Closed loop roll and yaw control for satellites

Closed loop roll and yaw control for satellites
United States Patent [191
[111 3,834,653,
[451 Sept. 10,1974
Primary Examiner~George E. A. Halvosa
Assistant Examiner-Barry L. Kelmachter
[75] Inventor. Harold Perkel, Levlttown, Pa.
Attorney, Agent’ or Firm_ Edward 1 Norton‘
[73] Assignee: RCA Corporation, New York, NY.
Joseph D. Lazar
[22] Filed:
21] A
Mar. 27, 1972
1 No ' 238 483
A magnetic torquing control system for the attitude
[52] U-S- 0- ----------- n 244/1 SA, 235/1502, 244/32l
[5 l ] Int. Cl. ............................................ .. B64g 1/10
[58] Field of Search ........... .. 244/ 1 SA, 1 SS, 77 S5,
343/ 100 ST; 235/ 150.2, 150-25, 150-27
control of pitch momentum biased satellites utilizing a
closed loop for roll-axis control by interacting the sat~
eilite’s magnetic dipole with the earth’s magnetic ?eld,
The closed-loop system includes a pair of attitude sen
sors whose output error signals are processed in the
satellite~mounted logic circuits to control correcting
torques. At a predetermined clock-controlled time or,
References Clted
in response to control or sensing signals from a mag
netometer, a torquer such as a magnetic dipole is en
ergized at the position of its satellite’s orbit relative to
the magnetic equator to develop a magnetic ?eld
which interacts with the magnetic ?eld 0f the earth to
torque, primarily, the roll axis to correct thereby the
Adams ____________________________ __ 244” SA
Whitaker ____ ,_
Gill et al. .................... .. 244/1 SA x
Buckingham et a]. .......... .. 244/! SA
Braga-llla et al. .............. .. 244/1 SA
Entner ..................... .. 235/150.27 X
Phillips ........................... .. 244/1 SA
errors in attitude of the pitch axis_
7 Claims, 8 Drawing Figures
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FIG. 16
control system for aligning the pitch axis of a satellite
with the orbit normal, includes one or more attitude
sensors with electronic logic responding to the sensed
attitude error generated by the sensors to energize a
1. Field of the Invention
This invention relates to attitude control for pitch
magnetic torquer with energizing currents of appropri
ate polarity and magnitude to effect the necessary
torque to correct the satellites attitude. The polarity
and direction of the control torque is primarily along
the local vertical, the local vertical being the line be
momentum biased satellites and more particularly to
control of the roll and yaw axes by automatic magnetic
10 tween the satellite and the center of the earth.
torquing in a closed loop control system.
2. Description of the Prior Art
FIG. 1a is a schematic diagram of a satellite showing
A stabilized orbiting satellite requires a means for
changing its attitude when it has deviated from its de
sired orientation or position relative to its orbit.
the three axes thereof as related to the momentum and
velocity vectors.
FIG. lb is a diagram showing the axes in inertial con
ventions related to the orbit normal.
FIG. 2 is a block diagram of a closed-loop roll control
?eld from torquers such as a coil or electromagnet to
illustrating one form of the invention.
interact with the magnetic ?eld of the earth to develop
a reaction torque which causes the reference axis of the 20 FIG. 3a is a diagram illustrating the cones tracked by
the horizing sensor optical axes mounted on a spinning
satellite to be repositioned an amount proportional to
momentum wheel of a dual-spin satellite.
the torquing time and ?ux magnitude as known in the
Magnetic torquing of spin-stabilized satellites is
known. Such magnetic torquing systems use a magnetic
FIG. 3b is a diagram illustrating the path traced on
art. Known systems require that ground control com
mand signals be transmitted to the satellite to effect the
the earth by the optical axes of the sensors.
desired magnetic torquing operations. In one of the 25 FIG. 4 are waveforms illustrating the outputs of the
sensors and detectors for determining the attitude of
known systems, a series of the satellites known as
the satellite.
TIROS operated by NASA, a clock aboard the satellite
FIG. 5 is a plot of the pitch axis trajectories under
provides time signals according to a pre-set schedule
for controlling the operation of the magnetic torquing
system relying on assumed attitude errors.
roll/yaw control.
FIG. 6 is a diagram showing the regions for torquing.
