Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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A~ uDE POlh.l~G ER~OR CORRECTION ~Y~TEM AND
M~THOD FOR GEO~YNCHRONOUS ~ATELLITES
Technical Field
The present invention relates to attitude control for
5 geosynchronous satellites and, more particularly, to
attitude control systems and methods for compensating
roll and yaw pointing errors that occur as a consequence
of orbit deviation from the nominal equatorial orbit
plane.
Backqround Art
Communications and navigation satellites are
typically placed in a circular orbit, known as a
geosynchronous or geostationary orbit, having a period of
revolution equal to that of the earth to provide
15 synchronized rotational velocities. Ideally, the
satellite is placed in an orbit plane coincident with the
equatorial plane of the earth so that the antenna or
antennas of the satellite can be pointed to desired
terrestrial locations. In general, geosynchronous
20 satellites are momentum stabili~ed, either by spinning the
satellite itself or providing a momentum wheel, with the
spin axis maintained normal the desired equatorial orbit
plane and the global beam boresight aligned normal to the
spin axis. In this ideal situation, the global beam
25 boresight points to a subsatellite area that remains fixed
as the satellite and earth rotate in synchronism.
Several factors induce orbital drift by which the
satellite orbit tilts relative to the nominal equatorial
orbit plane. This orbit tilt, which accumulates with
30 time, creates roll and yaw po.inting errors. More
specifically, the gravitational effect of the sun and the
moon on the satellite and the variations in the earth's
gravitational field caused by the non-spherical shape of
the earth introduce orbit perturbing effects which cause
35 the plane of the satellite's orbit to tilt with respect
the desired equatorial plane. The net effect of these
orbit-disturbing influences is to cause the inclination of
the satellite orbit to drift slowly at a rate of between
$~
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0.75~ and 0.95~ per year.
As the orbit inclination increases, the terrestrial
illumination pattern of the satellite's antenna or
antennas drifts from the desired aiming area as a
5 consequence of the roll and yaw pointing errors. For
example and as shown in ~IGS. 1 and 2, a satellite 'S'
moving in an earth orbit in the direction indicated at an
angle i to the equatorial orbit plane will intersect the
equatorial plane at an ascending node Na where the
10 satellite passes from the southern hemisphere to the
northern hemisphere and again intersect the equatorial
orbit plane at the descending node Nd when moving from the
northern hemisphere to the southern hemisphere. ~s the
satellite progresses from its ascending node Na to its
15 maximum northern latitude, it passes through its north
anti-node Nn~ and, conversely, as the satellite progresses
from its descending node Nd to its maximum southern
latitude, it passes through its south anti-node Ns~
As a consequence of the inclination angle i between
20 the actual satellite orbit and the nominal equatorial
plane, the antenna illumination pattern that the satellite
projects onto the surface of the earth will suffer from
the adverse effects of sinusoidal variations of the
north-south and rotational motions, corresponding to the
25 spacecraft roll error and yaw errors, respectively. For
example, in the case where the satellite spin axis is
normal to the inclined orbit plane, as shown in FIG~ 2, as
the satellite progresses through its ascending node Na~
the roll error (FIG. 3A) of the terrestrial illumination
30 pattern is zero while the yaw error (FIG. 3B) is at a
maxima. As the satellite progresses towards its north
anti-node Nn~ the roll error increases until attaining a
maxima at the north anti-node Nn while the yaw error
reduces to zero. As shown in FIG. 2, when the satellite
35 is at its north anti-node Nn~ the global beam boresight
will be directed to point Sl on the earth's surface.
Conversely, as the satellite progresses from the north
anti-node Nn~ the roll error diminishes to zero and the
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yaw error once again increases to a maxima at the
descending node Nd. When the satellite attains its south
anti-node NS I as shown in FIG. 2, the global beam
boresight will be directed to point S2 on the earth's
5 surface.
