This application incorporates by reference subject matter contained
in U.S. Patent Number 4,931,942 issued to Garg et al. on June 5, 1990.
BACKGROUND OF THE INVENTION1. Field of the Invention
This invention relates to a method of damping nutational motion in
satellites and other spacecraft systems, and more particularly to providing a smooth
transition from a station-keeping mode in which the spacecraft is under thruster
control to an on-orbit operational status in which control is maintained using
momentum wheels to make small orientational corrections.
2. Description of Background Art
The improvements described in this disclosure incorporate by reference
the subject matter described in U.S. Patent No. 4,931,942 issued to Garg et al.
on June 5, 1990. The Garg patent describes a method for controlling nutational
motion during spacecraft transition from a station-keeping mode to an on-orbit
mode using a feedback control system to control multiple thruster pulse firings.
Although the problems of thruster non-idealities and orbital dynamic nonlinearities
were raised, no solutions were offered beyond convergence to stability through
successive feedback controlled thruster pulses.
U.S. Patent No. 4,289,051 issued to Goschel relates to the stabilizing of a
satellite relative to the three major axes prior to the point in time when the
satellite is to change orbits, whereupon the engine system for reaching the new
orbit is switched on. No separate nutation-damping scheme is disclosed.
U.S. Patent No. 4,537,375 issued to Chan describes a method of pre-biasing
individual thruster motors to compensate for motor offsets and mismatches. The
damping of nutational motion is not addressed.
U.S. Patent No. 4,725,024 issued to Vorlicek describes a method for spinning-up
a three-axis controlled spacecraft. Nutational motion compensation is not described.
U.S. Patent No. 4,759,957 issued to Hubert et al. discloses a method for simultaneously
processing and nutation-damping a spinning spacecraft that includes thruster firing
in response to feedback from angular momentum gyros. This patent has no disclosure
of the subject three-pulse thruster firing scheme, nor does it address the topic
of thruster compensation.
Other patents uncovered which contain additional information on the
general topics of nutation, attenuation, correction in spacecraft systems and the
like are as follows:
U.S. Patent No. Inventor 3,624,367Hamilton, et al. 3,643,897Johnson, Jr. 3,866,025Cavanagh 3,937,423Johansen 3,944,172Becker 3,984,071Fleming 3,997,137Phillips 4,023,752Pistiner, et al. 4,174,819Bruederle, et al. 4,370,716Armieux 4,386,750Hoffman 4,521,855Lehner, et al.
In accordance with the present invention, a method is provided for
eliminating nutation in a three-axis stabilized spacecraft (1) employing internal
momentum wheels (3) as an attitude stabilizer. Nutation damping is effected using
a closed loop control system in which the momentum wheels (3) work in conjunction
with spacecraft thrusters (5). This invention discloses two advancements over the
prior art. The first advancement is the addition of a thruster compensation mechanism
(81,83) to the conventional transition mode control system. The second improvement
is the incorporation of a modified deadbeat thruster timing sequence, in which
the nutating spacecraft (1) is brought under on-orbit control within three pulses
of the thrusters (5).
The thruster compensation mechanism (81,83) comprises a method of
correcting thruster (5) inefficiencies which occur in extremely short duration
firings, often used in attitude control. During short pulsing periods, fuel is
inadequately mixed in the combustion chamber, resulting in power loss. The method
consists of equating empirical data on thruster (5) inefficiencies to a polynomial
expression and using this polynomial to compensate the error correction coefficients
in the solution of the control system equations.
The second advancement presented is the disclosure of a modified
thruster (5) sequence for stopping nutation and orienting the spacecraft (1) for
on-orbit operation. The prior art teaches that a deadbeat sequence of two pulses
is theoretically sufficient for transition from the station-keeping mode to on-orbit
operation. In practice, nonlinearities of the dynamic system and non-idealities
in the control mechanism require three or more pulsings for complete transition
within the requirements of on-orbit operation. Using the three thruster (5) firing
technique disclosed below, a first pulse (31) is used to minimize nonlinear spacecraft
dynamics and to permit orientation using two additional adjustment pulses (35,39)
which act as a deadbeat sequence.
