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High Accuracy Attitude Control for Pointing to the Sun
HIGH ACCURACY ATTITUDE CONTROL FOR POINTING TO THE SUN
Tsunenori HONDA The Department of Applied Physics and Systems Engineering , The Government Mechanical Laboratory , Japan
Tsuguo KOHNO The Department of Applied Physics and Systems Engineering , The Government Mechanical Laboratory , Japan
exampl e a granul ar spot , and study more detail s of the activity of the sun. For this purpose , more accurate attitude control system of rocketnosecone and a high accuracy sun fo llower are required .
ABSTRACT Many observations of solar ultraviolet rays in terms of rockets have been made . The accuracy of pointing of a roc ket towards the sun is now within one a rc-min and spectrum anal yses on the whole surface or the fringe of the sun were made with this pointing accuracy .
The re l ationships between the purposes of observ ation of the sun and the required point i ng accuracy towards the sun are summerized as shown in Tabl e 1:
Astronomers , however , wish to study particular small parts of the sun . For that purpose , accuracy of attitude control of the rocket has to be within one arc-sec about pitch , yaw and rol l axis , respectively .
Tabl e 1.
Such high accuracy attitude control system planned was outlined and the di gital computer simul ation was made. The system is assumed to consist of three parts : (1) the coarse control system in terms of gas jets (2) the fine contro l system in terms of re act ion wheels (3) the sunfollower . (see Fig. 1)
Purposes of observation and the required poi nting accuracy
Purposes of observation
Required pointing accuracy towards the sun
l. Average spectrum
at most a few arc - min
or; a v/hole image of the sun
First, initially spinnin~ nos econe is control l ed to despin anrl to su~press precess ion. Secondly , the reaction wheels co ntr ol the attitude of nosecone within the error of a few arc - sec . Final l y the sun- follower keeps the image of the sun within the error of one arc - sec .
2 . Spectrum of a
part of the sun
3. Spectrum of a granul ar spot , a black spot , etc.
In this paper , responses of both the coarse and the fine control system a re discussed based on the di gita l computer simulation.
a few arc - sec better than a few arc - sec
In order to satisfy the demand of high reso l ution observation , the third term in Table 1, an attitude control system of rocket - nosecone for pointing towards the sun was pl anned and the digital computer simul ation of the system was made . The control system to get high accuracy pointing towards the sun consists of three parts : a coarse control system of three axes , pi tch, yawand roll axis ; a fine control system of three axes ; a sun- follower .
INTRODUCTION Nany kinds of observations of the sun have ever been performed in terms of rockets without disturbance of air and much val uable data have been obtai ned . Spectrum ana lyses of ul traviolet rays of the sun , however , have been li mited to the average va lue on a whole i mage of the sun. This is because the accuracy of the present attitude contro l of rocket nosecone is at most one arc - min and the resolution is at most one-t enth of the diameter of the sun .
2.
Recent l y, astronomers wish to obtain the spectrum of particular small parts of the sun , for
The coarse contro l system despins initial spinning about the roll axis , suppress the precession and
In this paper , both the coa r se control system and the fine control system are discussed.
532
OUTLI NE
make the nose cone point towards the sun within the accuracy of one arc-min. It is assumed that gas jets are used to get control torque and three rategyros as sensors of three angular rates. Hence, accuracy within an -arc-min cannot be expected.
The purposes of the coarse control stage are despinning, suppressing precession using rategyros as rate sensors and controlling attitude to the error of one arc-min in terms of gas jets. The despin control is not bang-bang but continuous because the continuous control is expected to be surer and more accurate. The dual mode control is better than simple linear control as shown in Fig. 3. In this example, the maximum control torque C is equal to 0.7kg.m, and a few switchin~Zlevels from maximum control to linear one were tried as shown with dashed lines. Fig. 4 shows the relationships between the time requi re d in the coarse control for despin,wIO and
When the squared sum of angular pitch rate W)(, yaw rate
w im•
As for pitch and yaw rate, both linear and dual mode control were also discussed. Responses of the continuous control to an ititial rate are shown in Fig. 5. On the other hand, Fig. 6 shows a response of dual control. This sophisticated dual control make the frequency of oscillation slightly small, but is worse in damping. Thus the linear control is thought more practical.