The roll and yaw errors introduced by orbit
inclination depend on the orientation of the spacecraft
spin axis. In the general case where the spin axis is
tilted by an angle ~ from the axis normal to the
10 equatorial plane, the roll error will be (1.178i-~)
SIN nt and the yaw error will by -~ COS nt, where i is
the orbit inclination, n is the orbit angular rate, and t
= time with t = 0 at the ascending node. As can be
appreciated roll and yaw error are functionally related
15 and one can be determined as a function of the other.
One technique proposed for the reduction of the roll
pointing error is to intentionally tilt the vehicle spin
axis relative to the equatorial orbit normal. As shown in
FIG. 2, the satellite spin axis ~dotted line illustration)
20 is tilted at an angle ~ to effectively reposition the
global beam boresight of the satellite to the area SO
obtained with the satellite in the equatorial orbit.
While the roll error will be effectively zero, the yaw
error will be increased by the contri~ution of the spin
25 axis tilt angle e and is represented by -(i+~) COS
nt. Where circularly polarized communications or narrow
spot beams are utilized, the increased yaw error is
unacceptable.
In conventional satellite systems, thrusters are used
30 to periodically correct the inclination of the orbit by
expending fuel, this use being termed north-south
station-keeping. In particular and for a ten-year
mission, this station-keeping function can require as much
as 20% of the total initial mass of the satellite with a
35 substantial fraction of the propellant, approximately 90%,
used for orbit inclination correction and the remainder
used for other in-orbit maneuvers including pitch error
correction (FIG. 3C). In general, the operating life of a
--4--
geosynchronous satellite is limited by the station-keeping
fuel requirements and operating life can be extended by
terminating north-south station-keeping. However,
cessation of north-south station-keeping introduces
5 attitude errors which must be corrected.
In recognition of the substantial on-board fuel
requirements for inclination correction maneuvers, various
attitude control systems have been proposed to correct
attitude errors introduced by orbit inclination. For
10 example, U.S. Patent No. 4,084,772 to Muhlfelder presents
a system for roll/yaw vehicle steering in which the
vehicle is stabilized by a momentum wheel in which angular
velocity of ~he wheel is varied in a sinusoidal manner
during the course of the orbit revolution to vary the
15 associated vehicle momentum and effect a sinusoidal
variation in the roll attitude of the vehicle with each
orbit revolution. In U.S. Patent No. 4,062,509 to
Muhlfelder et al., a magnetic torquing system is provided
by which a vehicle magnetic ~ie7d is established to
20 interact with the earth's magnetic field to provide a
measure of roll and yaw attitude control.
Disclosure of Invention
The present invention provides a system and method
for attitude control in a geosynchronous satellite to
25 compensate for pointing errors consequent to orbit
inclination variation from the nominal equatorial orbit
plane. A momentum vector is established for the satellite
with the momentum vector fixed in inertial space and
coupled to the satellite through a gimbal system providing
30 at least a one degree-of-freedom relationship between the
vehicle and the momentum vector. The gimbal axis is
provided along at least one of the major satellite axes,
such as roll and/or yaw axis, with a gimbal torquer
provided to torque the satellite about the inertially
35 fixed momentum vector to correct the attitude errors. The
roll and yaw errors due to orbit inclination depend on the
angular momentum direction and can be determined
analytically as a function of orbit inclination and the
39
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location of the satellite in its orbit. Depending upon
the particular configuration, the gimbal torquer rotates
the spacecraft about the roll axis and/or the yaw axis in
the proper timed relationships to correct the pointing
5 errors as the satellite revolves about the earth. In
addition to the roll and yaw errors introduced by orbit
inclination, additional pointing errors introduced by
other external disturbance torques, such as a solar
torques, are corrected by usiny a conventional attitude
10 control system consisting of an earth sensor and attitude
control torquers.
In a first embodiment of the present invention, a
spin-stabilized satellite includes a spun section, which
provides an inertially fixed momentum vector, and a despun
15 antenna assembly that is coupled to the spun section
through a two degree-of-freedom gimbal set having a first
gimbal mounted for rotation about the roll axis and the
other gimbal mounted for rotation about the yaw axis.