In other known systems, the satellite is provided with
sensing devices which produce signals representing the
attitude of the satellite. The sensor signals information
are processed and transmitted to a ground station
which in turn provides the necessary command or con 35
Referring to FIG. la, there is shown a body 10 which
trol signals for directing the motion of the satellite to
may be a spacecraft or satellite of any suitable or de
correct for the anomalies which may have occurred.
The command signals for altering the attitude may ac
tuate any of the attitude control devices to effect the
three mutually perpendicular spacecraft axes desig
sired shape. Extending from the center of mass are
nated as l, 2, and 3 corresponding to conventionally
designated yaw, roll, and pitch axes respectively.
The pitch (3) axis is de?ned to be that direction in
required torques. Either of such previous systems, just
described, are known in the art as an “open-loop” con
trol system.
The problem with such open-loop control systems is
in effecting a correcting command signal at a time dur
ing the orbit of the satellite during which the magnetic
the spacecraft 10 collinear with the total angular mo
mentum vector H when the spacecraft 10 is operating
in its intended mission. The pitch axis is parallel to the
axis 12 about which a momentum wheel 14 is rotated.
field of the earth is properly situated relative to the po
sition of the satellite. To effect the proper magnetic
The sign convention is that the pitch axis, shown in
FIG. la, is positive and is in the positive direction of the
torque for correcting a given or known error in atti
angular momentum vector H. Thus, according to the
usual convention in this art, the angular momentum
tude, the phasing of the torquer must be in phase with
the polarity of the earth’s magnetic ?eld. Heretofore
the method for effecting such magnetic torquing opera
tions required ground station commands in the control
loop. A disadvantage in such open-loop systems is that
the ground station link in the control system necessi 55
tates delays in the correction operations by personnel
who must interpret satellite signals and provide the ap
propriate and timely command signals. Such delays
may make it di?icult to achieve attitude corrections
that are best made more frequently as the satellite be
comes properly positioned in the magnetic ?eld of the
earth. The expense of operating ground stations with
personnel serving attitude correction problems is also
a burdensome disadvantage in such open-loop control
According to the present invention a closed loop
possessed by the spacecraft 10 is equivalent to having
the body 10 spinning clockwise about the pitch axis as
shown along the arrow direction 16 representing the
angular velocity 003 about the pitch axis. The yaw and
roll axes are mutually perpendicular and orthogonal to
the pitch axis. The axis system as de?ned and used
herein according to the usual convention is right
handed in the order 1-2-3. The 3 axis shall at times, it
should be noted, be referred to herein as the pitch or
spin axis. The 3 axis is parallel to the axis 12 of the spin
ning wheel 14.
According to the laws of motion, the spacecraft 10
includes a ?rst (translational) motion of the center of
mass 20 and a second motion of the spacecraft 10
65 about its center of mass 20. The motion about the cen
ter of mass 20 is represented by w, conventionally
called the angular velocity vector, which is shown pass
ing through the center of mass 20 along the ‘line about
which the spacecraft 10 is rotated. The length of the
vector is proportional to the angular speed of the
The satellite 10 may be either a dual-spin type as
shown or a spinning type not shown but well known in
the art. For spinning type satellites the sensors are suit
spacecraft 10 about that line. The arrow head 16 of the
angular velocity vector indicates the direction of rota
ably mounted to provide signals needed to indicate the
tion, in this case clockwise, about the line as shown.
attitude of the satellite.
For the purposes of describing one embodiment of
the present invention, the momentum vector H is as
sumed to be collinear with the pitch axis 3. Further the
pitch axis is normal to the plane of the orbit of the satel»
An orbiting satellite which has stored angular mo
The signal output from the sensors are ampli?ed by
preampli?ers 26 and 28 developing waveforms 30 and
32, which are applied to a pair of threshold detectors
34 and 36. The output signals generated by the thresh
mentum can be oriented in such a way that the direc
old detectors are indicated by waveforms 38 and 40.
Signals 38 and 40 are applied to the earth time detec
tors 42 and 44 which determine the period of time that
tion, de?ned by the angular momentum vector I-I (FIG.