BRIEF DESCRIPTION OF THE DRAWINGS
Figure 1 is a schematic representation of a prior art satellite orbiting in
a three-dimensional vector space;
Figure 2 is a diagram showing the prior art damping of the momentum vector
in the X-Z plane by deadbeat impulse firing of a three-axis stabilized satellite;
Figure 3 is a diagram showing the damping of transverse momentum of the present
invention by deadbeat impulse firing of a three-axis stabilized spacecraft 1;
Figure 4 is a flow diagram showing the modified thruster sequence steps of
the present invention;
Figure 5 is a schematic diagram of the prior art nutational damping control
Figure 6 is a schematic diagram of the thruster compensation and sequencing
section of the nutational damping control system of the present invention; and
Figure 7 is a flow diagram showing the thruster loss compensation algorithm
of the present invention.
BEST MODE FOR CARRYING OUT THE INVENTION
Figure 1 illustrates a conventional orbiting satellite 1. Under normal
on-orbit operation, attitude control is maintained through one or more spinning
momentum wheels 3. Each momentum wheel 3 is rigidly attached to frame 2 of the
satellite 1 and provides inertial stability, represented by a perpendicular momentum
vector 7, which in the example shown in FIG. 1, points along the -Y 7 direction.
Small changes in satellite 1 orientation can be effected by changing the speed
of one or more momentum wheels 3 and thereby redirecting momentum vector 7.
Periodically, satellite 1 is commanded into a station-keeping mode
in order to adjust the orbit or trajectory of operation. This station-keeping mode
is implemented using one or more thrusters 5 which fire for a set duration to adjust
the orbit of satellite 1. A byproduct of the station-keeping mode is the introduction
of various attitudinal perturbations produced by the thruster 5 forces. Among these
disturbances is the tendency of satellite 1 to develop a nutational motion about
its pitch or Y-axis 6. This nutational motion can be understood by imagining the
application of a momentary perpendicular force to the rotational axis of a spinning
top or gyroscope. The perpendicular force will cause the top to begin to nutate
around the axis of its new momentum vector. The satellite's nutation prevents momentum
wheel 3 from controlling the attitude, since the momentum of the nutation greatly
exceeds the momentum capability of control wheel 3.
The goal of the transition mode correction sequence is to utilize
short pulses of thruster 5 creating impulses to stop the nutation and to orient
momentum vector 7 in a desired direction, such that attitudinal control by momentum
wheel 3 can be resumed. Figure 2 shows a graphical representation of this transition
mode, where H(0) represents the initial center 13 of the tip of momentum vector
7 in the X-Z plane nutating along an initial circular nutation path 15. From the
example above, this graph can also be thought of as representing the view looking
down on the nutating gyroscope along the momentum axis as momentum vector 7 traces
the path of nutation. The spacecraft origin 11, formed by the intersection of the
X (roll) and Z (yaw) axes including biases if desired, represents the desired
momentum vector 7 position which, when achieved, will enable momentum wheel 3 to
control spacecraft 1 stability during on-orbit mode operation.
The prior art teaches that in the ideal system, deadbeat nutation
damping allows the initial center of momentum 13 to be moved to origin 11 in two
pulses of thrusters 5 from any arbitrary initial condition. The first pulse is
triggered as the spacecraft 1 nutates to point 17. This first firing creates a
nutational trajectory 20 of momentum vector 7 which will cross the origin 11. At
the point of intersection of the X and Z axes, thrusters 5 are fired a second time
to stop momentum vector 7 at origin 11. At this point, the nutational component
is eliminated and momentum vector 7 will be controllable by the momentum wheels
3. U.S. Patent 4,931,942 teaches additional firings near the origin 11 to compensate
for non-idealities which may prevent exact intersection with origin 11.
Deadbeat Firing Sequence
The present invention makes use of a compensated thruster 5 control
system as well as a modified deadbeat sequence to more accurately and efficiently
shift momentum vector 7 from any initial position to origin 11 in three thruster
5 firings. The modified deadbeat sequence is graphically illustrated in FIG. 3.
