A flight system identification
By A. H. Haji
Although several numerical methods most commonly based on CFD techniques have developed and used for extraction of aerodynamic coefficients of a flight system, the system identification approach is still regarded as a part of the empirical evaluation of the coefficients obtained by CFD methods. The following code is written for a 2-D linearized rigid body flight dynamics. In this code the observable data are simulated with the exact coefficients in the model defined by the input arguments. Then using the so reached observable data set the system which is made unknown in the same coefficients is identified.
The following executed example shows that 3 of the 4 estimated coefficients have a relatively small error: -0.49967, -20 and -45.408 for -0.5, -20 and -50 respectively. The only coefficient which has a large error is bC_z_alfa (the modified drag along vertical direction(height)). Due to its small magnitude, a large estimation error may be expected for bC_z_alfa .
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aeroestim_alfadot_teta1(-.5,-.2,-20,-50,u,.01,0)
var_alfadot =
0.0094
var_teta =
0.0201
State-space model:
dx/dt = A x(t) + B u(t) + K e(t)
y(t) = C x(t) + D u(t) + e(t)
A =
x1
x2
x3
x1 -0.49967
0.0027982
1
x2 0
0
1
x3 -20
0
0
B =
u1
x1 2.5983
x2 0
x3 -45.408
C =
x1
x2 x3
y1 -1.7315
0.0027982
1
y2 0
1
0
D =
u1
y1 -0.20003
y2 0
K =
y1
y2
x1 0
0
x2 0
0
x3 0
0
x(0) =
x1
0
x2 0
x3 0
Estimated using PEM from data set
estimData
Loss function 0.249718 and FPE
0.252732
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