Mục đích của bài báo này là ước lượng các tham số ổn định và điều khiển của máy bay từ dữ liệu thử nghiệm bằng 2 phương pháp: Equation Error, Maximum Likelibood. Bài báo cũng trình bày những ưu nhược điểm của từng phương pháp được nhận dạng với các tín hiệu bay thử nghiệm dưới dạng xung vuông 3-2-1-1 kiểu truyền thống,... Mời các bạn cùng tham khảo.
Trang 70 0.5 1 1.5 2 2.5 3 0
1
2
x 10
frequency (Hz)
Power Spectral Density (Rudder)
0
2
4
x 10-4
frequency (Hz)
Power Spectral Density (Aileron)
0
1
2
x 10
frequency (Hz)
Power Spectral Density (Rudder)
0
2
4
x 10-4
frequency (Hz)
Power Spectral Density (Aileron)
Trang 80 5 10 15 20 -5
0 5
-5
0
-2 0 2
-20 0 20
-0.1
0 0.1
-20 0 20
195
200
205
-20 0 20
1 2 3
Optimal Input and Output Variables for Lateral Maneuver
-5 0 5
-5 0 5
-20 0 20
-2 0 2
-20 0 20
-0.1
0 0.1
-20 0 20
Trang 90 2 4 6 8 10 12 14 16 18 20
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
flight data regression model
-2
-1.5
-1
-0.5
0
0.5
1x 10
-4
Bảng 3
Bảng 2
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
flight data regression model
-2
-1.5
-1
-0.5
0
0.5
1x 10
-4
Bảng 3 Bảng 2
Trang 100
0.1
data model
-1
0
1
-0.5
0
0.5
-1
0
1
-0.2
0
0.2
time (sec)
Bảng 4
-0.1
0
0.1
data model
-1
0
1
-0.5
0
0.5
-1
0
1
-0.2
0
0.2
time (sec)
Bảng 4
-0.1
0
0.1
Output-Error Modeling
model
-1
0
1
-1
0
1
-1
0
1
-0.2
0
0.2
Bảng 5
-0.1
0
0.1
Output-Error Modeling
model
-1
0
1
-1
0
1
-1
0
1
-0.2
0
0.2
Bảng 5
Trang 116.42E-04 1.59E-04
3.45E-05 7.57E-06
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 4.20E-09 0.0000
0.0000
Cno
0.6 1.11E-03 -0.0689
0.1 5.08E-04 -0.0694
0.2 2.24E-04 -0.0692
1.4 4.16E-07 -0.0703
-0.0693
Cndr
4.8 1.11E-03 0.0113
8.7 5.33E-04 0.0099
13.7 3.45E-04 0.0093
3.5 7.01E-07 0.0112
0.0108
Cnda
0.6 2.40E-03 -0.0941
0.8 1.31E-03 -0.0938
2.5 5.25E-04 -0.0922
0.0 1.20E-06 -0.0946
-0.0946
Cnr
3.3 3.45E-03 -0.0667
3.6 1.71E-03 -0.0715
6.1 1.11E-03 -0.0732
0.0 2.22E-06 -0.0690
-0.0690
Cnp
0.3 9.77E-04 0.0724
1.5 4.66E-04 0.0715
2.0 2.94E-04 0.0711
5.6 6.27E-07 0.0767
0.0726
Cnbeta
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 1.54E-05 0.0000
0.0000
Clo
35.2 3.74E-03 0.0032
20.3 1.48E-03 0.0019
0.6 7.61E-04 0.0024
231.0 4.14E-04 0.0079
0.0024
Cldr
2.4 2.60E-03 -0.1736
0.8 1.41E-03 -0.1682
0.4 1.03E-03 -0.1689
0.9 5.75E-04 -0.1709
-0.1695
Clda
4.1 8.05E-03 0.2622
0.2 4.07E-03 0.2514
0.8 2.29E-03 0.2540
0.0 1.66E-03 0.2518
0.2519
Clr
1.5 7.09E-03 -0.5127
0.6 4.02E-03 -0.5023
0.1 2.90E-03 -0.5048
0.6 1.96E-03 -0.5020
-0.5051
Clp
3.1 3.42E-03 -0.1341
0.2 1.52E-03 -0.1303
0.2 1.01E-03 -0.1297
18.7 6.96E-04 -0.1543
-0.1300
Clbeta
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 6.45E-07 0.0000
0.0000
CYo
2.9 1.45E-02 0.1858
4.7 7.68E-03 0.1824
0.6 2.80E-03 0.1926
0.1 7.89E-05 0.1912
0.1914
CYdr
10.3 7.51E-03 -0.0827
4.1 3.68E-03 -0.0719
5.2 1.47E-03 -0.0711
0.4 3.76E-05 -0.0747
-0.0750
CYda
0.8 1.43E-02 -0.8370
0.3 6.47E-03 -0.8278
0.2 2.53E-03 -0.8282
5.9 6.20E-05 -0.8793
-0.8300
CYbeta
Error STDV Cal.