1), is aligned with the orbit normal, by an automatic
suitable integrator or counter will serve this function.
the earth is being viewed by the respective sensors. Any
These earth-viewed time period signals are represented
by the pulses 46 and 48 developed at the output of the
respective detectors 42 and 44. The pulses 46 and 48
means, according to the invention, which includes con
ventional torquers, sensors, and electronic logic cir
cuits in a closed-loop without the need of ground con
trol command.
are applied to a logic detector circuit comprising an
error detector 50, which developes a pulse 52 repre
Referring now to FIG. 1b there is shown a diagram of
20 senting the error of the difference of the sensor signals
several of the parameters that will be used in the de
22 and 24.
scription to follow of one form of the invention. The 1,
The attitude sensors may be arranged in any suitable
2, and 3 axes described above with respect to FIG. 1a
manner known in the art. Typically a pair of sensors
are shown in their relative postions in FIG. 1b, it being
may be arranged to view the horizon in a “V” con?gu
understood that these axes are identical to the axes 25
ration at 60° with the local vertical such that the paths
heretofore described. The local vertical vector or di
110, 112 traced on the earth 111 from horizon to hori
rection 22a is colinear with the desired reference direc
zon by a pair of sensors will be as shown in FIG. 3b. The
tion for orienting the spacecraft yaw axis (1 ). The vec
sensors No. 1 and No. 2 mounted on a wheel will trace
tor 24a indicates the direction perpendicular to the
cones 114, 116 such as shown in FIG. 3a, the space
orbit plane of the spacecraft. The line 26a represents 30 craft’s axis being shown in relation to the sensor axes.
the position of the yaw axis if the spacecraft were to
Point 118 is the projection of the satellite on the earth‘s
have a yaw angle r11 (psi) and a roll angle 4; (phi) but
surface sometimes referred to as the nadir (N).
no pitch angle 0,, (theta) relative to the orbital coordi
The attitude error detected by the earth sensors 22
nates 22a, 24a, and 23a. The line 28a similarly repre
sents the position of the roll axis, with a yaw angle ll;
and a roll angle (i), but no pitch angle 0,,. The angles as
axis and the orbit normal 24 (FIG. lb). It is to be noted
shown by the several vectors and directions are de?ned
as follows:
6,, is the spacecraft pitch error, de?ned as the angle
between the yaw axis and the plane formed by the pitch
axis and the local vertical 22a;
(1) is the spacecraft roll angle de?ned as the angle be
tween the pitch axis and the plane formed by the orbit
normal (24) and velocity vector 23a;
(l: is the spacecraft yaw angle de?ned as the angle be
tween the orbit normal 24a and the plane de?ned by
the pitch axis 3, and the local vertical 22a.
The practice of this invention depends on the prop
erty of a spinning satellite which is essentially a gyro
scope. One property of a gyroscopically stabilized
spacecraft is that the direction of its spin axis in space
cannot move unless deliberately torqued.
that roll is the rotation of the satellite roll axis with re- '
spect to the plane that is formed by the velocity vector
(23a, FIG. 1a) and the orbit normal 240. A counter 58
40 of conventional design is arranged to measure the pulse
duration of the waveform 52. Counter 54 counts the
cycles of a clock 56, for example, generating clock
pulses at the rate 256 kHz. The count is directly pro
portional to the magnitude of misalignment of the an
45 gular momentum (H) with respect to orbit normal 24a.
When the time differences are zero, or within a speci
?ed limit determined by an over?ow detector 58, the
torquer is cut-off or de-energized.
The over?ow detector 58 is conventionally a register
of a ?xed number of pulses which, upon saturation,
generates an output pulse as one input to logic circuit
59. When an error is determined by detector 50, the
Since roll and yaw interchange sinusoidally through
out the orbit for such a spin oriented spacecraft, the po
sition of the spin axis is uniquely determined without
and 24 indicates a misalignment (1; between the angular
momentum axis (H) and the plane formed by the roll
the necessity of direct yaw measurement, which is most
difficult to measure for an earth oriented spacecraft.
According to the invention, the errors in roll are used
as the control input parameter of the closed-loop sys
torquer, 94 aligned parallel to the pitch axis 1 (FIGS.
1a, 1b), is energized to effect the required torquing
flux, provided, the satellite is in a proper region of the
earth’s magnetic ?eld as will be explained. If the error
is greater than a predetermined minimum value, the
sense of the current ?owing in the electromagnet of the
torquer 94 is determined by two parameters. One pa—
tem as will be described.
rameter is the error sense which indicates by the error
FIG. 2 is a block diagram of a closed loop control cir
cuit chosen for purposes of illustrating the invention. A
pair of sensors 22 and 24 suitably positioned on the mo
mentum (?y) wheel 14 of the satellite [0 are oriented 65
sensor 51 which of the sensor outputs precedes the
to respond to light energy preferably in the infrared
range for viewing the earth’s surface on each scan of
rotation on the momentum wheel 14.
other indicating the sense of the roll error. Error sensor
51 is a suitable phase detector comparing the signals 46
and 48. The second parameter depends on which por
tion of the orbit the error is being detected.
