Digital filter based method for measuring thrust response time of satellite-borne micro-thruster
The present disclosure belongs to the technical field of space satellite propulsion, and particularly relates to a digital filter based method for measuring thrust response time of a satellite-borne micro-thruster. The method for measuring thrust response time in the present disclosure includes the following steps: S 1 : zeroing non-zero initial conditions of a torsional pendulum thrust measurement system to obtain an oscillating differential equation for a thrust measurement system after variable substitution; S 2 : connecting the digital filter in series behind the thrust measurement system after variable substitution to obtain an equivalent-sensitivity high-frequency thrust measurement system; S 3 : determining a system response of the equivalent-sensitivity high-frequency thrust measurement system; S 4 : determining and reading thrust response time of the satellite-borne micro-thruster from the system response; and S 5 : computing thrust to be measured by means of the system response inversely, and further confirming the thrust response time.
1. A digital filter based method for measuring thrust response time of a satellite-borne micro-thruster, comprising the following steps:
S 1 : zeroing non-zero initial conditions of a thrust measurement system to obtain an oscillating differential equation for the thrust measurement system after variable substitution;
S 2 : connecting the digital filter in series behind the thrust measurement system after variable substitution to obtain an equivalent-sensitivity high-frequency thrust measurement system;
S 3 : determining a system response of the equivalent-sensitivity high-frequency thrust measurement system;
S 4 : determining and reading thrust response time of the satellite-borne micro-thruster from the system response; and
S 5 : inversely computing thrust to be measured by means of the equivalent-sensitivity high-frequency thrust measurement system.
2. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 1 , wherein in the step S 1 , the system response θ(τ) is measured by a displacement sensor under the action of the thrust f′(t) to be measured, variable substitution is carried out according to the non-zero initial conditions (θ 0 , {dot over (θ)} 0 ),and by making
θ( t )=θ′( t )−{dot over (θ)} 0 t−θ 0 , {dot over (θ)}( t )={dot over (θ)}′( t )−{dot over (θ)} 0 and {umlaut over (θ)}( t )={umlaut over (θ)}′( t ),
the oscillating differential equation for the thrust measurement system after variable substitution is obtained:
θ
¨
(
t
)
+
2
ζω
n
θ
˙
(
t
)
+
ω
n
2
θ
(
t
)
=
L
f
J
f
(
t
)
f
(
t
)
=
f
′
(
t
)
+
f
0
(
t
)
f
0
(
t
)
=
-
J
L
f
(
2
ζω
n
θ
˙
0
+
ω
n
2
θ
˙
0
t
+
ω
n
2
θ
0
)
wherein f 0 (t) represents equivalent thrust related to the non-zero initial conditions, f′(t) represents the thrust to be measured, θ′(t) represents the system response measured by the displacement sensor under the action of the thrust, ζ represents a damping ratio, ω n represents a natural vibration frequency, J represents moment of inertia, L f represents a moment arm, θ 0 represents an initial torsion angle, θ 0 and θ 0 and {dot over (θ)} 0 and are constants, θ(t) represents the system response after variable substitution, and initial conditions θ(0)=0 and {dot over (θ)}(0)=0 are satisfied.
3. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 2 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
4. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 1 , wherein in the step S 2 , a transfer function of the digital filter is,
D
(
s
)
=
ω
n
1
2
ω
n
2
[
1
-
2
(
ζ
1
ω
n
1
-
ζω
n
)
s
+
ζ
1
ω
n
1
(
s
+
ζ
1
ω
n
1
)
2
+
ω
d
1
2
)
-
(
ω
n
1
2
-
ω
n
2
)
-
2
(
ζ
1
ω
n
1
-
ζ
ω
n
)
ζ
1
ω
n
1
ω
d
1
·
ω
d
1
(
s
+
ζ
1
ω
n
1
)
2
+
ω
d
1
2
]
s represents the complex parameter variable,
and, a unit impulse response function of the digital filter is,
d
(
t
)
=
C
ω
2
[
δ
(
t
)
-
2
(
ζ
1
C
ω
-
ζ
)
ω
n
e
-
ζ
1
C
ω
ω
n
t
cos
(
1
-
ζ
1
2
C
ω
ω
n
t
)
-
(
C
ω
2
-
1
)
-
2
(
ζ
1
C
ω
-
ζ
)
ζ
1
C
ω
1
-
ζ
1
2
C
ω
ω
n
e
-
ζ
1
C
ω
ω
n
t
sin
(
1
-
ζ
1
2
C
ω
ω
n
t
)
]
wherein ω n represents the natural vibration frequency, ζ represents the damping ratio, ω n1 represents a natural frequency of the equivalent-sensitivity high-frequency thrust measurement system, ω n1 =C ω ω n , C ω represents a frequency ratio, ζ 1 represents a damping ratio of the equivalent-sensitivity high-frequency thrust measurement system, and ω d1 =√{square root over (1−ζ 1 2 )}ω n1 represents an improved vibration frequency.
5. The method for measuring thrust response time of athe satellite-borne micro-thruster according to claim 3 , wherein C ω >1.
6. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 5 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
7. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 4 , wherein ζ 1 =0.7˜0.9.
8. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 7 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
9. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 4 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
10. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 1 , wherein in the step S 3 , input of the digital filter is θ(τ), θ(τ) is computed according to a measured value θ(τ) of a displacement sensor, and the system response θ(τ) output by the digital filter is computed θ 1 (t)=∫ 0 t θ(τ)d(t−τ)dτ, wherein τ is an integral variable, the displacement sensor is used for obtaining the system responses of the thrust measurement system.
11. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 10 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
12. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 1 , wherein in the step S 4 , under the situation that the system response is 1 % greater than or less than a steady-state system response, the corresponding time is the thrust response time determined and read in S 4 .
13. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 12 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
14. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 1 , wherein in the step S 5 , a unit impulse response function h 1 (t) of the equivalent-sensitivity high-frequency thrust measurement system is,
h
1
(
t
)
=
ω
n
1
2
L
f
k
ω
d
1
e
-
ζ
1
ω
n
1
t
sin
(
ω
d
1
t
)
ω n1 represents a natural frequency of the equivalent-sensitivity high-frequency thrust measurement system;
ω d1 represents an improved vibration frequency;
ζ 1 represents a damping ratio of the equivalent-sensitivity high-frequency thrust measurement system;
L f represents a moment arm;
k represents a torsional stiffness coefficient;
what is known is that output of the digital filter is θ(t), and nominal thrust f(τ) is computed by means of an integral thrust equation for the equivalent-sensitivity high-frequency thrust measurement system: θ 1 (t)=∫ 0 t f(τ)h 1 (t−τ)dτ.
15. The method for measuring thrust response time of athe satellite- borne micro-thruster according to claim 14 , wherein an estimated value F′ (t) of the thrust f′ (t) to be measured is: F′(t)=F(t)−f(t)−f 0 (t), wherein
f
0
(
t
)
=
-
J
L
f
(
2
ζω
n
θ
˙
0
+
ω
n
2
θ
˙
0
t
+
ω
n
2
θ
0
)
,
f 0 (t) represents an equivalent thrust related to the non-zero initial conditions, F(t) represents an estimated value of the nominal thrust f(t), ζ represents a damping ratio, ω n represents a natural vibration frequency, J represents moment of inertia, L f represents a moment arm, θ 0 represents an initial torsion angle, and θ 0 and {dot over (θ)} 0 are constants.
16. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 15 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
17. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 14 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.
18. The method for measuring thrust response time of the satellite-borne micro-thruster according to claim 1 , wherein the thrust response time comprises thrust increasing time and thrust decreasing time.