CA2006199C - Attitude pointing error correction system and method for geosynchronous satellites - Google Patents
Attitude pointing error correction system and method for geosynchronous satellitesInfo
- Publication number
- CA2006199C CA2006199C CA 2006199 CA2006199A CA2006199C CA 2006199 C CA2006199 C CA 2006199C CA 2006199 CA2006199 CA 2006199 CA 2006199 A CA2006199 A CA 2006199A CA 2006199 C CA2006199 C CA 2006199C
- Authority
- CA
- Canada
- Prior art keywords
- satellite
- axis
- orbit
- roll
- theta
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Landscapes
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
A system and method for attitude control in a geosynchronous satellite (10) to compensate for roll and yaw pointing errors consequent to orbit inclination variation from the nominal equatorial orbit plane provides for an inertially fixed momentum vector coupled to the satellite (10) through a gimbal system (22) providing a one and preferably two degree-of-freedom relationship with the momentum vector. In a two degree-of-freedom embodiment, the momentum vector is established by spinning the satellite (10) about an axis or providing an independent momentum wheel (54) with the gimbal axes provided along the roll and yaw axes. Gimbal torquers (30,34) torque the satellite (10) about the inertially fixed momentum vector in a time-varying manner to effect correction of the roll and yaw pointing errors.
Additionally, a conventional thruster (Tn) system is provided for pitch axis error correction and large orbit corrections attendant to the station-keeping function.
Roll and yaw pointing errors consequent to orbit inclination drift from the nominal equatorial orbit are corrected in a fuel-efficient manner to extend the operating life of the satellite (10).
Additionally, a conventional thruster (Tn) system is provided for pitch axis error correction and large orbit corrections attendant to the station-keeping function.
Roll and yaw pointing errors consequent to orbit inclination drift from the nominal equatorial orbit are corrected in a fuel-efficient manner to extend the operating life of the satellite (10).
Description
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 $~
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 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 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 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~
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;
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 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 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~
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.
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 $~
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 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 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 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~
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;
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 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 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~
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.
Claims (47)
1. A method of correcting pointing errors in a geosynchronous satellite consequent to orbit inclination, characterized by the steps of:
establishing the momentum vector along an axis other than an axis normal to the equatorial orbit plane;
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with at least a selected one of the roll or yaw axes for effecting rotation of the satellite relative to the momentum vector about the selected axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and torquing the satellite about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of an orbit inclination angle i.
establishing the momentum vector along an axis other than an axis normal to the equatorial orbit plane;
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with at least a selected one of the roll or yaw axes for effecting rotation of the satellite relative to the momentum vector about the selected axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and torquing the satellite about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of an orbit inclination angle i.
2. The method of claim 1, wherein said coupling step further characterized by:
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the roll axis for effecting rotation of the satellite relative to the momentum vector about the roll axis.
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the roll axis for effecting rotation of the satellite relative to the momentum vector about the roll axis.
3. The method of claim 2, wherein said torquing step further characterized by:
torquing the satellite about the roll axis as a function of -~ SIN
nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and ~ has a maximum value of 0.178i.
torquing the satellite about the roll axis as a function of -~ SIN
nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and ~ has a maximum value of 0.178i.
4. The method of claim 1, wherein said coupling step further characterized by:
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the yaw axis for effecting rotation of the satellite relative to the momentum vector about the yaw axis.
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the yaw axis for effecting rotation of the satellite relative to the momentum vector about the yaw axis.
5. The method of claim 4, wherein said torquing step further characterized by:
torquing the satellite about said yaw axis as a function of i COS
nt where t = time with t = 0 at the ascending node and n = the orbit angular rate.
torquing the satellite about said yaw axis as a function of i COS
nt where t = time with t = 0 at the ascending node and n = the orbit angular rate.
6. The method of claim 5, wherein said torquing step further characterized by:
establishing the momentum vector along an axis tilted by an angle .theta. from the inclined orbit normal; and torquing the satellite about said yaw axis by (i+.theta.) COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate, .theta. has a maximum value of 0.178i.
establishing the momentum vector along an axis tilted by an angle .theta. from the inclined orbit normal; and torquing the satellite about said yaw axis by (i+.theta.) COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate, .theta. has a maximum value of 0.178i.