Gimbal torquers are provided to apply a torque to the
20 gimbal associated with the respective roll or yaw axis
correction and thus torque the antenna assembly about the
inertially fixed momentum vector established by the spun
section to correct the roll and yaw pointing errors
introduced by orbit inclination. The roll and yaw gimbal
25 torquers are driven in a sinusoidal manner using a 24 hr.
period. By utilizing the satellit~ body as the angular
momentum device and effecting selectively controlled
coupling to the antenna assembly through the two
degree-of-freedom gimbal set, a substantial measure of
30 pointing error correction is provided without the need to
expend fuel for orbit inclination correction. While a two
degree-of-freedom relationship is preferred, a one
degree-of-freedom relationship along at least one of the
roll or yaw axes can be provided to effect correction
35 a]ong one of the axes.
In another embodimen~ of the present invention, a
momentum wheel is coupled to the vehicle through a two
degree-of-freedom gimbal set with torquers provided along
2~
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the roll and yaw axes to effect rotation of the vehicle
about the inertially fixed momentum vector. As in the
case of the first embodiment, the roll and yaw gimbal
torquers are driven in a sinusoidal manner using a 24 hr.
5 period.
In still another embodiment of the present invention,
the angular momentum direction is selected such that one
of the two errors, either roll or yaw, due to orbit
inclination becomes zero. The other error is corrected by
lQ providing a single degree-of-freedom gimbal along that
axis and rotating the spacecraft to the error, which is
accomplished by a combination of torques applied to the
gimbal to rotate the vehicle relative to the inertially
fixed momentum vector.
The present invention advantageously provides an
apparatus and method by which a geosynchronous satellite
can readily compensate for roll and yaw pointing errors
consequent to orbit inclination drift from the nominal
equatorial orbit in a fuel-efficient manner to
20 dramatically extend the operating life of the satellite in
comparison with prior systems and methods that depend upon
fuel-expending thrusters to correct orbit inclination.
Brief Description of the Drawings
The present invention is described below, by way of
25 example, with reference to the accompanying drawings,
wherein:
FIG. 1 is a perspective view, in schematic form, of
an equatorial orbit plane and an inclined orbit plane
about the earth and illustrating various orbit nodes and
30 anti-nodes;
FIG. 2 is a two-dimensional schematic view of the
inclined and equatorial orbits of FIG. l;
FIG. 3A is a view of the terrestrial surface and the
effect of roll axis pointing error on a terrestrial
35 antenna illumination pattern;
FIG. 3B is a view of the terrestrial surface and the
effect of yaw axis pointing error on a terrestrial antenna
illumination pattern;
-7
FIG. 3C is a view ~ ~he terrestrial surface and the
effect of pitch axis pointing error on a terrestrial
antenna illumination pattern;
FIG. 4 is a pictorial view, in schematic:form, of a
5 first embodiment of the present invention;
FIG. 5 is an isometric projection of a two
degree-of-freedom gimbal set used with the embodiment of
FIG. 4;
FIG. 6 is a representative control loop, illustrated
10 in schematic block diagram form, for effecting control of
a gimbal;
FIG. 7 is a pictorial representation, in schematic
form, of a second embodiment of the present invention;
FIG. 8 is a pictorial representation, in schematic
15 form, of a third embodiment of the present invention; and
FIG. 9 is a pictorial representation, in schematic
form, of a fourth embodiment of the present invention.
Best Mode for Carryinq Out the Invention
A satellite incorporating the present invention is
20 shown in FIG. 4 in pictorial form and is designated
therein generally by the reference character 10. The
satellite 10 is of the spin stabilized type intended for
use in a geosynchronous orbit and includes a spun section
12 and a despun antenna tower 14. The spun section 12 is
25 designed to rotate about the primary vehicl~ axis Ax and
is of conventional design including a generally
cylindrical hull, for example, of the Longeron-type, and a
despin motor and bearing assembly indicated in schematic
form at 16. Depending upon its intended mission, the
30 satellite 10 is equipped with appropriate tracking,
telemetry, and command systems; primary power systems;
thermal control systems; and a propulsion system. As
shown in FIG; 4, the satellite 10 includes a thruster
control system including first, second, and third
35 thrusters Tl, T2, and T3. The thrusters Tn are of
conventional design and are operated in response to
signal-controlled valves to eject propellant, typically
hydrazine, to change the angular momentum of the satellite
~~199
--8~
10. The thrusters Tn illustrated in FIG. 4 are exemplary
only and other thruster Tn organizations are suitable
depending upon the satellite configuration.
