Tracking system for tracking targets with a spacecraft

• US 5,400,033 A
• Filed: 02/07/1994
• Issued: 03/21/1995
• Est. Priority Date: 02/07/1994
• Status: Expired due to Fees

• Current Assignee: Rockwell International Corporation
• Original Assignee: Rockwell International Corporation
• Inventors: Hablani, Hari B.
• Primary Examiner(s): Sotomayor, John B.
• Application Number:
  US08/192,877
• Time in Patent Office: 407 Days
• Field of Search: 342/95, 342/52, 342/58, 342/62, 342/75, 342/77, 342/81, 342/96, 342/97, 342/352, 342/357, 342/354, 342/355, 342/358, 342/417, 342/420, 342/421, 342/76
• US Class Current: 342/95
• CPC Class Codes: B64G 1/244 Spacecraft control systems
• CPC Class Codes: B64G 1/26 using jets
• CPC Class Codes: B64G 1/36 using sensors, e.g. sun-sensors, horizon sensors

Abstract

This invention comprises the use of integral pulse frequency modulation (IPFM) reaction jet controllers for multi-axis precision tracking of moving objects with flexible spacecraft, and vibration suppression. Two sets of position, rate and accelertion command profiles for multi-axis tracking are disclosed: one for a payload initially facing the zenith and the commands based on a pitch-roll sequence; the other for a payload facing the nadir and the commands based on a roll-pitch sequence. The procedure for designing an IPFM controller for tracking a given, inertial acceleration command profile is disclosed. Important elastic modes of a spacecraft are identified according to their spontaneous attitude and rate response to the minimum impulse bit of the thrusters. The stability of the control-structure interaction is shown to be governed by the ratio of the moments of inertia of the flexible to the rigid portions of the spacecraft. If this ratio is below unity for any axis, the spacecraft is stable; otherwise, not. The stability inequality for symmetric elastic modes, when they induce attitude motion because of a moment arm from the vehicle mass center, is formulated.

Claims

1. A tracking system for tracking a target with a spacecraft, comprising:

at least one integral pulse frequency modulation reaction jet control system for tracking the target with small tracking errors,

said at least one reaction jet control system comprising;

a) means for utilizing target trajectory data (r_T) and spacecraft trajectory data (r_S) to determine line of sight trajectory data l_I ; and

line of sight rate l_I ;

b) means for determining spacecraft attitude command (Θ

_C) and rate command (ω

_C) utilizing said l_I and said l_I ;

c) means for utilizing said (Θ

_C) and (ω

_C) in conjunction with actual attitude signals (Θ

) and rate signals (ω

) of said spacecraft for determining spacecraft attitude error (Θ

_e) and error (ω

_e);

d) means for multiplying said ω

_e with a diagonal rate gain matrix (K_D), and adding the resultant value, K_D ω

_e, to said Θ

_e to provide a combined error e;

e) means for integrating said e and comparing the integrated combined error (e_I) with a threshold vector (A_I), jets of said spacecraft being turned on about an axis if the corresponding element of said (e_I) exceeds the corresponding element of said A_I, said previous steps being repeated if any element of said A_I exceeds the corresponding element of said e_I ; and

f) means for zeroing any element of e_I whenever it exceeds the corresponding element of A_I and starting its integration afresh, repeating the above steps.

2. The tracking system of claim 1, wherein said means for utilizing said θ

_C, ω

_C, θ and

ω

for determining θ

_e and ω

_e, comprises;

rate gyros about roll, pitch and yaw axes of said spacecraft for determining ω and

θ

.

3. The tracking system of claim 1, wherein said means for utilizing said θ

_c, ω

_c, θ and

ω

for determining θ

_e and ω

_e, comprises;

a rate gyro about a yaw axis of said spacecraft to determine spacecraft yaw rate (ω

_z) and, means for determining an instantaneous location of a target image on a spacecraft focal plane, from which roll and pitch position errors, θ

_xe and θ

_ye, are determined by the equations;

##EQU16## where (l_xb, l_yb) locate the target image on the spacecraft focal plane and l is the distance from the spacecraft to the target.

4. The tracking system of claim 1, further including means for determining said A_I and said K_D, comprising:

means for utilizing said l_I and its derivatives l_I and l_I for determining angular acceleration commands (ω

_c) and using said ω

_c to determine the threshold vector A_I and the diagonal matrix K_D.