Value Error Standard Deviation
Cal.
Value Error STDV Cal.
Value
Error (%)
Standard Deviation
Calculated Value
True
Value
Parameter
stdv = 10% stdv = 5%
stdv = 2%
Maximum Likelihood (Aerosonde_lat_data1.mat) Equation Error
Square Inputs
6.42E-04 1.59E-04
3.45E-05 7.57E-06
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 4.20E-09 0.0000
0.0000
Cno
0.6 1.11E-03 -0.0689
0.1 5.08E-04 -0.0694
0.2 2.24E-04 -0.0692
1.4 4.16E-07 -0.0703
-0.0693
Cndr
4.8 1.11E-03 0.0113
8.7 5.33E-04 0.0099
13.7 3.45E-04 0.0093
3.5 7.01E-07 0.0112
0.0108
Cnda
0.6 2.40E-03 -0.0941
0.8 1.31E-03 -0.0938
2.5 5.25E-04 -0.0922
0.0 1.20E-06 -0.0946
-0.0946
Cnr
3.3 3.45E-03 -0.0667
3.6 1.71E-03 -0.0715
6.1 1.11E-03 -0.0732
0.0 2.22E-06 -0.0690
-0.0690
Cnp
0.3 9.77E-04 0.0724
1.5 4.66E-04 0.0715
2.0 2.94E-04 0.0711
5.6 6.27E-07 0.0767
0.0726
Cnbeta
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 1.54E-05 0.0000
0.0000
Clo
35.2 3.74E-03 0.0032
20.3 1.48E-03 0.0019
0.6 7.61E-04 0.0024
231.0 4.14E-04 0.0079
0.0024
Cldr
2.4 2.60E-03 -0.1736
0.8 1.41E-03 -0.1682
0.4 1.03E-03 -0.1689
0.9 5.75E-04 -0.1709
-0.1695
Clda
4.1 8.05E-03 0.2622
0.2 4.07E-03 0.2514
0.8 2.29E-03 0.2540
0.0 1.66E-03 0.2518
0.2519
Clr
1.5 7.09E-03 -0.5127
0.6 4.02E-03 -0.5023
0.1 2.90E-03 -0.5048
0.6 1.96E-03 -0.5020
-0.5051
Clp
3.1 3.42E-03 -0.1341
0.2 1.52E-03 -0.1303
0.2 1.01E-03 -0.1297
18.7 6.96E-04 -0.1543
-0.1300
Clbeta
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 6.45E-07 0.0000
0.0000
CYo
2.9 1.45E-02 0.1858
4.7 7.68E-03 0.1824
0.6 2.80E-03 0.1926
0.1 7.89E-05 0.1912
0.1914
CYdr
10.3 7.51E-03 -0.0827
4.1 3.68E-03 -0.0719
5.2 1.47E-03 -0.0711
0.4 3.76E-05 -0.0747
-0.0750
CYda
0.8 1.43E-02 -0.8370
0.3 6.47E-03 -0.8278
0.2 2.53E-03 -0.8282
5.9 6.20E-05 -0.8793
-0.8300
CYbeta
Error STDV Cal.
Value Error Standard Deviation
Cal.
Value Error STDV Cal.
Value
Error (%)
Standard Deviation
Calculated Value
True
Value
Parameter
stdv = 10% stdv = 5%
stdv = 2%
Maximum Likelihood (Aerosonde_lat_data1.mat) Equation Error
Square Inputs
-6 -6
-17 6
% change
6.02E-04 1.50E-04
2.88E-05 5.15E-05
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 1.71E-08 0.0001
0.0000
Cno
0.0 8.43E-04 -0.0693
1.2 4.17E-04 -0.0685
0.5 2.09E-04 -0.0690
1.4 8.90E-07 -0.0703
-0.0693
Cndr
3.3 1.63E-03 0.0104
10.8 8.29E-04 0.0096
3.9 4.56E-04 0.0104
3.5 1.33E-06 0.0112
0.0108
Cnda
2.2 2.06E-03 -0.0926
2.1 9.41E-04 -0.0926
1.2 4.80E-04 -0.0935
0.0 2.25E-06 -0.0946
-0.0946
Cnr
5.4 5.55E-03 -0.0727
4.2 2.68E-03 -0.0719
2.1 1.48E-03 -0.0704
0.0 4.03E-06 -0.0690
-0.0690
Cnp
2.4 1.63E-03 0.0708
2.5 7.99E-04 0.0708
1.3 4.39E-04 0.0716
5.6 1.26E-06 0.0767
0.0726
Cnbeta
0.0 0.00E+00 0.0000
0.0 0
0 0.0 0 0 0.0 5.70E-05 0.0002
0.0000
Clo
95.7 3.48E-03 0.0047
81.2 1.47E-03 0.0005
65.1 7.03E-04 0.0008
296.9 9.79E-04 0.0095
