Aircraft Stability Analysis Including Unsteady Aerodynamic Effects

703 Model Parameters Identifications3.1 Parameter Identification MethodThe identification method used here is the minimum mean-square error approach. Themodels have their parameters identified using experimental data in three phases and thesquared error is minimized through an unconstrained optimization process. In the firsttwo phases, the parameter identification is done using static experimental data. First, weidentify the parameters involved with the determination of the static terms of the normallifting forces ( x rCN). These parameters are those related to the quadratic polynomials thatdetermine the stability derivatives with respect to the motion variables ( a , b , cthose that are used to determine the static values of the internal state variables∗panel i, namely , σα(•) (•)jjj), andxifor each. Next, we identify only the parameters associated with the armsof the rolling moment coefficients ( x r Cl) using the experimental static values of the rollingmoment coefficient. In those first two phases of the parameter identification, theparameters related to the dynamic behavior of the model are kept out of the optimizationprocess. These dynamic parameters are the coefficients ( a , b , c) of the quadraticpolynomials that represent the stability derivatives with respect to the time-rate of themotion variables, and the time-constant and time-delay parameters, stored in vectorjjjx r dyn.We then take the parameter values previously determined in the two identification phasesdescribed above and use them as initial guess for the third identification phase. In thisthird phase, the model parameters are determined when the mean squared error withrespect to dynamic experimental data is minimized for each value of the sting pitch angle.The dynamic phase of the identification is done using the experimental values of therolling moment time histories obtained as described in Section 3.2. Table 3-1 and Table3-2 show the elements of vectors x r CN, x r Cl, and x rdynfor the first and the secondinvestigated models, respectively.