CA1041608A - Minimization of residual spacecraft nutation due to disturbing torques - Google Patents

Abstract

Abstract of the Disclosure Spacecraft nutation caused by applying attitude and/or orbit control forces to a spacecraft along an axis which does not pass through the spacecraft's center of gravity is minimized by a signal responsive control system which first operates the attitude and/or orbit control forces for a predetermined time period and automatically after an appropriate non-operating time period, the attitude and/or orbit control forces are again operated for the same predetermined time period.

Description

RCA 66,833 1 Field of the Invention -This invention relates to spacecraft attitude and/or olbit control systems and is particularly directed to systems f'or controlling spacecraft nutation caused by external forces and torques used to change spacecraft attitude or orbit,

2 Description of the Prior Art A problem freq~lently encountered in applying thrust forces from thrustels in dual-spin or spin stabilized.
spacecraft for controlling spacecraf't attitude and/or station keeping orbital ad,justments is an undesirable space- . . -craft nutation or coning movement, Spacecraft nutation is caused by a misaligned torque due to a thrust force directed along an axis which does not pass through the spacecra~t center of gravity. Such a thrust force will be referred to as a misaligned thrust force.~ The nutation causing torque resulting from the misaligned thrust force has n component at right angles to the sp~cecraft's total . ~ . - , ~ ~- , momentum!;vector.~ Many systems have been proposed heretofQre.
for controlling such undesirable spacecraft nutation. Some ; :.
prior art attitude and/or orbit control systems use a combination of passive elements arranged to dissipate the ~ undesirable spacecraft nutation~ Other prior art attitude and/or o~ control systems counteract spacecraft nutation . . -. ' . .:
.by use of In extern11 lorce or forces generated by special ~.
spacecraft thrusters activated by electrical signals from sensors which detect spacecraft nutation, ~ A combination of special nutation counteracting thrusters and sensors or passive elements arranged solely for the dissipation or damping of spacecraft nutation . . ' . ' ~ .

..
.:

RCA 66,833 1~16~8 1 due to thrust force misalignment increase the complexity of spacecraft control system design. Accordingly, it is desirable to minimize spacecraft nutation caused by thrust misalignments without substantially increasing the complexity of spacecraft attitude and orbit control systems.
Summary of the Invention Spacecraft nutation caused by operating a force generating means for effecting changes in spacecraft attitude and/or orbit is minimized by a spacecraft attitude and orbit control system comprising receiver means coupled to logic means for automatically controlling operating and non-operating time periods for the force generating means.
The receiver means receives and transmits signals determining ' ' a predetermined operating time period, Tl, for the force - ' generating means. The logic means are coupled to the ' ;' ' receiver means and responsive to the receiver transmitted ;~
signals which cause the logic means to transmit signals for '' `
turning on and thus activating the force generating means for the~predetermined operating period Tl. The logic means 'automatically turns off and thus deactivates the force generating means for a predetermined waiting period, Tw, and -~
then automatically turns on and thus activates the force "
generating means again for the samè predetermined time period T~
Br'i'ef' Description of the Drawing Figure l(a) is a diagrammatic representation of - -a de-spun spacecraft embodying the attitude and orbit control system of the present invention.
Figure l(b) is a graphical representation of a path over which a transverse angular momentum vector, hx y(t), and spacecraft angular momentum vector H may move

-3- -~

: ...... ,., .,:,, - . . .. .... .... : .... : . :. :

-RCA 66,833 1 in time within a spacecraft co-ordinate system over a spacecraft nutation cycle.
Fi~ure 2 is a more detailed graphical representa-tion of a path over which a transverse angular momentum vector hx y(t) may move in time within a spacecraft co-ordinate system over a spacecraft nutation cycle when a force generating means is periodically turned on and off Des_riptiQn of the Preferred Embodiment Orbiting spacecraft in one form or another often require a change in spacecraft attitude or orientation in keeping with a desired spacecraft mission. Such spacecraft may be a spinning type in which the entire body spins, a dua~l spin type or a de-spun type containing a spinning ;
mom~ntum;wheel from which the remainder of the spacecra~t - - :
15~ is de-spun, all of which types provide spacecraft gyro ~ :

:scopic stiftness as is well known in the art. Both .spinning and de-spun spacecraft have a to$al angular ~ ~

~ . momentum represented as a vector, ~9 preferably directed . ~ -:~: . along or aligned.with a spacecraft principal axis of , inertia .(x, y or z). The angular momentum vector of a .

