THE TRANSPORT AIRCRAFT
1.2 THE RIGID LFT MODEL
We come back to the problem of chapter 2 (subsection 1.1), and note first that the 14 stability derivatives enter in an affine way the state-space equations (2.1), (2.2) and (2.3) of the aerodynamic aircraft model. The LFT model can thus be computed with Morton’s method.
Note that the parametric uncertainties in the stability derivatives could be directly introduced in the physical model, as in the missile case. Nevertheless, it is simpler here to apply Morton’s method, because of the complexity of the aerodynamic equations (2.1), (2.2) and (2.3).
It is moreover interesting to emphasize that the 14 stability derivatives enter as rank-one model perturbations the state-space aerodynamic model, even when these coefficients simultaneously enter the state matrix A and output matrix C (this is e. g. the case of Yp). When considering the jth uncertain parameter, this means that the corresponding matrix Pj in equation (3.5) is a rank one matrix, so that the associated real scalar Sj is non repeated.
As a consequence, the LFT model of the rigid transport aircraft contains 16 inputs (2 physical inputs and 14 fictitious inputs) and 18 outputs (4 physical outputs and 14 fictitious outputs). The associated model perturbation contains 14 non repeated real scalars. This LFT model is minimal.