In ~ddition to the roll and yaw pointing errors
5 introduced by orbit inclination, as discussed above, there
may be additional errors introduced by other external
disturbance torques, such as a solar torques. These
additional errors are corrected by using a conventional
attitude control system consisting of an earth sensor and
lo attitude control torquers. The output of the earth sensor
is provided to attitude controllers, for example,
thrusters which then function to correct the satellite
attitude caused by the external disturbance torques. An
exemplary earth sensor system is disclosed, for example,
15 in the afore-mentioned U.S. Patent 4,084,772 to
Muhlfelder.
The antenna tower 14, which is also illustrated in
exemplary form, includes a mast 18 and a laterally
extending spar 20 with antennas A1, A2, and A3 mounted at
20 the ends of the mast 18 and spar 20. Depending upon the
vehicle mission, the antennas An are pointed at one or
more terrestrial areas for effecting communications for
broad area and/or spot beam coverage. The mast 18
includes structure for conveying microwave energy from
25 output amplifiers (not specifically shown) of the spun
section 12 to the antennas ~n and, conversely, conveying
received energy to receivers (not shown) within the spun
section 12.
A gimbal unit 22, shown in schematic form in FIG. 4
30 and in detail in FIG. 5, is connected between the despin
motor and bearing assembly 16 and the antenna tower 14.
The gimbal unit 22 allows a selected tilting of the
antenna tower 14 relative to the spun section 12 along two
axes, viz., the roll and yaw axes. Accordingly, the
3~ principal axis of the antenna tower Aant can be
controlled, as explained below, to be coincident with the
principal axis Ax of the spun section 12 or aligned at an
angle relative to the principal axis Ax. As shown in ~IG.
g
5, the gimbal unit 22 includes a support ring 24 that is
structurally connected to the antenna tower 14, an outer
gimbal 26, and an inner gimbal 28 connected to the despin
motor and bearing assembly 16 by a suitable structural
5 member, such as a hollow column (not shown). The outer
gimbal 26 is coupled to the support ring 24 by an outer
gimbal torquer 30 and an outer gimbal position sensor 32
having their respective axes of rotation co-aligned with
the roll axis, for example. In a similar manner, the
10 outer gimbal 26 is coupled to the inner gimbal 28 by an
inner gimbal torquer 34 and an inner gimbal position
sensor 36 having their respective axes of rotation
co-aligned along the yaw axis. The gimbal torquers 30 and
34 are of conventional design, for example, an
15 electrically driven motor and gear train for effecting
relative rotation of the affected gimbal. The gimbal
position sensors 32 and 34 provide output information
regarding the relative angular relationship of the gimbals
and can include, for example, resolvers or optical
20 encoders to provide the necessary angular position
information. Gimbal stops (not shown) are provided to
limit the angular displacement of the gimbals to within
acceptable limits.
The movement of the gimbals 26 and 28 as well as
25 final positioning is controlled by a gimbal control loop,
an exemplary architecture being illustrated in FIG. 6. As
shown, a torquer drive unit 38 accepts an input signal
'CMD' from a command source 40 designating a desired
position and provides an appropriate electrical output
30 signal to the torquer which, in turn, drives its
mechanically connected gimbal (represented in dotted line
illustration in FIG. 5), toward its new position. The
command source 40 can provide the input signal 'CMD', in
part, by command from ground ~ontrol or from on-board
35 processing. A clock CLK provides a 24 hr. timing signal t
with t=0 at the ascending node Na ~FIG. 1). The gimbal
control signal thus varies with time in a sinusoidal
manner as the satellite revolves about the earth. More
CA 02006199 1998-03-20
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specifically, the command signal CMD, as explained more
fully below, includes a SIN nt function for roll axis
correction and a COS nt function for yaw axis correction.