: ~ de-spun spacecraft is proportional to the angular ~eloclty .

-: o~ the spinning momentum wheel and, in the absence of - .
- .~ spanecraft.nutation, is directed along the axis abont - which the momentum wheel is spinning. When the.total : 25. an~ular momentum vectol, }1, is directed along the z axis, , : the x and y axes are in a plane transverse to the z axis.
.
The x-y~plane will be referred to as the .transverse plane.

Thrusters capable of generating a force are appropriately mounted on the spacecraft. The thrusters 3~ are iired at a predetermined time for producing the :: , ' ' RCA 66,~33 1 necessary force or thrust required to effect a desired ch~n~e in spacecraft a-ttitude or velocity. Spacecraft nttitude may also be controlled in response to an applied torque from a spacecraft reaction wheel having a spin axis transverse to the momentum wheel. If the thrust axis, or the axis alon~ which the thrust force is directed, does not pass through the spacecraft center of gravity and the .
resulting torque9 T, applied to the spacecral't has a component orthogronal to the spacecraft total angular ':~

momentum vector, H, there results an undesirable spacecraft nutatlon or wobble at l're~uency ~n. The spacecraft nuta~
tion frequency, ~n~ is determined by~
.
~n ~ sec. (1) where H is the total spacecraft angular momentum, Ix is .
the spacecraft moment o~ inertia about the x axis, a principal axis of lnertia in the transverse plane, and Iy is the spacecraft moment of inertia about the y axis, a pri~cipàl~axis of inertia orthogonal to the x axis and '' also in the transverse plane '~ ' -Prior to nutation, the angular momentum vector, -- H,'of either a spinning spacecraft or a de-~pun spacecraft, '~

-~ is preferably d~rected along or aligned with a spacecraft -~
~ principal àxis of inertia, ~'or example, t'he z axis. When~

a spacecraft is subjected to a nutation-causing torque, . .
the sp.lcecrnft momentum vector, Hg will no longer be aliRned wlth the z axis but will have a directlon whlch ' '~
vnries With time in the spacecraft x, y, z coordinate ~ system, the torque vector and the thrusting period. A
spacecraft subjected to nutation will have angular momentu~
:
- 5 - :

, .
.. . .

RCA 66,833 3L6~8 1 components of the tota]. spacecraft momentum vector, H, in a plane transverse to the spin axis. In other words, the tip oL the momentum vector, H, of a spacecraft subjected to nutation, moves along a predictable path in the x, y and z body coordinate system. The path is determined by ~ . -known spacec.raft parameters, the torque magnitude and the torque thrusting period. Therefore, knowing the path along which the spacecraft momentum vector, H, will move, a control system is described below which automatically activates and controls a jet engine thrusting period or the thrusting period of a force generating means in order to align the spacecraft momentum vector, H, with the space- . ;
craft z axis or the wheel spin axis in a ~ual~spin or de~
. spun space¢raft and thus minimize spacecraft nutation and ~ -~
: 15 ~ transverse angular momentum components of the total space-craft momentum vector H.
: , . . . . : . .
Referring to Figure l(a), there is shown a . ~
de-spun spacecraft 10 haYing a momentum wheel 11 spinning. . -.
in the;counterclockwise direction shown about a spacecrait ~... ;

prlncipal axls (z axis) with an angular veloclty, ~f. ~Thç .
operation of a de-spun spacecraft 10 will be described :-~n more~-detail later. Figure l(b) is a graphical repre~
~: .: .sentation of the spacecraft's angular mamentum vector, H,.
-~when spac~craft 10 is subjected to a nutation causing . ~ - - . ~:
25. torq-l-e~ Tx- The spacecraft z axis will be.referred to as .: .
llie spin axis ~ecallsc it is the axis about which momentum wheel ll is spinning. In the absence of spacecraft nutation spacecralt~momentum vector H is substanti.ally equal to hz and is aligned with the z axis. The magnitude of the :
spacecraft angular momentum, hz, prior to nutation is ;~ - 6 ~
. . . . . ~ - .
., ~ - , : . . , : : . .