Estimation of moment of inertia about each axis
About roll axis: moment of inertia of cover
0.0075 kg.m.sec
m.i. of gas cylinders
0.0011
m.i. of fine controller
0.0336
In ac tua l sensors and actuators, noise and error are inevitable. Fig. 7 shows an example in which 2.5% random noise was assumed to disturb the roll rate sensor.
2
4. m.i. of observation devices and others I
0.0066
= C = 0 .05 kg.m.sec
z
When the squared sum of three axes rates is less than 0.1, and also angular deflection is less than one arc-min, the coarse control is stopped and a fine c(mtrol system starts its control operation. Three angular rates are very small and the differential output of solar sens ors gives the angular deflection of attitude. The error signal on each axis is transmitted to a compensation circuit and drives a reaction wheel. The block diagram is shown in Fig. 8.
2
About pitch or yaw axis: moment of inertia of cover
I 3.
0.15 kg.m.sec
m.i. of gas cylinders
0.16
m.i. of fine controller
0.04
m.i. of observation devices and others
0.44
I
x
y
=
1.0 kg .m.sec
2
The responses of pitch and yaw angle to initial deflections are shown in Fig. 9. Very stable transient responses were resulted in. Fig. 10 shows examples of responses to disturbance torque. In practice, whenever any part of observation devices operate, disturbance torque causes the error of attitude. This situation is supposed and simulated. The figure illustrates such examples and in this figure, the disturbance torque of 0.02 kg.m. in amplitude were given at arrow-marks.
2
COARSE COTROL SYSTEM The dynamics of nose cone are described as
.
A-C
Wy
c-A
Wx :=
=
Wl =
A
A
WYWi
FINE CONTROL SYSTEM
c
+ ---;i\
+
5.
Cy ~
CONCLUSION
In order to make a pointing towards the sun within one arc-sec in accuracy, an attitude control system is outlined and examined i n terms of digital computer simulation.
Cx C
The block diagram of the coarse control system is shown in Fi g . 2 .
The coarse control system with gas jets has a dual mode for despin control and a linear control mode for pitch and yaw axes.
533
Jl-~~~~-- 17KJ-". ~ o -,
cz '
. L-. -.
ill ----~
Llntor mode 0 0
co
Observation DevIces -
o·
f-
..
8 '" Fine Controt
'"
_. l_
L
Devices
Fi g . 1
Outline of a sounding rocket nosecone
L1ZE] ,ill
U <1>
Fig. 2
."
20
...
Linear
3
2
cont rol
Dual mode control
10
-----
:----------
- - - - - - -- -- - - -
2.0 2
4
5
6
7
t
Fig. 3
8
(s~C)
Responees of coarse control for despinning
534
~
'!i
~HI~ ·3
.t1
~
>-
.3'
·3
w. Iwr i I
I
i
J
CoarEe control systerr for desp i nning
I z = 0.05 kg·m·sec'
'-
o
- "!
,
30
;:
._-
t:,ti ,~
5\ N
~
-3>- 3 3 3'
.."+ "~ '~"
o·
N
Coarse Control
ID--
Line-ar ~
0
Devices
--- ( The same os below)
0
0.6
10 pitch rot. control torque
w zo=3U
0 .'
•
! 0. 2
J
: i \ /\: \]\j V "'.: '-2 "-'
1 \1 V\j 1 t (sec) Ht--ft+\H-\---------------------------.jo.2 \ ~ \~
- 02
0.5
1.0
- 03
Fig. 4
Relationship betw. switching level and time required for coarse control for despinning
0.3
"\
H,-'----------------------------------lo. • ,
,,
2.0
;l-- - ----------------- -- -- -----10. - -------------~
Fig. 6
1000
1 pitCh
0
.'-
~ ?SO
0.1
0
-;4:__...._="__ _+
3
SOO
----------------1
I
, ,/
,
~\,~ ,, ,
--
without noise with random noise
I' 2.5 S I
!
,
I
I ._-----------_. --------~ I
Fig. 5
1 \
i ,I
tine) -0 .1
-0 2
,
.
rat.
yOW (at.
