Ước lượng các tham số ổn định và điều khiển của máy bay từ dữ liệu bay thử nghiệm
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power spectrum
-6
2
1
0
0
x 10
pow er spectr um
Power Spectral Density (Rudder)
x 10
0.5
-4
1
1.5
frequency (Hz)
2
2.5
3
2.5
3
Power Spectral Density (Aileron)
4
2
0
0
0.5
1
1.5
frequency (Hz)
2
5
beta(deg)
ail(deg)
5
0
-5
0
5
10
15
p(deg/s)
rdr(deg)
0
-2
0
5
10
15
0
15
20
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
5
10
15
20
0
0
-0.1
10
-20
20
r(deg/s)
0
5
20
20
0.1
ay(g)
-5
0
20
2
0
0
-20
5
10
15
20
0
phi(deg)
alt(m)
205
200
195
0
5
15
0
(deg)
0
2
4
6
r(deg)
p(deg/s)
-5
0
5
10
15
2
0
-2
0
0
-20
0
20
0
-20
5
10
15
20
0
20
(deg)
0.1
0
-0.1
0
20
20
r(deg/s)
a(deg)
0
0
-5
0
8
5
ay(g)
-20
20
2
1
0
Optimal Input and Output Variables for Lateral Maneuver
5
3
IOPTU
10
20
0
-20
5
10
15
20
0
Equation-Error Parameter Estimation
Bảng 2
0.08
flight data
regression model
0.06
CY
0.04
0.02
0
-0.02
-0.04
-0.06
0
2
4
6
8
10
12
14
16
18
20
-4
1
x 10
Bảng 3
0.5
r esid u al
0
-0.5
-1
-1.5
-2
0
2
4
6
8
10
time (sec)
12
14
16
18
20
b et a (r a d )
Output-Error Modeling
0.1
Bảng 4
data
model
0
-0.1
p (r p s)
1
0
-1
r (r p s )
0.5
0
p hi ( r ad )
-0.5
1
0
-1
a y (g)
0.2
0
-0.2
0
2
4
6
8
10
time (sec)
12
14
16
18
20
beta (rad)
Output-Error Modeling
Bảng 5
0.1
data
model
0
-0.1
p (rps)
1
0
-1
r (rps)
1
0
phi (rad)
-1
1
0
-1
ay (g)
0.2
0
-0.2
0
2
4
6
8
10
time (sec)
12
14
16
18
20
Square Inputs
Parameter
CYbeta
CYda
CYdr
CYo
Clbeta
Clp
Clr
Clda
Cldr
Clo
Cnbeta
Cnp
Cnr
Cnda
Cndr
Cno
∑σ2
True
Value
-0.8300
-0.0750
0.1914
0.0000
-0.1300
-0.5051
0.2519
-0.1695
0.0024
0.0000
0.0726
-0.0690
-0.0946
0.0108
-0.0693
0.0000
Optimal Inputs
Equation Error
Calculated Standard Error
Value
Deviation (%)
-0.8793
-0.0747
0.1912
0.0000
-0.1543
-0.5020
0.2518
-0.1709
0.0079
0.0000
0.0767
-0.0690
-0.0946
0.0112
-0.0703
0.0000
6.20E-05
3.76E-05
7.89E-05
6.45E-07
6.96E-04
1.96E-03
1.66E-03
5.75E-04
4.14E-04
1.54E-05
6.27E-07
2.22E-06
1.20E-06
7.01E-07
4.16E-07
4.20E-09
7.57E-06
5.9
0.4
0.1
0.0
18.7
0.6
0.0
0.9
231.0
0.0
5.6
0.0
0.0
3.5
1.4
0.0
Equation Error
Parameter
True Calculated Standard Error
Value
Value Deviation (%)
CYbeta
-0.8300 -0.8784
1.01E-04
5.8
CYda
CYdr
CYo
Clbeta
Clp
Clr
Clda
Cldr
Clo
Cnbeta
Cnp
Cnr
Cnda
Cndr
-0.0750
0.1914
0.0000
-0.1300
-0.5051
0.2519
-0.1695
0.0024
0.0000
0.0726
-0.0690
-0.0946
0.0108
-0.0693
-0.0746
0.1910
-0.0008
-0.1516
-0.4925
0.2571
-0.1679
0.0095
0.0002
0.0767
-0.0690
-0.0946
0.0112
-0.0703
1.16E-04
1.42E-04
1.68E-06
1.75E-03
5.98E-03
2.98E-03
1.68E-03
9.79E-04
5.70E-05
1.26E-06
4.03E-06
2.25E-06
1.33E-06
8.90E-07
0.5
0.2
0.0
16.6
2.5
2.1
1.0
296.9
0.0
5.6
0.0
0.0
3.5
1.4
Cno
0.0000
∑σ2
% change
0.0001
1.71E-08
5.15E-05
6
0.0
Maximum Likelihood (Aerosonde_lat_data1.mat)
stdv = 2%
stdv = 5%
stdv = 10%
Cal.