RCA 66,833 38 ~:
1 determined by the equation:
hæ -= ~f If ~2) where ~f is the angular velocity o~ momentum wheel ll and I is the moment of inertia of momentum wheel ll. It f . ~ -should be noted that the magnitude of total spacecraft . .:
momentum vector, H, is substantially equal to the magnitude oi spacecraft momentum vector hz when the transverse momentum components of total angular momentum, H, have ~- .
a relatively small magnitude. Therefore, under these -conditions, spacecraft nutation frequency, ~n' may be .
determined by: h ~n ~I x Iy - where hz is determined by eq~uat1on (2), Ix is the space~
15~ . cra~t moment of inertia about the x axls ahd Iy is the :. .spacecraft moment.of inertia about the y axis.
In the event force, F, ~rom tbruster 12 ls appl~ed to spacecraft lO such that it causes a system , ~ .
: disturbance torque, Tx, (defined as a component of a total . ;~ :
~ 20 : torque vector, F x d, directed along the x axis, where F . .
~ is the position vector of force F and d is the position .: , ~: yector of the perpendicular distance from the spacecra~t . center of~mass, 0 to the vector F) about the spacecraft x axis or an axis transverse to the spin axis or z axis.
Torquo, Tx, causos a time varying angular momentum in tbe . ~ .
tr.1nsvcrse x-y plane of the spacecraft represented in Fi~ure l(b) as a transverse angular momentum vector :
~ hx y~t) having a time varying component along the x axis, hx(t), and a time varying component along the y axis, ~y(t). Thus, transverse angular momentum hx y(t) is equal , .. _ 7 _ :. . . ' ' ,. , -, . ~ .
,:, .

.. . . . .

RCA 66,833 6~8 I -I to the vector sum of hX(t) ~ hy(t). The magnitude and I ~ ' direction oi' the total spacecraft momentum vector, H, is equal to the vector sum of hX(t) + hy(t) ~ hz(t). The magnitude of the time varying angular momentum component, hX~t), along the x axis is determined by the equation: .
T . ~.
hX(t~ = ~ sin ~nt (4) ' . '.

where Tx is the magnitude of the applied torque about the ~ x axis, t is the time period from the instant of applica- :
10. tion of'.torque Tx, and ~n is the spacecraft nutation t'requency defined by equation (1). The magnitude of the ~ ;
time varying angular momentum component, hy(t) along the .. ' ' : .
. . . ..
- : y axis is'determined by the equation ; hy(t) = ~ x ~x (1 - cos ~ t) (5) : ~ where I'y is the spacecraft moment of inertia about the ~' ~ y axis, Ix is the spacecraft moment of inertia about the : X axis, Tx is the magnitude of.the~appli~ed torque, t~ iB
the time period f'rom the instant of application of tor~ue Tx,.and.~n is the spacecraft nutation frequency defined hy ~ :
e~uation'(l). . . ~' In a de~spun spacecraf't~, the.tip of the trans-verse momontum vector, hx y(t)~ moves in an elliptical pat~
........ as a l'unction of' time, in the transverse.~x-y plane when the 25. moment ol' inertia, lx, about the x axis is~not equal to . '~
the moment ol' inertia, Iy, about the y axiB~ It is apparent i'rom equations (4) and (5) that the tip of the transvorse momentum vector, bx y(t), movès in a circular path as a function of time in the transverse x-y plane when the moment of inertia about th~e x axis, Ix, is ~ . - ' ~;.
" ' ~'' ':' . - 8 - . ~ ~
.

.
.. . .