The diagram shown in FIG. 6 illustrates the portions
of the orbit '72 de?ned by regions 74 and 76 during
which the magnetic field of the earth is of sufficient
magnitude to provide the roll correction reaction
torque needed. These regions are in the vicinity of the
earth’s equatorial plane. The magnetic ?eld vector 78
p = 152 to 138
is in orthogonal relation to the control torque vector 80
that is developed to cause a correction movement of
the roll axis along vector 82 which is in the plane of the
orbit. A correction in the opposite direction of vector
p = 332 to 28
82 as shown would be caused by a control torque in the
opposite direction of vector 80 as shown. Since the
*For momentum vector 82 along positive orbit normal (FIG. 6)
where [3 = True Anomaly (Measured for Ascending Node).
magnetic ?eld of the earth may be changing direction
with respect to the local vertical as the satellite moves
in its orbit, as, for example, occurs when the satellite
passes the north pole, it is necessary to determine the 15 The table indicates that for a + roll error which is ar
bitrarily a clockwise rotation of the roll axis, a negative
direction of the resultant torque 82 and particularly
error thus being a counterclockwise rotation, a mag
whether that roll-correcting torque will be primarily
netic dipole would be excited by a current to develop
along the local vertical.
a negative ?ux ?eld for the portion of the orbit between
The onboard control logic determines if the earth’s
magnetic ?eld is within the acceptable direction. The
determination of the condition of the magnetic ?eld
20 a true anomaly of 152 to 138° as measured from the as
cending node of the orbit as it crosses the plane of the
can be made in one of two ways. One method is in the
use of a counter and clock that is arranged to be reset
A negative roll error in the same portion of the orbit
would require a positive ?ux to correct the error. The
as the satellite crosses the plane defined by the earth’s 25 orbit angle between 332° and 28° requires a positive di
pole correction for a positive roll error and a negative
correction for a negative error. A similar table for a
formation requires a prior knowledge of the magnetic
control law of other orbits will be apparent to those
?eld of the earth with respect to the position of the sat
in this art.
ellite in orbit.
The curved traces shown in FIG. 5 are plotted on a
The second method for such a determination of the
series of concentric circles marked by angles in degrees
sense of the earth’s magnetic ?eld is in the use of a
increasing from the center 60 which corresponds to the
magnetometer situated in the spacecraft. As known in
pitch axis. The roll error is de?ned by the angle be
equator or some known reference in the orbit. Such in
the art, a magnetometer measures the direction and
magnitude of the magnetic ?eld of the earth relative to
the spacecraft in the orbit.
With such determined information, whether by the
tween the orbit normal and the momentum vector H
35 which is coincident with the pitch axis 3 for those situa
tions under consideration in which there is no nutation.
The orbit normal is point 60 at the center of the dia
gram, pointing outward from the plane of the paper.
The concentric circles 62, 64, 66, 68, and 70 represent
' known data based on a prior knowledge or byrdirect
indication of the magnetometer, the resulting direction
of the required torque can be determined as to when 40 the cones on which the pitch axis could appear at any
meridian. The radial distance is plotted as the angular
displacement between the pitch axis and the orbit nor
_the torquer is to be energized.
For use of the a prior knowledge method a clock 90
mal as just indicated. The curved traces or trajectories
show the motion of the pitch axis as it moves due to
provides control signals to the logic circuit 59 for gat
ing the signals from detector 58 with appropriate polar
ity to energize the torquer 94 with the proper polarity
of flux. For use of direct sensing of the earth’s magnetic
field, a magnetometer 96, rather than a clock 90, pro
vides signals corresponding to the magnitude and direc
tion of the earth’s magnetic ?eld to the logic circuit 59
over path 92. The torquer is energized to develop the
required torque if an error is indicated.
A typical series of waveforms developed by a pair of
sensors is illustrated in FIG. 4. Waveform 30 is gener
ated by sensor No. l (22) and waveform 32 by sensor 55
No. 2 (24). The threshold levels are shown on the
waves at the portions where the earth-to-sky disconti
nuities occur. The horizon~to-horizon pulse duration,
shown by pulses 33 and 35 for waveform 30 as com
pared to pulses 37 and 39 for waveform 32 shows a roll
error exists by waveform 30a leading waveform 32a by
magnetic torquing from each of four typical anomalies.