Cal. Standard
Cal.
STDV Error
Error
STDV Error
Value
Value Deviation
Value
-0.8282
-0.0711
0.1926
0.0000
-0.1297
-0.5048
0.2540
-0.1689
0.0024
0.0000
0.0711
-0.0732
-0.0922
0.0093
-0.0692
0.0000
2.53E-03 0.2 -0.8278 6.47E-03 0.3 -0.8370 1.43E-02 0.8
1.47E-03 5.2 -0.0719 3.68E-03 4.1 -0.0827 7.51E-03 10.3
2.80E-03 0.6 0.1824 7.68E-03 4.7 0.1858 1.45E-02 2.9
0.00E+00 0.0 0.0000 0.00E+00 0.0 0.0000 0.00E+00 0.0
1.01E-03 0.2 -0.1303 1.52E-03 0.2 -0.1341 3.42E-03 3.1
2.90E-03 0.1 -0.5023 4.02E-03 0.6 -0.5127 7.09E-03 1.5
2.29E-03 0.8 0.2514 4.07E-03 0.2 0.2622 8.05E-03 4.1
1.03E-03 0.4 -0.1682 1.41E-03 0.8 -0.1736 2.60E-03 2.4
7.61E-04 0.6 0.0019 1.48E-03 20.3 0.0032 3.74E-03 35.2
0.00E+00 0.0 0.0000 0.00E+00 0.0 0.0000 0.00E+00 0.0
2.94E-04 2.0 0.0715 4.66E-04 1.5 0.0724 9.77E-04 0.3
1.11E-03 6.1 -0.0715 1.71E-03 3.6 -0.0667 3.45E-03 3.3
5.25E-04 2.5 -0.0938 1.31E-03 0.8 -0.0941 2.40E-03 0.6
3.45E-04 13.7 0.0099 5.33E-04 8.7 0.0113 1.11E-03 4.8
2.24E-04 0.2 -0.0694 5.08E-04 0.1 -0.0689 1.11E-03 0.6
0.00E+00 0.0 0.0000 0.00E+00 0.0 0.0000 0.00E+00 0.0
3.45E-05
1.59E-04
6.42E-04
Maximum Likelihood (Aerosonde_lat_opt_data2.mat)
stdv = 2%
stdv = 5%
stdv = 10%
Cal.
Cal.
Cal.
STDV Error
STDV Error
STDV Error
Value
Value
Value
-0.8254 2.28E-03
-0.0736
0.1922
0
-0.1307
-0.5109
0.2515
-0.1708
0.0008
0
0.0716
-0.0704
-0.0935
0.0104
-0.0690
0.6
1.96E-03 1.8
2.24E-03 0.4
0
0.0
9.88E-04 0.5
2.86E-03 1.1
1.27E-03 0.1
8.23E-04 0.8
7.03E-04 65.1
0
0.0
4.39E-04 1.3
1.48E-03 2.1
4.80E-04 1.2
4.56E-04 3.9
2.09E-04 0.5
0.0000 0.00E+00
2.88E-05
-17
0.0
-0.8323 4.85E-03
0.3
-0.8180 1.04E-02
-0.0755
0.1933
0
-0.1294
-0.5040
0.2500
-0.1687
0.0005
0
0.0708
-0.0719
-0.0926
0.0096
-0.0685
5.24E-03
6.42E-03
0
1.98E-03
5.73E-03
2.52E-03
1.72E-03
1.47E-03
0
7.99E-04
2.68E-03
9.41E-04
8.29E-04
4.17E-04
0.7
1.0
0.0
0.5
0.2
0.8
0.5
81.2
0.0
2.5
4.2
2.1
10.8
1.2
-0.0752
0.1753
0.0000
-0.1318
-0.5148
0.2572
-0.1706
0.0047
0.0000
0.0708
-0.0727
-0.0926
0.0104
-0.0693
9.67E-03 0.3
1.27E-02 8.4
0.00E+00 0.0
4.44E-03 1.4
1.08E-02 1.9
6.01E-03 2.1
3.38E-03 0.7
3.48E-03 95.7
0.00E+00 0.0
1.63E-03 2.4
5.55E-03 5.4
2.06E-03 2.2
1.63E-03 3.3
8.43E-04 0.0
1.4
0.0000
0.00E+00
1.50E-04
-6
0.0
0.0000
0.00E+00
6.02E-04
-6
0.0