3'
Response and control torque in dual mode coarse control
Responses in linear coarse control t (sec J
Fig. 7
535
Effects of random noise in coarse despinning control
O2
wy =C-A ww > Fy>Dy A x A
w,
Z
Reaction heel s
Fig. 8
Dynamics of nosecone
Fine attitude control system in terms of reaction wheels
-4,---------------------,--------------------,
,'0
10 I--------------------~
,
g
8
'" 'f~ ~ '" i··,I
0 .5
1.0
1.5
Z.O
t (sec)
Fig. 9
- - 1 sec
Responses of pitch and yaw angle in fine control
t
Fig. 10
536
( se c)
Responses of pitch angle in fine control to impulse disturbances
Following the coarse control, a fine control in terms of reaction wheels operates and the angular errors about three axes will be within one arcsec.
DISCUSSION
Q. What hypothesis have you made on the centre of brilliance of the sun?
The s un-follower, which was not included in this paper, is to keep the complete image of the s~ within the range of the o bse rvation device s i n higher accuracy.
A. We have assumed random noise and we simulated it. We took different amplitudes with a maximum of 2.5% of the instantaneous angular velocity (on each axis).
NOMENCLATUR~:
I
Moment of inertia
A
Moment of i nertia about pitch or yaw ax i s
C (without subscripts) : Momen t of iner t i a about roll axis
w: Angu l ar velocity W : Switching level from coarse to fine contro l 6l
i n squared sum of three angular velocities C (with subscripts) : Coarse control torque s : Laplace
~ ~e r ator
K, K , K , Km' Cm : Conu t ants A I ~
m
: Time constants of re action wheels
S
Angle
E
Angular error
F:
Fine contro l torque
D:
Distu rbance torque
x
PLtch ax is
y
YaH a xis
z
Roll ax is
m
Allow ab le maximum va l ue
0
Initi al val ue
s
Switching
REFERENCE M. HI GASHIGUCHI and K. SHIRO~A : Simulat i on of Automatic Contro l of a Spinning Rocket (written in J apanese) , PrPlrint of the Seventh Meeting of the Japan ese Society of Inzt rument and Control Engin eers: Se ptembe r 1968 , p.355 - 356
53 7
Tsunenori HONDA The Department of Applied Physics and Systems Engineering , The Government Mechanical Laboratory , Japan
Tsuguo KOHNO The Department of Applied Physics and Systems Engineering , The Government Mechanical Laboratory , Japan
exampl e a granul ar spot , and study more detail s of the activity of the sun. For this purpose , more accurate attitude control system of rocketnosecone and a high accuracy sun fo llower are required .
ABSTRACT Many observations of solar ultraviolet rays in terms of rockets have been made . The accuracy of pointing of a roc ket towards the sun is now within one a rc-min and spectrum anal yses on the whole surface or the fringe of the sun were made with this pointing accuracy .
The re l ationships between the purposes of observ ation of the sun and the required point i ng accuracy towards the sun are summerized as shown in Tabl e 1:
Astronomers , however , wish to study particular small parts of the sun . For that purpose , accuracy of attitude control of the rocket has to be within one arc-sec about pitch , yaw and rol l axis , respectively .
Tabl e 1.
Such high accuracy attitude control system planned was outlined and the di gital computer simul ation was made. The system is assumed to consist of three parts : (1) the coarse control system in terms of gas jets (2) the fine contro l system in terms of re act ion wheels (3) the sunfollower . (see Fig. 1)
Purposes of observation and the required poi nting accuracy
Purposes of observation
Required pointing accuracy towards the sun
l. Average spectrum
at most a few arc - min
or; a v/hole image of the sun
First, initially spinnin~ nos econe is control l ed to despin anrl to su~press precess ion. Secondly , the reaction wheels co ntr ol the attitude of nosecone within the error of a few arc - sec . Final l y the sun- follower keeps the image of the sun within the error of one arc - sec .
2 . Spectrum of a
part of the sun
3. Spectrum of a granul ar spot , a black spot , etc.
In this paper , responses of both the coarse and the fine control system a re discussed based on the di gita l computer simulation.
a few arc - sec better than a few arc - sec
In order to satisfy the demand of high reso l ution observation , the third term in Table 1, an attitude control system of rocket - nosecone for pointing towards the sun was pl anned and the digital computer simul ation of the system was made . The control system to get high accuracy pointing towards the sun consists of three parts : a coarse control system of three axes , pi tch, yawand roll axis ; a fine control system of three axes ; a sun- follower .
