US 5,702,067 AGranted

Method and apparatus for determining the angular momentum vector of a satellite

AssigneeDaimler-Benz Aerospace AG

InventorErnst Bruederle

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Abstract

The invention relates to a method for determining the angular momentum vector of a satellite, located in an external magnetic field, relative to a satellite-integral orthogonal system of coordinates. The satellite has a torque generating system to generate pulse-shaped torques around all three axes. A magnetometer measuring on three axes is used, whose measured values are fed to a computer. In the latter, at successive points in time and using the current measured values, an observer equation is integrated, with new estimated values being determined for the angular momentum vector. Using these as well as the current measured values, an inequality is continuously checked; when it is not fulfilled, the torque generating system operates briefly, so that finally the fulfillment of the inequality is forced and identity of the last estimated value that has been determined with the rotary pulse vector to be determined is achieved.

Method for determining an angular momentum vector H of an object located in an externally generated magnetic field B, relative to an orthogonal system of coordinates whose axes x,y,z coincide with main inertia axes of the object, said object having a magnetometer for measuring magnetic field strength in the direction of said x, y and z axes, and a torque generating system for producing torque pulses about all three axes, said method comprising the steps of:

measuring magnetic field strength B of said externally generated magnetic field along said x, y and z axes by means of said magnetometer, wherein B=(B.sub.i).sup.T (i=x.sub.1 y,z);
entering measured values of said magnetic field strength B into a computer;
said computer calculating estimated values H of angular momentum of said object at successive points in time, for each calculation using most recently measured values of said magnetic field strength and integrating the observer equation
H=H.times.I.sup.-1 H+I.sup.-1 A.sup.T K(Y-AI.sup.-1 H)+M
with ##EQU20## wherein M is an estimated value for an angular torque vector;
I is an inertia matrix of the satellite, and I.sup.-1 is its inverse matrix;
A is a quadratic matrix of rank 3 with three mutually orthogonal line vectors, one of which coincides with a normalized magnetic field vector b.ident.B/.vertline.B.vertline., and A.sup.T is its transposed matrix;
K is a quadratic starting matrix K=(k.sub.lm) with rank 3 (l,m=1,2,3), with coefficients k.sub.lm equal to zero in a column whose number coincides with a number of the line in matrix A in which the normalized magnetic field vector b is located, and whose other coefficients must be determined in such fashion that the matrix ##EQU21## is positively definite or semi-definite;
with ##EQU22## wherein I.sub.x,y,z represent diagonal components of inertia matrix I;
continuously checking calculated values H and current measured values of said normalized magnetic field vector b to determine whether an inequality
(Ib.times.b).sup.T H.gtoreq.0
is satisfied;
if said inequality is not satisfied, said torque generating system applying a torque M=(M.sub.x,M.sub.y,M.sub.z).sup.T to said object for time intervals .DELTA.t.sub.x, .DELTA.t.sub.y, .DELTA.t.sub.z, to cause a change in angular momentum .DELTA.H=(M.sub.i .DELTA.t.sub.i).sup.T whereby said inequality is satisfied;
and
performing successive integrations until such integrations no longer result in a change in .vertline.H.vertline., whereby the calculated value of H is equal to an actual angular momentum vector H of said object.

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Facts

Application

08/526,566Filed 11 Sep 1995

Priority

DE P 44 32 265.810 Sep 1994

Granted

30 Dec 1997

Term ends

Not estimatedThe source records don’t support an estimate.

Classification5 codes

B64G 1/366
Using sensors, e.g. sun-sensors, horizon sensors: using magnetometers
B64G 1/244
Guiding or controlling apparatus, e.g. for attitude control: spacecraft control systems
B64G 1/32
Guiding or controlling apparatus, e.g. for attitude control: using earth's magnetic field
B64G 1/245
Spacecraft control systems: attitude control algorithms for spacecraft attitude control

Abstract

Claims6