For example, starting at position 1, the attitude error
is completely that of roll at 3°. As the satellite is con
trolled through the two torque correcting cycles indi
cated by portions 61 and 63, roll corrections also cause
yaw deviations in the process. As the trajectory, as
shown, converges towards orbit normal at point 60
both roll and yaw deviations have been completely
The curve traces illustrated in FIG. 5 starting at
points 2, 3, and 4 are the paths followed during the cor
rection of the attitude error indicated by the respective
starting positions in the manner described with respect
to the initial error starting at position 1. It is to be noted
that the starting positions 1 and 4 represent the maxi
mum roll error that are corrected according to the in
vention about the pitch axis 60 while starting positions
2 and 3 represent the maximum yaw errors that occur
The following table summarizes the boundary condi
tions within which the closed loop system is controlled,
according to the invention. for a spacecraft in a 200
nautical mile orbit inclined at 84° with respect to the
about the pitch axis 60.
Although the invention has been illustrated by refer
equatorial plane.
ence to a satellite operating in a circular and high incli
nation orbit, it should be understood that its use is not
limited only to circular orbits or to a speci?c inclina
tion. A high inclination orbit is one in which the angle
between the earth’s polar axis and the orbit normal is
gize said magnetic torquing means to correct the
deviation of said roll axis to change the orientation
of said momentum vector without changing the
approximately a right angle. Such an orbit causes an or
biting satellite to pass through the strongest portions of
magnitude of said momentum vector.
2. A system according to claim 1 wherein said ener
the earth’s magnetic field. Low inclination orbits gener
ally cause the satellite to pass through portions of the
gizing means includes a clock programmed to generate
a signal when said satellite is in a portion of its orbit
earth’s magnetic ?eld that have low but still useful mag
netic ?eld strengths. The only essential requirement is
having signi?cant magnetic ?eld strength of the earth’s
that the orbit be of suf?cient altitude that the satellite
pass through a sensible magnitude of the earth’s mag
netic field. Any of the lowest feasible orbits known in
3. A system according to claim 1 wherein said ener
gizing means includes a magnetometer for sensing the
magnetic ?eld of the earth, and means for generating
a signal from said magnetometer for energizing said
magnetic torquing means to correct deviations in said
roll axis.
4. A system according to claim 1 wherein said ener
the art increasing in altitude to what is known as a geo
synchronous equatorial orbit may be utilized according
to the invention for magnetic torquing to correct roll
and yaw errors.
At synchronous low inclination orbits, the closed
loop control, according to the invention, may be used
throughout the orbiting period i.e., on a continuous ba
sis. However, the magnetic dipole of the torquer must
be reoriented to produce the torquing dipole along the
velocity vector (roll axis). This dipole interacts with the
primary magnetic ?eld which is perpendicular to the
gizing means includes means to determine the sense of
the magnetic ?eld generated by said torquing means to
correspond to the sense of the earth’s magnetic ?eld.
5. A system according to claim 1 wherein said satel
lite is of the dual-spin type having a momentum wheel,
and said error sensing means comprise a pair of horizon
orbit plane.
What is claimed is:
1. A magnetic torquing system in a closed-loop sys 25 sensors oriented to scan the earth’s surface on opposite
sides of the local vertical.
6. A system according to claim 5 wherein said mag
netic torquing means has a major axis which is oriented
to be parallel with the spin axis of the momentum
'7. A system according to claim 5 wherein said satel
lite is in a geo-synchronous orbit whereby the satellite
remains in substantially a ?xed position above the
tem in an orbiting pitch momentum biased satellite for
automatically controlling the roll error and yaw error
of the satellite, to thereby orient the pitch axis to a de
sired attitude, said pitch axis being colinear with the
momentum vector of the satellite, comprising:
a closed loop consisting essentially of:
a. roll error sensing means for generating a signal rep
resenting a deviation of the roll axis from said de
earth’s surface on the equatorial plane of the earth, and
sired attitude relative to the pitch axis,
b. magnetic torquing means comprising a single mag 35 wherein said magnetic torquing means is oriented in
netic dipole for developing a magnetic torque only
said satellite to be substantially parallel to the roll axis
along a selected axis of the satellite, and
of the satellite.
c. means responsive to said roll error signal to ener
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