0.0024
Cldr
0.7 3.38E-03 -0.1706
0.5 1.72E-03 -0.1687
0.8 8.23E-04 -0.1708
1.0 1.68E-03 -0.1679
-0.1695
Clda
2.1 6.01E-03 0.2572
0.8 2.52E-03 0.2500
0.1 1.27E-03 0.2515
2.1 2.98E-03 0.2571
0.2519
Clr
1.9 1.08E-02 -0.5148
0.2 5.73E-03 -0.5040
1.1 2.86E-03 -0.5109
2.5 5.98E-03 -0.4925
-0.5051
Clp
1.4 4.44E-03 -0.1318
0.5 1.98E-03 -0.1294
0.5 9.88E-04 -0.1307
16.6 1.75E-03 -0.1516
-0.1300
Clbeta
0.0 0.00E+00 0.0000
0.0 0
0 0.0 0 0 0.0 1.68E-06 -0.0008
0.0000
CYo
8.4 1.27E-02 0.1753
1.0 6.42E-03 0.1933
0.4 2.24E-03 0.1922
0.2 1.42E-04 0.1910
0.1914
CYdr
0.3 9.67E-03 -0.0752
0.7 5.24E-03 -0.0755
1.8 1.96E-03 -0.0736
0.5 1.16E-04 -0.0746
-0.0750
CYda
1.4 1.04E-02 -0.8180
0.3 4.85E-03 -0.8323
0.6 2.28E-03 -0.8254
5.8 1.01E-04 -0.8784
-0.8300
CYbeta
Error STDV Cal
Value Error STDV Cal
Value Error STDV Cal
Value
Error (%)
Standard Deviation
Calculated Value
True
Value
Parameter
stdv = 10% stdv = 5%
stdv = 2%
Maximum Likelihood (Aerosonde_lat_opt_data2.mat) Equation Error
Optimal Inputs
-6 -6
-17 6
% change
6.02E-04 1.50E-04
2.88E-05 5.15E-05
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 0.00E+00 0.0000
0.0 1.71E-08 0.0001
0.0000
Cno
0.0 8.43E-04 -0.0693
1.2 4.17E-04 -0.0685
0.5 2.09E-04 -0.0690
1.4 8.90E-07 -0.0703
-0.0693
Cndr
3.3 1.63E-03 0.0104
10.8 8.29E-04 0.0096
3.9 4.56E-04 0.0104
3.5 1.33E-06 0.0112
0.0108
Cnda
2.2 2.06E-03 -0.0926
2.1 9.41E-04 -0.0926
1.2 4.80E-04 -0.0935
0.0 2.25E-06 -0.0946
-0.0946
Cnr
5.4 5.55E-03 -0.0727
4.2 2.68E-03 -0.0719
2.1 1.48E-03 -0.0704
0.0 4.03E-06 -0.0690
-0.0690
Cnp
2.4 1.63E-03 0.0708
2.5 7.99E-04 0.0708
1.3 4.39E-04 0.0716
5.6 1.26E-06 0.0767
0.0726
Cnbeta
0.0 0.00E+00 0.0000
0.0 0
0 0.0 0 0 0.0 5.70E-05 0.0002
0.0000
Clo
95.7 3.48E-03 0.0047
81.2 1.47E-03 0.0005
65.1 7.03E-04 0.0008
296.9 9.79E-04 0.0095
0.0024
Cldr
0.7 3.38E-03 -0.1706
0.5 1.72E-03 -0.1687
0.8 8.23E-04 -0.1708
1.0 1.68E-03 -0.1679
-0.1695
Clda
2.1 6.01E-03 0.2572
0.8 2.52E-03 0.2500
0.1 1.27E-03 0.2515
2.1 2.98E-03 0.2571
0.2519
Clr
1.9 1.08E-02 -0.5148
0.2 5.73E-03 -0.5040
1.1 2.86E-03 -0.5109
2.5 5.98E-03 -0.4925
-0.5051
Clp
1.4 4.44E-03 -0.1318
0.5 1.98E-03 -0.1294
0.5 9.88E-04 -0.1307
16.6 1.75E-03 -0.1516
-0.1300
Clbeta
0.0 0.00E+00 0.0000
0.0 0
0 0.0 0 0 0.0 1.68E-06 -0.0008
0.0000
CYo
8.4 1.27E-02 0.1753
1.0 6.42E-03 0.1933
0.4 2.24E-03 0.1922
0.2 1.42E-04 0.1910
0.1914
CYdr
0.3 9.67E-03 -0.0752
0.7 5.24E-03 -0.0755
1.8 1.96E-03 -0.0736
0.5 1.16E-04 -0.0746
-0.0750
CYda
1.4 1.04E-02 -0.8180
0.3 4.85E-03 -0.8323
0.6 2.28E-03 -0.8254
5.8 1.01E-04 -0.8784
-0.8300
CYbeta
Error STDV Cal
Value Error STDV Cal
Value Error STDV Cal
Value
Error (%)
Standard Deviation
Calculated Value
True
Value
Parameter
stdv = 10% stdv = 5%
stdv = 2%
Maximum Likelihood (Aerosonde_lat_opt_data2.mat) Equation Error
Optimal Inputs