INTRODUCTION Nany kinds of observations of the sun have ever been performed in terms of rockets without disturbance of air and much val uable data have been obtai ned . Spectrum ana lyses of ul traviolet rays of the sun , however , have been li mited to the average va lue on a whole i mage of the sun. This is because the accuracy of the present attitude contro l of rocket nosecone is at most one arc - min and the resolution is at most one-t enth of the diameter of the sun .
2.
Recent l y, astronomers wish to obtain the spectrum of particular small parts of the sun , for
The coarse contro l system despins initial spinning about the roll axis , suppress the precession and
In this paper , both the coa r se control system and the fine control system are discussed.
532
OUTLI NE
make the nose cone point towards the sun within the accuracy of one arc-min. It is assumed that gas jets are used to get control torque and three rategyros as sensors of three angular rates. Hence, accuracy within an -arc-min cannot be expected.
The purposes of the coarse control stage are despinning, suppressing precession using rategyros as rate sensors and controlling attitude to the error of one arc-min in terms of gas jets. The despin control is not bang-bang but continuous because the continuous control is expected to be surer and more accurate. The dual mode control is better than simple linear control as shown in Fig. 3. In this example, the maximum control torque C is equal to 0.7kg.m, and a few switchin~Zlevels from maximum control to linear one were tried as shown with dashed lines. Fig. 4 shows the relationships between the time requi re d in the coarse control for despin,wIO and
When the squared sum of angular pitch rate W)(, yaw rate
w im•
As for pitch and yaw rate, both linear and dual mode control were also discussed. Responses of the continuous control to an ititial rate are shown in Fig. 5. On the other hand, Fig. 6 shows a response of dual control. This sophisticated dual control make the frequency of oscillation slightly small, but is worse in damping. Thus the linear control is thought more practical.
Estimation of moment of inertia about each axis
About roll axis: moment of inertia of cover
0.0075 kg.m.sec
m.i. of gas cylinders
0.0011
m.i. of fine controller
0.0336
In ac tua l sensors and actuators, noise and error are inevitable. Fig. 7 shows an example in which 2.5% random noise was assumed to disturb the roll rate sensor.
2
4. m.i. of observation devices and others I
0.0066
= C = 0 .05 kg.m.sec
z
When the squared sum of three axes rates is less than 0.1, and also angular deflection is less than one arc-min, the coarse control is stopped and a fine c(mtrol system starts its control operation. Three angular rates are very small and the differential output of solar sens ors gives the angular deflection of attitude. The error signal on each axis is transmitted to a compensation circuit and drives a reaction wheel. The block diagram is shown in Fig. 8.
2
About pitch or yaw axis: moment of inertia of cover
I 3.
0.15 kg.m.sec
m.i. of gas cylinders
0.16
m.i. of fine controller
0.04
m.i. of observation devices and others
0.44
I
x
y
=
1.0 kg .m.sec
2
The responses of pitch and yaw angle to initial deflections are shown in Fig. 9. Very stable transient responses were resulted in. Fig. 10 shows examples of responses to disturbance torque. In practice, whenever any part of observation devices operate, disturbance torque causes the error of attitude. This situation is supposed and simulated. The figure illustrates such examples and in this figure, the disturbance torque of 0.02 kg.m. in amplitude were given at arrow-marks.
2
COARSE COTROL SYSTEM The dynamics of nose cone are described as
.
A-C
Wy
c-A
Wx :=
=
Wl =
A
A
WYWi
FINE CONTROL SYSTEM
c
+ ---;i\
+
5.
Cy ~
CONCLUSION
In order to make a pointing towards the sun within one arc-sec in accuracy, an attitude control system is outlined and examined i n terms of digital computer simulation.
Cx C
The block diagram of the coarse control system is shown in Fi g . 2 .
The coarse control system with gas jets has a dual mode for despin control and a linear control mode for pitch and yaw axes.