5. The tracking system of claim 4, wherein said ω

_c, comprises ω

_xc, ω

_yc and ω

_zc defined as follows;

space="preserve" listing-type="equation">ω

.sub.xc =(l.b.sub.2 -2lω

.sub.xc)/l+ω

.sub.yc ω

.sub.zc (

     1)

space="preserve" listing-type="equation">ω

.sub.yc =-(l.b.sub.1 +2lω

.sub.yc)/l-ω

.sub.xc ω

.sub.zc (

     2)

space="preserve" listing-type="equation">ω

.sub.zc =-ω

.sub.yc tan θ

.sub.xc -ω

.sub.xc ω

.sub.yc sec.sup.2 θ

.sub.xc (

     3)

where l.b₁ and l.b₂ are the components of the line-of-sight acceleration (l) along the spacecraft roll and pitch axes, respectively;

l is the rate of change of the line-of-sight l along the negative yaw axis (the sensor boresight), said control parameters A_I and K_D being determined for each axis as follows;

##EQU17## where θ

_ss is the acceptable steady-state pointing error, 2 θ

_L is the angular rate increment caused by minimum impulse bit of the thrusters, ω

_xc,max is the maximum commanded angular acceleration about the x-axis, and ζ

_c =0.707 is the damping coefficient of an equivalent linear controller, A_I and K_D being similarly defined for the y-axis and z-axis.

6. A tracking system for tracking a target with a spacecraft, comprising:

at least one integral pulse frequency modulation reaction jet control system for tracking the target with small tracking errors,

said at least one reaction jet control system, comprising a single reaction jet control system for single-axis slew, said single reaction jet control system, comprising;

a) means for determining instantaneous time-and-fuel-optimal position command (Θ

_c) and rate command ω

_c about a slew axis;

b) means for utilizing said Θ

_c and ω

_c in conjunction with an actual attitude signal (Θ

) and rate signal (ω

) of said spacecraft about the axis under consideration, for determining attitude error Θ

_e and rate error ω

_e ;

c) means for multiplying said ω

_e with a rate gain K_D, and adding the resulting value K_D ω

_e to said Θ

_e to provide a combined error e;

d) means for integrating said e and comparing the integrated combined error e_I with a threshold A_I, jets of said spacecraft being turned on about the slew axis if A_I exceeds |e_I |, the sign of the torque being the same as the sign of e_I, said previous steps being repeated if A_I exceeds |e_I |; and

e) means for zeroing e_I when |e_I | exceeds the threshold A_I and starting its integration afresh, repeating the above steps,

said Θ

_c and ω

_c about the other two axes of the spacecraft being zeroed.

7. The single-axis reaction jet control system for single-axis slew as defined in claim 6, wherein said control parameters A_I and K_D are determined as follows:

##EQU18## where θ

_ss is the acceptable steady-state difference between commanded slew angle (θ

_c) and actual slew angle θ

, 2 θ

_L is the angular rate increment caused by minimum impulse bit of the thrusters, ω

_slew,max is the maximum commanded slew acceleration, and ζ

_c =1/√

2 is the damping coefficient of an equivalent linear controller.

8. A tracking system for tracking a target with a spacecraft, comprising:

at least one integral pulse frequency modulation reaction jet control system for tracking the target with small tracking errors,

wherein said spacecraft has a flexible portion, said spacecraft being modeled by quantifying the importance of each vehicle elastic mode by the following criteria;

space="preserve" listing-type="equation">Δ

Θ

.sub.μ

=Φ

.sub.μ

Φ

.sub.μ

eq T.sub.c τ

.sub.w(

     1)

space="preserve" listing-type="equation">Δ

Θ

.sub.μ

=Φ

.sub.μ

Φ

.sub.μ

,eq T.sub.c τ

.sub.w /ω

.sub.μ

(

     2)

wherein Δ

Θ

.sub.μ

is the spontaneous attitude response and Δ

Θ

.sub.μ

is the attitude rate response arising from μ

-th vehicle elastic mode excited by the minimum impulse T_c τ

_w of the thrusters, and wherein

T_c =control torque produced by the thrusters

τ

_w =minimum pulse width of the thrusters

Φ

.sub.μ

=the slope of the mode μ

contributing to the spacecraft attitude Θ

as measured by a gyro ##EQU19## =equivalent modal slope at the thruster locations χ

.sub.μ

j =μ

-th translational modal coefficient at the j-th thruster location

ω

.sub.μ

=frequency of μ

-th mode

a_j =unit vector along the force of the j-th thruster

l_eq =equivalent moment arm corresponding to all thrusters firing simultaneously to produce the torque T_c =fl_eq

f_j =force vector produced by j-th thruster, f_j =a_j f

f=|f_j | ##EQU20## =summation over all j-th thrusters firing simultaneously to produce the torque T_c,j critical modes being selected based on dominant Δ

Θ

.sub.μ

.

9. The tracking system of claim 8, wherein stability conditions are determined by the following criteria:

Condition 1;

Δ

θ

.sub.μ

<

<

2θ

_L,

or equivalently

Condition 2;

I_f /I_r <

<

1,

the first condition being applied to the most critical mode, based on said dominant Δ

θ

.sub.μ

, I_f and I_r =moments of inertia, respectively, of flexible and rigid portions of the spacecraft at the vehicle mass center and about the principle axis under consideration.

10. The tracking system of claim 8, wherein the locations of the spacecraft thrusters are determined by the following stability criterion:

space="preserve" listing-type="equation">Φ

.sub.μ

Φ

.sub.μ

,eq >

0,

the control system being unstable if this criterion is not satisfied.