Подпись: Figure 6.7.Transport aircraft – robust stability (P4) – the mixed /1 upper bound by

Fan et al is represented in solid line – the star (resp. the circle) represents the u. lower bound of section 3. of chapter 5 (resp. the one by (Magni and Doll, 1997)).

With reference to chapter 2, the rigid aircraft of subsection 1.1 is considered, and the robustness properties of the static output feedback controller of subsection 1.2 are studied. The case of the flexible aircraft will be considered in chapter 10. The model perturbation consequently contains 14 real non repeated scalars, corresponding to uncertainties in the stability derivatives. The weights in these stability derivatives are chosen as 10 %. Because of the large number of uncertainties, only polynomial time methods can be applied to this problem. See table 6.1 for a summary of numerical results.


Figure 6.7 presents the mixed /supper bound as a function of frequency ш. The maximal value is 0.229 at r = 0.70 rad/s. The corresponding

THE TRANSPORT AIRCRAFTuncertainties in the stability derivatives are 10%/0.229 « 43.5%. The robust stability properties of the flight control system are thus very good.

The star on Figure 6.7 represents the ц lower bound of section 3. of chapter 5 (method # 1 – see chapter 10 for a comparison of methods #1 to #3 in the case of the flexible aircraft). This /і lower bound is obtained as 0.184 at ш = 0.63 rad/s. The gap between the bounds of the maximal s. s.v. over the frequency range is about 19 %, which is acceptable. The circle on this same Figure represents the /і lower bound by (Magni and Do 11, 1997), which is obtained as 0.177 atw = 0.63 rad/s. The two lower bounds give thus a rather equivalent result in the case of this example.

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