RCA 66,833 6'~
1 equal to the moment of inertia about the y axis, I .
Ellipse D in Figure l(b) graphically represents an elliptical path describing the movement, in time, of transverse momentum vector hx y(t) in response to the magnitude o~ applied torque Tx. Thus, ellipse D suggest that by selectively choosing the period or the time ~ ~-duration of the applied force, F, or resulting torque, ;
Tx, the magnitude of transverse momentum vector hx y(t) can be minimized causing spacecra~t momentum vector, H, moving in time along elliptical path E~ to be aligned substantially along the z axis and reducing spacecraft nutation due to thrust misalignment.
Referring to Figure 2, there is shown a more detailed graphical representation of the movement in time of the tip of transverse momentum vector, fiX y(t), in the transverse x-y plane when jet engine 12 (Fig~ la) is pulsed on and off. It is assumed for purposes of illustration, and not limitation, that the tip of transverse momentum vector, hx y(t), moves in elliptical paths as a function of time in response to a nutation causing torque, Tx, applied about a de-spun spacecraft x axis. It is further assumed that spinning momentum wheel 11 causes an angular momentum represented by momentum vector, hz, aligned along the z axis.
Ellipse A describes a path along which the tip of transverse momentum vector hx y(t) will move as a function of time in the x-y plane if the nutation causing torque, Tx, is applied over one cycle of nutation frequency, ~n~ defined by equation (1). The components of hx y(t), (hX(t) and hy(t)), are determined from equations (4) and (5).

::: : , .. . . -:
RCA 66,833 )8 1 Ellipse B describes a path of residual nutation along which the tip of transverse momentum vector hx y(t) will move as a .function of time in the x-y plane if the .
nutation causing torque, Tx, was suddenly withdrawn a~ter being applied to spacecraft lO for a time period Tl during which timc pcriod the tip o~ transverse momentum vector hx y(t) movcd along elliptical path A from point O to point M. In other words, ellipse B, centered at the origin 0, is a plot of the ensuing residual spacecraft : 10 nutation or the path the tip of transverse momentum ~ ~ :
vector hx y~t) would move if tbe nutation causing torque, Tx, sudden1y ceased after having been applied to spacecra~t.
lO for a time period Tl. It will be assumed that the :~ .; magnitude o~ Iy is less than the magnitude of I ~or ~ -~ purposes of illustrating the shàpe.of ell1pses A and B .
.. . in Figure 2. Ellipse B may be plotted when the minor to.
.
~ major axis ratio, R, and:the coordinates of a point (M) :~ . on ellipse A are known. Minor to major.axls ratio, R, or both ellipse A and B is defined~by~

: ~ ~x (6) ~

w`here Iy 1S the spacecraft moment of inertia about the y . ~ -~axis, and ~Ix is the spacecraft moment of inertia about.the ~ .

* axis.

. ~pacecraft nutation or coning is often re~erred :to in terms of the half coning angle, ~,~.determined by~
h (t) _xly (7) -~ :
æ

. whore hx y(t) is the transverse~angular momentum previously 3~) doiinod al1d hz is defined by equation (2) As seen in .
-- 10 _ . ' '.

.

RCA 66,833 .

I Figures l(b) and 2, the magnitude of transverse momentum vector hx y(t) and the half cone angle ~ is minimum at origin 0. Therefore, if thruster 12 is operated for a time period, Tl, transverse momentum vector hx y(t) moves in an elliptical path along ellipse A from origin 0 to point M at which time spacecraft thruster 12 is turned off by firing electronics circuit 16 in Figure l(a).
Residual nutation will cause transverse momentum vector hx y(t) to move in time in an elliptical path along 1 ellipse B to point Q on ellipse A, at which time spacecraft thruster 12 is again turned on by firing electronics - ~ : circuit 16 in Figure l(a3 ~or time period~Tl causing . transverse momentum vector hx y(t) to move along ellipse~
A from point Q back to origin 0 where the magnitude of . ~ :

transverse momentum vector hx y~t) and undesirable .
; spacecraft.nutation is minimum. There~ore, knowing the total thruster operating time, 2Tl, required for a desired~;~spacecra~t maneuver, thruster 12 is first operated .~
or one-half the total thruster operating time,~ turned ~:

o~ for a predetermined waiting period~ Tw9~ and~then .
. . :
oper~ted a second tlme for one-half the~total thruster-:~ ~ operatIng time. Waiting period, Tw, is determined from : equation~

w ~n tan [ ~ ] (8~ ~

:.where ~n is the nutation frequency defined by equation (l) ~ .