7. The method of claim 1, wherein said coupling step further characterized by:
coupling the momentum vector to the satellite through a two degree-of-freedom connection coincident, respectively, with the roll and yaw axes for effecting rotation of the satellite relative to the momentum vector about the roll and yaw axes.
coupling the momentum vector to the satellite through a two degree-of-freedom connection coincident, respectively, with the roll and yaw axes for effecting rotation of the satellite relative to the momentum vector about the roll and yaw axes.
8. The method of claim 7, wherein said torquing step further characterized by:
torquing the satellite about the roll axis as a function of -.theta. SIN
nt and about said yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
torquing the satellite about the roll axis as a function of -.theta. SIN
nt and about said yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
9. The method of claim 8, wherein said torquing step further characterized by:
establishing the momentum vector along a normal to the inclined orbit plane; and torquing the satellite about the roll axis by -.theta. SIN nt and about said yaw axis by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
establishing the momentum vector along a normal to the inclined orbit plane; and torquing the satellite about the roll axis by -.theta. SIN nt and about said yaw axis by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
10. A method of correcting pointing errors in a geosynchronous satellite consequent to orbit inclination, the satellite of the type having a spun section that establishes a momentum vector along an axis and a despun section, characterized by the steps of:
establishing a momentum vector along an axis other than an axis normal to the equatorial orbit plane;
coupling the momentum vector of the spun section to the despun section through at least a single degree-of-freedom connection coincident with at least a selected one of the roll or yaw axes for effecting rotation of the despun section relative to the momentum vector about the selected axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and torquing the despun section about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of an orbit inclination angle i.
establishing a momentum vector along an axis other than an axis normal to the equatorial orbit plane;
coupling the momentum vector of the spun section to the despun section through at least a single degree-of-freedom connection coincident with at least a selected one of the roll or yaw axes for effecting rotation of the despun section relative to the momentum vector about the selected axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and torquing the despun section about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of an orbit inclination angle i.
11. The method of claim 10, wherein said coupling step further characterized by:
coupling the momentum vector of the spun section to the despun section through at least a single degree-of-freedom connection coincident with the roll axis for effecting rotation of the despun section relative to the momentum vector about the roll axis.
coupling the momentum vector of the spun section to the despun section through at least a single degree-of-freedom connection coincident with the roll axis for effecting rotation of the despun section relative to the momentum vector about the roll axis.
12. The method of claim 11, wherein said torquing step further characterized by:
torquing the despun section about the roll axis as a function of -.theta. SIN nt where t = time with t = 0 at the ascending node, n = the orbit angular rate and .theta. has a maximum value of 0.178i.
torquing the despun section about the roll axis as a function of -.theta. SIN nt where t = time with t = 0 at the ascending node, n = the orbit angular rate and .theta. has a maximum value of 0.178i.
13. The method of claim 10, wherein said coupling step further characterized by:
coupling the momentum vector of the spun section to the despun section through at least a single degree-of-freedom connection coincident with the yaw axis for effecting rotation of the despun section relative to the momentum vector about the yaw axis.
coupling the momentum vector of the spun section to the despun section through at least a single degree-of-freedom connection coincident with the yaw axis for effecting rotation of the despun section relative to the momentum vector about the yaw axis.
14. The method of claim 13, wherein said torquing step further characterized by:
torquing the despun section about the yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate.
torquing the despun section about the yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate.
15. The method of claim 14, wherein said torquing step further characterized by:
establishing the momentum vector along an axis tilted by an angle .theta. from the inclined orbit normal; and torquing the satellite about said yaw axis by (i+.theta.) COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
establishing the momentum vector along an axis tilted by an angle .theta. from the inclined orbit normal; and torquing the satellite about said yaw axis by (i+.theta.) COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
16. The method of claim 10, wherein said coupling step further characterized by:
coupling the momentum vector of the spun section to the despun section through a two degree-of-freedom connection coincident, respectively, with the roll and yaw axes for effecting rotation of the despun section relative to the momentum vector about the roll and yaw axes.
coupling the momentum vector of the spun section to the despun section through a two degree-of-freedom connection coincident, respectively, with the roll and yaw axes for effecting rotation of the despun section relative to the momentum vector about the roll and yaw axes.
