Procedures and Results
6 Results and discussion
At the beginning of system identification activity the vehicle static parameters were evaluated to improve the aerodynamic database accuracy. The results are presented in Table 1.
Table 1 Estimated aerodynamic static parameters.
Parameter Flap = 0° Variation with flap = 36°
KD 0.068 0.012
CLα 4.35 0
CD0 0.073 0.030
CL0 0.30 0.35
Then the nominal thrust coefficient curve CT(γ), provided by the producer of the propeller, was validated using experimental data gathered in dedicated flight tests. Since the nominal curve was shifted with respect to experimental CT values, it was corrected performing estimation from flight data.
Nominal and estimated thrust coefficients are presented in Fig. 3, together with the
Fig. 3 Nominal and identified thrust coefficient.
The difference between nominal and estimated curves is always lower than 20% and increases with respect to the advance ratio. It is worthy to note that error on thrust coefficient estimation could have relevant effect only on
the aerodynamic drag coefficient estimation, because the thrust is aligned to the vehicle longitudinal axis and the angle of attack experimented in flight is always small.
At that point the estimation of the aerodynamic derivatives, using the output error method based on the Maximum Likelihood estimation principle, was carried out.
Flight test manoeuvres were designed and performed in order to excite separately the aircraft longitudinal and lateral-directional modes. At that purpose two series of flight test were held. In the first series an elevator manoeuvre was selected as input to excite only the longitudinal mode. In the second series ailerons and rudder manoeuvres were used instead to excite only the lateral-directional mode. In both cases, the manoeuvres were performed with and without flap deflection. The types of manoeuvres that have been selected in both cases were the doublet and the 3-2-1-1.
The intensity and step period of these manoeuvres were optimized through numerical simulations using the model based on a priori aircraft derivative data set.
Fig. 4 Ailerons and rudder doublet manoeuvres held in flight in manual mode.
In Fig. 4 an example of ailerons and rudder doublet manoeuvres held in flight in manual mode is shown.
In order to perform system identification flight measurements of acceleration, velocity, height above ground level, angular rates, attitude, aerodynamic effectors and
aerodynamic angles were collected at the sampling rate of 10 Hz.
Fig. 5 Measured output and identified model output time histories match with a 3-2-1-1 stabilator
manoeuvre as input.
In Fig. 5 the comparison between flight measurements and estimated response provided by the linearized model for the longitudinal mode is shown, where θ is pitch angle. All the values presented in the figures are normalized with respect to trim conditions.
The matching between the flight measured response and the model estimated response is good.
Estimated longitudinal aerodynamic derivatives results are presented in Table 2.
Table 2 Estimated longitudinal aerodynamic derivatives.
Parameter Flap = 0° Variation with flap = 36°
KD 0.07 0
CLα 4.0 0.4
CLαdot 0.87 0
CLq 2.50 0
CLδe 0.52 -0.018
CMα -1.0 0.015
A. Fedele, N. Genito, A. Vitale and L. Garbarino
CMαdot -2.36 0
CMq -6.75 0
CMδe -1.4 0.05
CD0 0.07 0.023
CL0 0.36 0.32
CM0 -0.06 0.076
The lateral-directional results instead are presented in Fig. 6, where φ is roll angle. All the values presented in the figures are normalized with respect to trim conditions.
Fig. 6 Measured output and identified model output time histories match with an ailerons and rudder
doublet manoeuvres as input.
In this case the matching between the flight measured response and the model estimated response is very good for all the state parameters.
Estimated lateral-directional aerodynamic derivatives results are presented in Table 3.
The validation of the estimated parameters was carried out through a six degree of freedom non-linear model. The estimated aerodynamics derivatives and thrust coefficient were included in the non-linear simulation model, where the longitudinal and lateral-directional dynamics are coupled together. New series of flight tests were executed to collect flight measurements of system input and output. The measurements of
input were provided as input to the identified simulation model and the outputs of the simulation were compared with the correspondent flight measurements. All the simulations used for validation were open loop, that is, without the flight control system. In Fig.7-11 the comparison between flight measurements and identified model response provided by the non-linear model is shown. The input used is a 3-2-1-1 rudder manoeuvre and the output shown are angle of attack, angle of sideslip, roll rate, pitch rate and yaw rate.
Table 3 Estimated lateral-directional aerodynamic derivatives.
Parameter Flap = 0° Variation with flap = 36°
CDβ 0.2 0
CYβ -0.145 -0.103
CYp -0.008 0
CYr 0.341 0.286
CYδr 0.13 0.08
Clβ -0.04 -0.02
Clp -0.28 -0.07
Clr 0.09 0
Clδa 0.13 0.03
Clδr 0 0.0066
Cnβ 0.055 0.011
Cnp -0.003 -0.025
Cnr -0.13 -0.04
Cnδa -0.02 -0.002
Cnδr -0.05 -0.008
The matching between measured and simulated data is good confirming that the identification technique was successfully applied to flight data.
Fig. 7 Measured and estimated angle of attack time histories match with a 3-2-1-1 rudder manoeuvre as
input.
Fig. 8 Measured and estimated angle of sideslip time histories match with a 3-2-1-1 rudder manoeuvre as
input.
Fig. 9 Measured and estimated roll rate time histories match with a 3-2-1-1 rudder manoeuvre as input.
Fig. 10 Measured and estimated pitch rate time histories match with a 3-2-1-1 rudder manoeuvre as
input.
Fig. 11 Measured and estimated yaw rate time histories match with a 3-2-1-1 rudder manoeuvre as
input.
7 Conclusion
In this paper an output error method for aerodynamic model identification was applied to actual flight data of an experimental ultra-light aircraft.
The method chosen is based on the Maximum Likelihood estimation principle, which permits to obtain the stability and control derivatives estimation by minimizing a cost function through suitable numerical procedure.
To perform aerodynamic derivatives estimation, two decoupled linearized model (for
A. Fedele, N. Genito, A. Vitale and L. Garbarino
longitudinal dynamics and lateral-directional dynamics, respectively) were introduced. The estimation of the two models was performed independently by choosing suitable manoeuvres which in each test only excite the dynamic of interest. The identified parameters were finally included, together with the thrust coefficient also estimated from experimental data, in a nonlinear 6 degrees of freedom simulation model of the vehicle.
The validation of the identified model on data set not used in the identification process enhanced good capability of the model to reproduce the dynamics of interest and to match actual flight data, confirming that the identification technique was successfully applied to flight data.
Finally it is worthy to remark that the identified aerodynamic model was used to design a flight control system that successfully performed many autonomous take-off and landings [5][6][7].
References
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[2] Roskam J., Airplane Flight Dynamics and Automatic Flight Controls, 1st ed., DARcorporation, Lawrence KS, 2001, Chap. 1.
[3] Lewis G., “Using GPS to Determine Pitot Static Errors”, National Test Pilot School, 2003.
[4] Jategaonkar R.V., Flight Vehicle System Identification: A Time Domain Methodology, 1st ed., AIAA Progress in Aeronautics and Astronautics, Vol. 216, AIAA, Reston VA, 2006, Chap. 4.
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