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.
power spectrum -6 0 x 10 pow er spectr um Power Spectral Density (Rudder) x 10 0.5 -4 1.5 frequency (Hz) 2.5 2.5 Power Spectral Density (Aileron) 0 0.5 1.5 frequency (Hz) beta(deg) ail(deg) -5 10 15 p(deg/s) rdr(deg) -2 10 15 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 10 15 20 0 -0.1 10 -20 20 r(deg/s) 20 20 0.1 ay(g) -5 20 0 -20 10 15 20 phi(deg) alt(m) 205 200 195 15 (deg) r(deg) p(deg/s) -5 10 15 -2 0 -20 20 -20 10 15 20 20 (deg) 0.1 -0.1 20 20 r(deg/s) a(deg) 0 -5 ay(g) -20 20 Optimal Input and Output Variables for Lateral Maneuver IOPTU 10 20 -20 10 15 20 Equation-Error Parameter Estimation Bảng 0.08 flight data regression model 0.06 CY 0.04 0.02 -0.02 -0.04 -0.06 10 12 14 16 18 20 -4 x 10 Bảng 0.5 r esid u al -0.5 -1 -1.5 -2 10 time (sec) 12 14 16 18 20 b et a (r a d ) Output-Error Modeling 0.1 Bảng data model -0.1 p (r p s) -1 r (r p s ) 0.5 p hi ( r ad ) -0.5 -1 a y (g) 0.2 -0.2 10 time (sec) 12 14 16 18 20 beta (rad) Output-Error Modeling Bảng 0.1 data model -0.1 p (rps) -1 r (rps) phi (rad) -1 -1 ay (g) 0.2 -0.2 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 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 -0.1307 -0.5109 0.2515 -0.1708 0.0008 0.0716 -0.0704 -0.0935 0.0104 -0.0690 0.6 1.96E-03 1.8 2.24E-03 0.4 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 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 -0.1294 -0.5040 0.2500 -0.1687 0.0005 0.0708 -0.0719 -0.0926 0.0096 -0.0685 5.24E-03 6.42E-03 1.98E-03 5.73E-03 2.52E-03 1.72E-03 1.47E-03 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