As in the prior art diagram of FIG. 2, spacecraft 1 nutation is represented by
a momentum vector 7 tracing an initial nutation path 15 within the X-Z plane about
an initial center of momentum 13. After the mode is initiated by ground command,
the first pulsing in this modified sequence occurs anywhere on this path after
a fixed filter stabilization period in the control logic. At this firing point
thrusters 5 are pulsed for the exact duration necessary to eliminate most of the
nutation and move the center of momentum from initial center 13 to approximately
the first firing point 17. This first pulsing serves two purposes: first, momentum
vector 7 is moved closer to the origin; second, the nutation is minimized, linearizing
the dynamic system, and thus allowing more accurate calculation of the final deadbeat
pulse firings remaining to create the remaining origin-intercept vectors.
Following the first firing, the 2nd pulse width calculation is allowed
several seconds to stabilize, before a second firing initiates the nutational trajectory
20. The second firing causes the center of momentum to shift from first firing
point 17 to the center of momentum 22 along the nutational trajectory 20, which
is designed to intersect origin 11 in one-half of the nutation period. A final
third pulse is delivered at the origin 11 to bring the nutation to a halt at a
point where momentum wheel 3 control is possible. Additional firings should not
be necessary, since dynamic nonlinearities were minimized by the first firing and
the finest resolution of sensing and actuating has already been achieved.
Figure 4 shows a time-sequenced flow diagram of the disclosed transition
mode. Following the completion of station-keeping mode 25, spacecraft 1 enters
a transition mode 27 in which nutational motion is damped in preparation for on-orbit
mode 43. The first step of the transition mode is a first wait period 29 in which
the calculated pulse widths are allowed to reach a steady state. This first wait
29 nominally takes between 6 and 10 seconds. The first pulse 31 is then fired,
transferring nutation path 15 to the first transient nutation path 20. A second
wait 33 of 6 to 10 seconds is interjected to allow the calculated pulse widths
to stabilize. In a sequence, the second pulse is fired, with more accurate pulse
widths calculation, transferring the nutation path to a circular transient nutation
path 204. A third wait 37 of one-half of a nutation period is required to allow
the nutation path to intercept origin 11, at which time a third pulse 39 is fired,
killing the nutational movement and stopping momentum vector 7 at origin 11. A
fourth wait 41 of approximately one second is introduced to allow thruster 5 transients
to settle. Conversion to an operational on-orbit mode 43 automatically follows
the successful damping and spacecraft 1 orientation transition.
Figure 5 shows the prior art transition control system which also
forms the basis for thruster 5 compensation improvement of the present invention.
At the completion of the station-keeping maneuver, error calculator 55 receives
information relating to roll/yaw rates and yaw position from Digital Integrating
Rate Assembly (DIRA) 51 and information relating to spacecraft 1 roll position
from earth sensor 53. Error calculator 55 produces a pair of error coefficients
which are ultimately used to determine thruster 5 pulse duration times for yaw
and roll thrusters 71,73, respectively. Error calculator 55 produces yaw momentum
error 57 and roll momentum error 59 and transmits these coefficients into a pair
of low pass noise filters 61,63. The outputs of noise filters 61,63 are multiplied
by weighting factors 65,67 consisting of inertia components (I) divided by torque
components (T). These coefficients are then quantized and advanced to thruster
control timer 69 and used to control yaw and roll thrusters 71,73. A feedback
network is present by way of spacecraft dynamics 75.
The compensated thruster control system of the present invention
is shown in FIG. 6. As in the prior art, error coefficients are filtered in noise
filters 61,63. The outputs of noise filters 61, 63 are then applied respectively
to inertial and torque weighting factors in blocks 65 and 67. These are applied
to thruster compensators 81, 83, wherein empirical information relating to the
non-idealities of the averaged thruster's 5 performance is applied to the error
coefficients. These coefficients are quantized in blocks 85,87, and these new
error coefficients are implemented in a modified timing sequencer 89. This modified
timing sequencer calculates and transmits firing durations in yaw and roll thrusters
71, 73, respectively.
Prior to installing thrusters 5 on the spacecraft 1, experimental
burn data is collected by operating thrusters 5 over a range of burn durations,
while recording thruster 5 impulse as a function of duration. In the preferred
embodiment of the present invention data for burn periods of between 0 and 64
msec. is generally collected. This empirical data is used to derive a polynomial
approximation of the form where L(EPW)
represents the Loss (L≦1) or efficiency of the thruster 5 as a
function of the electrical pulsewidth in msec.