17. The method of claim 16, wherein said torquing step further characterized by:
torquing the satellite about the roll axis as a function of -.theta. SIN
nt and about said yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
torquing the satellite about the roll axis as a function of -.theta. SIN
nt and about said yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
18. The method of claim 17, wherein said torquing step further characterized by:
establishing the momentum vector along a normal to the inclined orbit plane; and torquing the satellite about the roll axis by -.theta. SIN nt and about said yaw axis by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
establishing the momentum vector along a normal to the inclined orbit plane; and torquing the satellite about the roll axis by -.theta. SIN nt and about said yaw axis by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
19. A method of correcting pointing errors in a geosynchronous satellite consequent to orbit inclination, characterized by the steps of:
rotating at least one mass about an axis to establish a momentum vector along the axis, the axis other than an axis normal to the equatorial orbit plane;
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with at least a selected one of the roll or yaw axes for effecting rotation of the satellite relative to the momentum vector about the selected axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and torquing the satellite about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of an orbit inclination angle i.
rotating at least one mass about an axis to establish a momentum vector along the axis, the axis other than an axis normal to the equatorial orbit plane;
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with at least a selected one of the roll or yaw axes for effecting rotation of the satellite relative to the momentum vector about the selected axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and torquing the satellite about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of an orbit inclination angle i.
20. The method of claim 19, wherein said coupling step further characterized by:
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the roll axis for effecting rotation of the satellite relative to the momentum vector about the roll axis.
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the roll axis for effecting rotation of the satellite relative to the momentum vector about the roll axis.
21. The method of claim 20, wherein said torquing step further characterized by:
torquing the satellite about the roll axis as a function of -.theta. SIN
nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
torquing the satellite about the roll axis as a function of -.theta. SIN
nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
22. The method of claim 19, wherein said coupling step further characterized by:
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the yaw axis for effecting rotation of the satellite relative to the momentum vector about the yaw axis.
coupling the momentum vector to the satellite through at least a single degree-of-freedom connection coincident with the yaw axis for effecting rotation of the satellite relative to the momentum vector about the yaw axis.
23. The method of claim 22, wherein said torquing step further characterized by:
torquing the satellite about the yaw axis as a function of i COS
nt where t = time with t = 0 at the ascending node and n = the orbit angular rate.
torquing the satellite about the yaw axis as a function of i COS
nt where t = time with t = 0 at the ascending node and n = the orbit angular rate.
24. The method of claim 23, wherein said torquing step further characterized by:
establishing the momentum vector along an axis tilted by an angle .theta. from the inclined orbit normal; and torquing the satellite about said yaw axis y (i+.theta.) COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate, .theta. has a maximum value of 0.178i.
establishing the momentum vector along an axis tilted by an angle .theta. from the inclined orbit normal; and torquing the satellite about said yaw axis y (i+.theta.) COS nt where t = time with t = 0 at the ascending node and n = the orbit angular rate, .theta. has a maximum value of 0.178i.
25. The method of claim 19, wherein said coupling step further characterized by:
coupling the momentum vector to the satellite through a two degree-of-freedom connection coincident, respectively, with the roll and yaw axes for effecting rotation of the satellite relative to the momentum vector about the roll and yaw axes.
coupling the momentum vector to the satellite through a two degree-of-freedom connection coincident, respectively, with the roll and yaw axes for effecting rotation of the satellite relative to the momentum vector about the roll and yaw axes.
26. The method of claim 25, wherein said torquing step further characterized by:
torquing the satellite about the roll axis as a function of .theta. SIN
nt and about said yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
torquing the satellite about the roll axis as a function of .theta. SIN
nt and about said yaw axis as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
27. The method of claim 26, wherein said torquing step further characterized by:
establishing the momentum vector along a normal to the inclined orbit plane; and torquing the satellite about the roll axis by -.theta. SIN nt and about said yaw axis by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
establishing the momentum vector along a normal to the inclined orbit plane; and torquing the satellite about the roll axis by -.theta. SIN nt and about said yaw axis by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
28. The method of claim 19, wherein the geosynchronous satellite is of the type having an earth sensor control loop for determining theattitude of the satellite relative to the earth and for correcting the attitude in response to the output of the earth sensor, further characterized by the step of:
introducing a bias value into the earth sensor control loop to offset the effect of the torquing step.
introducing a bias value into the earth sensor control loop to offset the effect of the torquing step.