The gimbal position sensor provides an electrical feedback
5 signal to the torquer drive unit 38 indicating the
position of the gimbal with the torquer drive unit 38
controlling the torquer to effect movement to the desired
position and maintenance of that position.
In order to effect roll and yaw axis correction in
10 the context of the organization of FIG. 4, the satellite
spin axis Ax is preferably initially aligned normal to the
inclined orbit plane (FIG. 2) of the satellite, this
inclination also aligning the spin axis Ax at an angle i
relative to the equatorial orbit plane normal. The roll
15 axis gimbal torquer 30 is then controlled by a
time-varying sinusoidal CMD signal -e SIN nt where the
maximum value of e is (0.178 i) and the yaw axis
gimbal torquer 34 is simultaneously controlled by a
time-varying sinusoidal CMD signal i COS nt. The value
20 0.178 is fixed by the geometry of the geosynchronous
orbit, that is, the radius of the earth and the attitude
of the orbit, and n represents the orbit angular rate.
The roll error is biased by -e SIN nt by introducing a
-e SIN nt offset factor into the satellite earth
25 sensor control loop to effect the -e SIN nt offset.
As can be appreciated, the antenna tower 14 will realign
its axis Aant relative to the axis Ax of the spun section
12 to achieve a continuously time-varying correction of
the roll and yaw pointing error with each revolution of
30 the satellite 10. While it is preferred that the
satellite spin axis Ax be initially aligned normal to the
inclined orbit plane of the satellite 10, this alignment
is not necessary and other alignments are possible so long
as the momentum vector of the spun section 12 remains
35 inertially fixed.
The embodiment of FIG. 4 has been described in the
context of a two degree-of-freedom context. If desire~d,
the coupling of the momentum vector provided by the spun
~36~
section 12 to the antenna tower 14 can be through a single
degree-of-freedom connection with the gimbal axis aligned
along one or the other of the roll or yaw axes. Thus
where the single degree-of-freedom connection is aligned
5 on the yaw axis, an of~set factor is introduced in the
earth sensor control loop to effect a roll axis pointing
correction while the gimbal-controlled axis is rotated in
a periodic manner to correct for the yaw axis error.
A second embodiment o~ a satellite incorporating the
10 present invention is illustrated in pictorial form in FIG.
7 and designated generally therein by the reference
character 50. As shown, the satellite 50 is ~ormed as a
parallelepiped with selected portions broken away to
present the interior of the vehicle. For reasons of
15 clarity, associated structure including solar panels,
antennas, and thrusters have been omitted from FIG. 7.
The satellite 50 includes an earth sensor 52 which is
used in conjunction with conventional torquers to correct
attitude errors introduced by external disturbances other
20 than those caused by orbit inclination, these external
disturbances including solar torques, for example. ~s
shown, a momentum wheel 54 is mounted for rotation about a
momentum wheel axis AmW and is carried in an inner gimbal
56 and an outer gimbal 58. The i~ner gimbal 56 is
25 rotatably connected to the outer gimbal by an inner gimbal
torquer 60 and an inner gimbal position sensor 62 having
their respective axes aligned along the yaw axis. The
outer gimbal 58 is rotatably connected to the vehicle
frame or structure by an outer gimbal torquer 64 and an
30 outer gimbal position sensor 66 having their respective
axes co-aligned with the roll axis.
The momentum wheel 54 is driven ky an electric motor
(not shown) and develops a momentum vector H in the
direction indicated with the momentum vector remaining
35 inertially fixed. Since the sinusoidal relationship
between the roll pointing error and the yaw pointing error
is known, a sinusoidally varying yaw axis correction
signal is determinable from the time-varying roll error
9~31
correction command and is likewise provided to the inner
gimbal torquer 60 to effect rotation of the vehicle about
its yaw axis relative to the inertially fixed momentum
vector H. As described above in connection with the
5 embodiment of FIG. 5, if the momentum wheel spin axis is
normal to the inclined orbit plane, the roll error is
biased by -9 SIN nt with the roll axis gimbal torquer
64 controlled by a time-varying sinusoidal CMD signal
e SIN nt where the maximum ~alue of e is (0.178 i)
10 and the yaw axis gimbal torquer 60 is simultaneously
controlled by a time-varying sinusoidal CMD signal i COS
nt. The commands for roll error bias and gimbal angle
control can be provided from ground control or from
on-board processing.