: . and Tl is the time period thruster 12 is ~irsb operated.

Thereforei~knowing only the thruster operatlng period ..

required for a desired spacecraft maneuver and the nutation frequency ~n determined from equation (1), - 1 1 - , :. .. . .
, . , , ~ . ! ' . ' . . . , ` .

RCA G6,833 , ~4 1 spacecraft nutation due to thruster misalignment is minimized.
Referring again to Figure l(a) 7 a command signal to fire or turn on thruster 12 and draw fuel, such as compressed ~as or the like, from tank 17 for a known time '-period T1 is $ransmitted from a ground station, not shown, ~ :
to an-tenna 13 and command or telemetry receiver 14. The ground station command signal may be in response to a -signal from a suitable spacecraft attitude deviation detecting sensor 19 mounted on spacecraft lO. Telemetry receiver 14 is any suitable prior art system which processes ' a received signal from a ground station and transmits the :
processe~d ground station signal to loglc circuit 15. . .
: ~ Spacecraft moments of inertia, Ix and Iy, and angular . ~.
momentum hz (determined f'rom equation (2)) are information ' h :
tored in a memory bank in logic circuit 15. Logic circuit 15:-is suitably arranged in a manner well known in the art, ' to compute e~uation (8) and generate an.output logic signal : ~ :
~ :: in response to an output signal f~om receiver 14~ The~
'20~ output~logic signal from lo~ic circuit 15 is a sequence . of signals indicating thruster I2 should first be turned ' .
on for time period Tl, then turned off for a time period, '~
Tw, determlned by equation ~8), and then turned on a' . second time for time period Tl, t.hus completing the total' jet ongine:operating period of' 2Tl. The output logic -~
. slgnal l'rom logic circuit 15 is transmi.tted.bo firing .
: elec~r'onics Cil-OUit 16 including a timer, not shown, . arran~ed to r.espond to the output signal.from logic .
circu1t l5 and turn on or fire thruster 12 for time period . T1. Thruster 12 is automatically turned off by firing ~ .

. . . ; ., : . .

RCA 66,833 6~
1 electronics circuit 16 at the end of time period Tl, for a waitin~ time pel~iod, Tw, detel~mined by equation (8) and the correspondin~ output logic signal from logic circuit I5. At the end ~i waiting time period, Tw, an ¦ ~ :
output logic signal from logic circuit 15 automatically triggers the timer in firing electronics circuit 16 to turn on thruster 12 for time period Tl. Thus, de-spun spaceoraft nutation or coning in an attitude or orbit changing maneuver is eliminated by automatically firing ¦
- 10 ~ spacecraf`t thruster 12 on and off in a predetermined sequence~ It should be noted that as an alternative embodiment, all control signals determining thruster on/off :
periods may be determined by logic circuits in the ground transmitting station. ~ ~
In another embodiment logic circuit 15 may be . . :
arranged ln a manner well known in the art to compute both .
the total thruster operating period, 2Tl, and the waiting period, ~, required for a desired spacecraft maneuver ~-~ n responee to a signal from attitude deviation detectlng ~ .
::20 sensor 1:9. Logic circuit 15 is arranged to transmit, to . . , .
flring electronics circuit 16, a signal~determining a ~ ~
first thruster operating period Tl, a waitlng period Tw ~ I -and a second thruster operating period Tl. This embodiment ~ ~ ~; -is referred to as a closed Ioop control system. :
: - :, :
In summary, a control system for~minimi~ing ~ l .
- nutation in a spacecrait due to operation of a spacecraft thruster is disclosed. The spacecraft thruster is first , operated for one-half the total operating period required ~ for a desired spacecraft maneuver and then the thruster 3 is turned off for a waiti~g period, Tw, determined by : ~ !
. - 13 - .

:. :.: . :- . . . . . .. . .