29. An attitude control system for a geosynchronous satellite, comprising:
means for establishing a momentum vector by rotation of a mass about a spin axis, the axis other than an axis normal to the equatorial orbit plane;
means for coupling the momentum vector to at least a portion of the geosynchronous satellite for controlled relative rotation of the satellite about at least a selected one of the roll axis or yaw axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and means for driving said coupling means to effect controlled rotation of said satellite about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of the orbit inclination angle i.
means for establishing a momentum vector by rotation of a mass about a spin axis, the axis other than an axis normal to the equatorial orbit plane;
means for coupling the momentum vector to at least a portion of the geosynchronous satellite for controlled relative rotation of the satellite about at least a selected one of the roll axis or yaw axis, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and means for driving said coupling means to effect controlled rotation of said satellite about the selected axis in a time-varying manner in synchronism with the orbit of the satellite and as a function of the orbit inclination angle i.
30. The attitude control system for a geosynchronous satellite of claim 29, wherein said first-mentioned means characterized by a momentum wheel mounted for rotation about a spin axis to develop a momentum vector therealong.
31. The attitude control system for a geosynchronous satellite of claim 29, wherein said first-mentioned means characterized by a first portion of the satellite mounted for rotation about a spin axis relative to another despun portion of the satellite.
32. The attitude control system for a geosynchronous satellite of claim 29, wherein said second-mentioned means characterized by a single degree-of-freedom gimbal means having an axis coincident with the roll axis for effecting rotation of the satellite relative to the momentum vector about the roll axis.
33. The attitude control system for a geosynchronous satellite of claim 32, wherein said gimbal means is controlled by said third-mentioned means as a function of -.theta. SIN nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.187i.
34. The attitude control system for a geosynchronous satellite of claim 29, wherein said second-mentioned means characterized by a single degree-of-freedom gimbal means having an axis coincident with the yaw axis for effecting rotation of the satellite relative to the momentum vector about the yaw axis.
35. The attitude control system for a geosynchronous satellite of claim 34, wherein said gimbal means is controlled by said third-mentioned means as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and i = the orbit inclination angle.
36. The attitude control system for a geosynchronous satellite of claim 35, wherein said first-mentioned means establishes the momentum vector along an axis tilted by an angle .theta. from the inclined orbitplane normal and said gimbal means is controlled by said third-mentioned means by (i+.theta.) COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and i = the orbit inclination angle.
37. The attitude control system for a geosynchronous satellite of claim 29, wherein said second-mentioned means characterized by a two degree-of-freedom gimbal means having axes coincident with the roll and yaw axes of the satellite.
38. The attitude control system for a geosynchronous satellite of claim 37, wherein the roll axis is controlled by said third-mentioned means as a function of -.theta. SIN nt where t = time with t = 0 at the ascending node, n = the orbit angular rate and .theta. has a maximum value of 0.178i.
39. The attitude control system for a geosynchronous satellite of claim 38, wherein said first-mentioned means establishes the momentum vector along a normal to the inclined orbit plane and the roll axis is controlled by said third-mentioned means by -(i+.theta.) SIN nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and .theta. has a maximum value of 0.178i.
40. The attitude control system for a geosynchronous satellite of claim 37, wherein the yaw axis is controlled by said third-mentioned means as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and i = the orbit inclination angle.
41. The attitude control system for a geosynchronous satellite of claim 40, wherein said first-mentioned means establishes the momentum vector along a normal to the inclined orbit plane and the yaw axis is controlled by said third-mentioned means by i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, and i = the orbit inclination angle.
42. The attitude control system for a geosynchronous satellite of claim 37, wherein the roll axis is controlled by said third-mentioned means as a function of -.theta. SIN nt and the yaw axis is controlled by said third-mentioned means as a function of i COS nt where t = time with t = 0 at the ascending node, n = the orbit angular rate, i = the orbit inclination angle, and .theta. has a maximum value of ratio of the earth's radius to the geosynchronous orbit altitude multiplied by the orbit inclination angle.
43. An attitude control system for a geosynchronous satellite of the type having a spun section that establishes a momentum vector and a despun section, characterized by:
means defining a two degree of freedom coupling between the spun and despun sections for controlled relative rotation of the spun and depsun sections of the satellite about orthogonal roll and yaw axes defined by the two degrees of freedom coupling, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and means for controlling said coupling means to effect controlled relative rotation between said spun and despun sections in a time-varying manner in synchronism with the orbit of the satellite about the earth and as a function of the orbit inclination angle i.
means defining a two degree of freedom coupling between the spun and despun sections for controlled relative rotation of the spun and depsun sections of the satellite about orthogonal roll and yaw axes defined by the two degrees of freedom coupling, the roll axis tangential to the orbit path and the yaw axis perpendicular to the roll axis in the orbit plane; and means for controlling said coupling means to effect controlled relative rotation between said spun and despun sections in a time-varying manner in synchronism with the orbit of the satellite about the earth and as a function of the orbit inclination angle i.
