Model-Based Approach for Determination of Drag Polar

In the model-based method, an explicit aerodynamic model for lift and drag coeffi­cients is formulated as shown below:

State model:

cfS F

V =———- CD H——- e cos (a + sT) + g sin (a — в)

mm

a = —_Й^_ cl – — sin (a + sT) + q + — cos (a — в) (9-65)

mV mV 4 V

в = q

Here, CL and CD are modeled as

V qc

CL = CLo + CLy— H CLaa + CLq~—— H CLSe de

u-o 2Uo

CD = CDo + CDV – H CDaa + CDa2 a2 + CDq —- H CDSede

Uo 2Uo

Observation model:

VV

v m v

The aerodynamic derivatives in the above equations could be estimated using OEM for stable aircraft (stabilized OEM for unstable aircraft) or using extended unit upper triangular-diagonal (UD) filter. In the extended KF, the aerodynamic derivatives in Equation 9.66 would form part of the augmented state model. The estimated CL and CD are then used to generate the drag polars [16,25-27].