RCA 66,833 ()8 1 equation ~8). The thruster is operated a second time for one-half the total operating period required for ~:
the desired spacecraft maneuver at the end of waiting period Tw.
Although an attitude or orbit control system for a de-spun spacecraft has be~n described, the general principle ol nutation control disclosed above is applicable to spinning or dual-spin spacecraft, Variations and modifications may be made without depart1ng from the - ~ ~
present invention. Accordingly, it should be understood~ :
~that the form of the present invention described above : -and shown in the figures of the accompanying drawing is llustrative only and is not intended to limit the scope.
: of the invention.

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Claims (7)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. A control system for minimizing nutation in a spacecraft of the dual-spin type having a spin axis and a characteristic nutation period, and further having a platform despun from a spinning member, comprising:
receiver means included in said spacecraft for receiving signals transmitted to said spacecraft, and generating in response thereto a receiver means output signal;
logic means coupled to said receiver means and in response to said receiver output signal generating a logic control output signal; and torque generating means mounted on said platform and coupled to said logic means and, in response to said logic control output signal, activating said torque generating means for a predetermined operating period Tl, said predetermined period Tl determined by said logic means to be a predetermined portion of said nutation period of said spacecraft, at the end of said period Tl automatically deactivating said torque generating means for a predetermined waiting period Tw, and at the end of said waiting period Tw, automatically activating said torque generating means again for said predetermined operating period Tl, wherein said waiting period, Tw, is determined by where .omega.n is spacecraft nutation frequency and Tl is said predetermined spacecraft operating period.

2. A control system according to Claim 1, wherein said torque generating means is at least one thruster.

3. A control system according to Claim 1, wherein said logic means includes a firing electronics circuit including a timer means arranged to respond to said logic output signals and to activate said force generating means for said predetermined operating period, Tl, then automatically deactivating said torque generating means for a predetermined waiting period, Tw, and then automatically activating said torque generating means again for said predetermined operating period, Tl.

4. A closed loop attitude control system for minimizing nutation in a spacecraft of the dual-spin type having a spin axis and a characteristic nutation period, and further having a platform despun from a spinning member, comprising:
detector means included in said spacecraft for detecting a deviation from a desired spacecraft attitude, and generating in response thereto a detector means output signal;
logic means coupled to said detector means and in response to said detector output signal generating a logic control output signal; and torque generating means mounted on said platform and coupled to said logic means and, in response to said logic control output signal, activating said torque generating means for a predetermined operating period Tl,

Claim 4 continued.

said predetermined period Tl determined by said logic means to be a predetermined portion of said nutation period of said spacecraft, at the end of said period Tl automatically deactivating said torque generating means for a predetermined waiting period Tw, and at the end of said waiting period Tw, automatically activating said torque generating means again for said predetermined operating period Tl, wherein said waiting period, Tw, is determined by:

where .omega.n is spacecraft nutation frequency and Tl is said predetermined spacecraft operating period.

5. A control system according to Claim 4, wherein said torque generating means includes at least one thruster.

6. A control system according to Claim 4, wherein said logic means include a firing electronics circuit including a timer means arranged to respond to said logic output signals and activate said force generating means for said predetermined operating period, Tl, then auto-matically deactivating said torque generating means for a predetermined waiting period, Tw, and then automatically activating said torque generating means again for said predetermined operating period, Tl.

7. A method for minimizing nutation in a space-craft of the dual spin type having a spin axis and a characteristic nutation period and further having a platform despun from a spinning member, comprising the steps of:
transmitting signals to spacecraft receiver means causing a receiver means output signal;
coupling said receiver output signal to logic circuit means causing a logic circuit means output signal;
activating a force generating means mounted on said platform a first time for a predetermined operating period Tl in response to said logic circuit ouput signal, said predetermined operating period determined by said logic means to be a predetermined portion of said nutation period of said spacecraft;
deactivating said force generating means for a waiting period Tw, in response to said logic circuit means output signal at the end of said predetermined operating period Tl;
activating said force generating means auto-matically a second time in response to said logic circuit means output signal for said predetermined operating period Tl after said waiting period Tw, wherein said waiting period, Tw, is determined by:

where .omega.n is the spacecraft nutation frequency and T1 is said force generating means operating period.