The positive, non-zero, integer n represents the order of the polynomial
function L(EPW). The value of n is chosen large enough to produce a close approximation
of the emperical thruster 5 performance. Values between 3 and 6 are typical in
the preferred embodiment of the present invention.
As discussed above this Loss function mathematically describes the
thruster 5 non-idealities experienced at short firing durations, typically less
than 40 msec. The object of the thruster 5 compensation is to generate a corresponding
compensation function C which, when multiplied by the Loss equation, L(EPW), cancels
the effects of the thruster 5 non-idealities. Such a function C of the Idealized
Pulsewidth (IPW) can be found by applying the Loss coefficients L&sub1;, ...Ln
solve for a set of corresponding compensation coefficients C&sub1;, ...Cn
using the relationship:
C(IPW) * L(EPW') = 1
EPW' = C(IPW) * IPW
The equation is necessarily recursive since, in the region of non-ideality, the
thruster 5 performance improves nonlinearly as pulsewidths increase. The compensation
function implemented within the thruster 5 compensation block 81,83 can be expressed
by the equation:
where C(IPW) is in msec. Alternatively, piecewise linear segments
can be used to approximate the polynomial in a numerically efficient method. In
the preferred embodiment, IPW's of interest range from 2 msec. to 40 msec. Additional
logic is provided to fix C at a constant value for IPW's less than 2 msec. and
for IPW's greater than 40 msec.
Figure 7 shows a flow chart for the method used in calculating the
compensated thruster 5 coefficients. Block 91 refers to the generation of thruster
5 loss data based on empirical information taken from the individual thruster
motors. This empirical data includes thruster 5 impulse as a function of burn time.
This thruster 5 loss data is then used to create a derating model from which polynomial
loss function coefficients can be generated as shown in step 93. The loss function
coefficients are then used to solve a polynomial compensation function in step
95, from which compensation coefficients can be extracted. Alternatively the coefficients
can be implemented in spacecraft as a piece-wise linear functions before quantization.
The quantization function applied by block 85, 87 is:
EPW = INT((EPW'-1.0)/2.0)*2.
The invention has now been explained with reference to specific embodiments.
Other embodiments will be apparent to those of ordinary skill in the art in light
of this disclosure. Therefore it is not intended that this invention be limited,
except as indicated by the appended claims.
A method for compensating thruster losses in a nutational damping control system,
wherein the method comprises the steps:
generating empirical loss data for at least one thruster;
characterizing the thruster loss data by a polynomial equation
of the form:
where EPW is the electrical pulsewidth of the thruster, L is the loss coefficient,
and n is a positive non-zero integer;
solving extended pulsewidth times from the recursive equation:
C(IPW) * L(EPW') = 1
EPW' = C(IPW) * IPW
and C(IPW) is the compensation function of the idealized pulsewidth (IPW);
quantizing the extended pulsewidth times using the function:
EPW = INT((EPW' + 1.0)/2.0) * 2.0; and
applying the quantized extended pulsewidths to thrusters by
incorporation into the nutational damping control system.
The method in claim 1, wherein the step for generating empirical thruster loss
data comprises the substeps:
operating the thrusters over a range of burn durations; and
recording thruster impulse as a function of burn duration.
The method in claim 2, wherein the range of burn durations extends from 0 to
A method for damping nutation in a spacecraft having a control system comprising
thrusters and noise filters, by using a modified deadbeat thruster firing sequence,
wherein the method comprises the steps:
firing a first thruster pulse to linearize spacecraft motion;
computing direction and duration of a second thruster pulse
allowing the momentum error filter to reach steady state through
a short wait period;
firing the second thruster pulse in order to nutate the spacecraft
to an origin point of desired on-orbit operation;
waiting one-half of a nutation period as the spacecraft nutates
to the origin; and
firing a third thruster pulse to stop nutation when the spacecraft
reaches the origin.
The method in claim 4, wherein the firing of the first thruster pulse is preceeded
by a short wait period for allowing the calculated coefficients to reach steady