103

104

-200

-150

-100

-50

0

50Bode Diagram

Mag

nitu

de (

dB)

10-1

100

101

102

103

104

-400

-350

-300

-250

-200

-150

-100

-50

0

Phas

e (d

eg)

Frequency (Hz)

Documents

Stepping Motor Driving Disturbance Test and Identification of ...Stepping Motor Driving Disturbance Test and Identification of Mathematical Disturbance Model Toshio Kamiya NEC TOSHIBA