The embodiment of FIG. 7, like that of FIG. 5,
provides a momentum vector, either by spinning the vehicle
itself or by spinning a separate body, and coupling to the
momentum vector through a two degree-of-freedom device to
allow torquing of the vehicle about its roll and yaw axes
20 to correct for the roll and yaw pointing errors as a
consequence of the inclination of the satellite orbit
relative to the nominal equatorial plane. In addition to
effecting torquing of the satellite about an inertially
fixed momentum vector H using a two degree-of-freedom
25 gimbal set as disclosed above, it is also contemplated
that pointing error correction can be effected with a
single-gimbal momentum wheel in combination with the
thruster control system as described below in connection
with the embodiments of FIGS. 8 and 9.
As shown in FIG. 8, a satellite 70 is provided with
an earth sensor 72 and a gimballed momentum wheel 74
mounted for rotation about an axis AmW to develop a
momentum vector H. The momentum wheel 74 is coupled to
the vehicle structure throuyh a single degree-of-freedom
35 gimbal 76. A gimbal torquer 78 and a gimbal position
sensor 80 are mounted in a co-linear relationship with the
yaw axis. The motion of the gimbal 76 throughout the
orbit revolution is controlled a control loop of the type
-13-
presented in FIG. 6 and includes the programmable gimbal
drive unit including a clock capable of precessing the
gimbal through a twenty-four hour cycle, as described
above in relationship to FIG. 6. The roll axis is biased
5 by -e SIN nt where e is the tilt angle with a
maximum value of 0.178 i where i is the orbit inclination.
Roll control is effected by using one or more of the
thrusters Tn in the usual manner to tilt the momentum
wheel spin axis AmW by an angle ~ from the inclined
lO orbit normal. The spacecraft is then rotated with respect
the inertially fixed momentum ~heel axis AmW about the yaw
axis to an angle (i+~) COS nt to correct the errors
introduced by orbit inclination. The commands for roll
error bias and gimbal precession along the yaw axis can be
15 provided from ground control or ~rom on-board processing.
Another embodiment of the present invention is
illustrated in FIG. 9 and, like the embodiment of FIG. 8,
includes a momentum wheel coupled to the vehicle structure
through a single degree-of-freedom gimbal. As shown, a
20 satellite 90 includes an earth sensor ~2 and a momentum
wheel 94 rotating about an axis AmW ~o develop a momentum
vector H. The momentum wheel 94 is coupled to the vehicle
structure through a single degree-of-freedom gimbal 96. A
gimbal torquer 98 and a gimbal position sensor 100 are
25 mounted in a co-linear relationship with the roll axis.
The motion of the gimbal 96 throughout the orbit
revolution is controlled a control loop of the type
presented in FIG. 6 and includes the programmable gimbal
drive unit including a clock capable of precessing the
30 gimbal through a twenty-four hour cycle. The spin axis
AmW of the momentum wheel 94 is nominally kept along the
north/south axis, normal to the equatorial orbit plane.
The satellite 90 is rotated with respect to the inertially
fixed momentum wheel axis AmW about the roll axis by an
35 angle -(i+~) SIN nt where ~ is the tilt angle with
a maximum value of 0.178 i and the roll error is biased by
a -e SIN nt offset value. The command for the roll
error bias and the roll axis gimbal anyles are provided
9~
-14-
from ground control or from on-board processing. The
magnitude of the roll error bias and the roll axis gimbal
angle are updated p~riodically by ground control to take
into account the change in orbit inclination.
The present invention advantageously provides system
and method for controlling a geosynchronous satellite to
continuously correct for pointing errors caused by orbit
inclination drift relative to the nominal equatorial plane
in a fuel-efficient manner. The present invention thus
lO allows for greatly increased service life for
geosynchronous satellites because of a significant
reduction in satellite station-keeping fuel requirements.