533
Jl-~~~~-- 17KJ-". ~ o -,
cz '
. L-. -.
ill ----~
Llntor mode 0 0
co
Observation DevIces -
o·
f-
..
8 '" Fine Controt
'"
_. l_
L
Devices
Fi g . 1
Outline of a sounding rocket nosecone
L1ZE] ,ill
U <1>
Fig. 2
."
20
...
Linear
3
2
cont rol
Dual mode control
10
-----
:----------
- - - - - - -- -- - - -
2.0 2
4
5
6
7
t
Fig. 3
8
(s~C)
Responees of coarse control for despinning
534
~
'!i
~HI~ ·3
.t1
~
>-
.3'
·3
w. Iwr i I
I
i
J
CoarEe control systerr for desp i nning
I z = 0.05 kg·m·sec'
'-
o
- "!
,
30
;:
._-
t:,ti ,~
5\ N
~
-3>- 3 3 3'
.."+ "~ '~"
o·
N
Coarse Control
ID--
Line-ar ~
0
Devices
--- ( The same os below)
0
0.6
10 pitch rot. control torque
w zo=3U
0 .'
•
! 0. 2
J
: i \ /\: \]\j V "'.: '-2 "-'
1 \1 V\j 1 t (sec) Ht--ft+\H-\---------------------------.jo.2 \ ~ \~
- 02
0.5
1.0
- 03
Fig. 4
Relationship betw. switching level and time required for coarse control for despinning
0.3
"\
H,-'----------------------------------lo. • ,
,,
2.0
;l-- - ----------------- -- -- -----10. - -------------~
Fig. 6
1000
1 pitCh
0
.'-
~ ?SO
0.1
0
-;4:__...._="__ _+
3
SOO
----------------1
I
, ,/
,
~\,~ ,, ,
--
without noise with random noise
I' 2.5 S I
!
,
I
I ._-----------_. --------~ I
Fig. 5
1 \
i ,I
tine) -0 .1
-0 2
,
.
rat.
yOW (at.
3'
Response and control torque in dual mode coarse control
Responses in linear coarse control t (sec J
Fig. 7
535
Effects of random noise in coarse despinning control
O2
wy =C-A ww > Fy>Dy A x A
w,
Z
Reaction heel s
Fig. 8
Dynamics of nosecone
Fine attitude control system in terms of reaction wheels
-4,---------------------,--------------------,
,'0
10 I--------------------~
,
g
8
'" 'f~ ~ '" i··,I
0 .5
1.0
1.5
Z.O
t (sec)
Fig. 9
- - 1 sec
Responses of pitch and yaw angle in fine control
t
Fig. 10
536
( se c)
Responses of pitch angle in fine control to impulse disturbances
Following the coarse control, a fine control in terms of reaction wheels operates and the angular errors about three axes will be within one arcsec.
DISCUSSION
Q. What hypothesis have you made on the centre of brilliance of the sun?
The s un-follower, which was not included in this paper, is to keep the complete image of the s~ within the range of the o bse rvation device s i n higher accuracy.
A. We have assumed random noise and we simulated it. We took different amplitudes with a maximum of 2.5% of the instantaneous angular velocity (on each axis).
NOMENCLATUR~:
I
Moment of inertia
A
Moment of i nertia about pitch or yaw ax i s
C (without subscripts) : Momen t of iner t i a about roll axis
w: Angu l ar velocity W : Switching level from coarse to fine contro l 6l
i n squared sum of three angular velocities C (with subscripts) : Coarse control torque s : Laplace
~ ~e r ator
K, K , K , Km' Cm : Conu t ants A I ~
m
: Time constants of re action wheels
S
Angle
E
Angular error
F:
Fine contro l torque
D:
Distu rbance torque
x
PLtch ax is
y
YaH a xis
z
Roll ax is
m
Allow ab le maximum va l ue
0
Initi al val ue
s
Switching
REFERENCE M. HI GASHIGUCHI and K. SHIRO~A : Simulat i on of Automatic Contro l of a Spinning Rocket (written in J apanese) , PrPlrint of the Seventh Meeting of the Japan ese Society of Inzt rument and Control Engin eers: Se ptembe r 1968 , p.355 - 356
53 7