44. The attitude control system of claim 43, wherein the momentum vector is established along an axis other than an axis normal to the equatorial orbit plane.
45. The attitude control system of claim 44, wherein said second-mentioned means controls said coupling means to provide relative rotation about said roll axis as a function of -.theta. SIN nt and relative rotation about said yaw axis as a function of i COS nut where t = time with t = 0 at the ascending node, n = the orbit angular rate, i = the orbit inclination angle, and.theta. having a maximum value of the ratio of the earth's radius to the geosynchronous orbit altitude multiplied by the orbit inclination angle.
46. The attitude control system of claim 44, wherein said second-mentioned means controls said coupling means to provide relative rotation about said roll axis as a function of -.theta. SIN nt, where t = time with t = 0 at the ascending node, n = the orbit angular rate, i = the orbit inclination angle, and .theta. has a maximum value of 0.178i.
47. The attitude control system of claim 44 wherein said second-mentioned means controls said coupling means to provide relative rotation about said yaw axis as a function of i COS nt with t = time with t = 0 at the ascending node, n = the orbit angular rate, i = the orbit inclination angle.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2006199 CA2006199C (en) | 1989-12-20 | 1989-12-20 | Attitude pointing error correction system and method for geosynchronous satellites |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CA 2006199 CA2006199C (en) | 1989-12-20 | 1989-12-20 | Attitude pointing error correction system and method for geosynchronous satellites |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CA2006199A1 CA2006199A1 (en) | 1991-06-20 |
| CA2006199C true CA2006199C (en) | 1998-12-01 |
Family
ID=4143849
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA 2006199 Expired - Fee Related CA2006199C (en) | 1989-12-20 | 1989-12-20 | Attitude pointing error correction system and method for geosynchronous satellites |
Country Status (1)
| Country | Link |
|---|---|
| CA (1) | CA2006199C (en) |
-
1989
- 1989-12-20 CA CA 2006199 patent/CA2006199C/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| CA2006199A1 (en) | 1991-06-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US4911385A (en) | Attitude pointing error correction system and method for geosynchronous satellites | |
| EP0568209B1 (en) | Spacecraft attitude control and momentum unloading using gimballed and throttled thrusters | |
| US5692707A (en) | Universal spacecraft attitude steering control system | |
| RU2114770C1 (en) | Satellite with three-axis attitude stabilization and method of control of this satellite | |
| US5067672A (en) | Method of placing a geostationary telecommunicaiton satellite in orbit | |
| AU639504B2 (en) | Satellite roll and yaw attitude control method | |
| US7113851B1 (en) | Practical orbit raising system and method for geosynchronous satellites | |
| US6481672B1 (en) | Gimbaled thruster control system | |
| EP0792800B1 (en) | Single axis correction for orbit inclination | |
| US6116543A (en) | Method and a system for putting a space vehicle into orbit, using thrusters of high specific impulse | |
| US5697582A (en) | Method of adjusting the position of satellites by means of solar pressure torques | |
| JP3667817B2 (en) | Spacecraft attitude determination system using sun sensor, earth sensor and space-to-ground link | |
| US7410130B2 (en) | Star-tracker-based attitude determination for spinning spacecraft | |
| US4084772A (en) | Roll/yaw body steering for momentum biased spacecraft | |
| US5054719A (en) | Active three-axis attitude control system for a geostationary satellite | |
| EP0356602B1 (en) | Method of orienting a synchronous satellite | |
| US20100059631A1 (en) | Unified attitude control for spacecraft transfer orbit operations | |
| JPS6047159B2 (en) | Satellite attitude control device | |
| JPH04231295A (en) | Spaceship earth-direction attitude acquiring method | |
| US6076773A (en) | Spin-stabilized spacecraft and methods | |
| CA1183241A (en) | Magnetically torqued nutation damping | |
| CN1025995C (en) | Attitude pointing error correction system and method for geosynchronous satellites | |
| CA2006199C (en) | Attitude pointing error correction system and method for geosynchronous satellites | |
| JP2971494B2 (en) | Attitude control method and apparatus for geostationary satellite | |
| JP2000128096A (en) | Method for retaining stationary orbit of three-axis attitude control satellite and device of the same |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| EEER | Examination request | ||
| MKLA | Lapsed |