APPLICATION OF THE BASIC ALGORITHM

APPLICATION OF THE BASIC ALGORITHM

As explained in chapter 4 (section 2.), uncertainties are simultaneously introduced in the 14 stability derivatives and in the natural frequencies of the 6 bending modes, whose natural frequencies are 7.35, 8.62, 12.5, 13.5, 14.1 and 14.3 rad/s. The weights in the stability derivatives are chosen as 10 %, while the weights in the frequencies are chosen as 20 %. The model perturbation contains 20 real non repeated scalars.

The basic algorithm of subsection 5.1 is first applied. 50 points were chosen for the initial gridding, namely 25 points between 0.01 and 100 rad/s and 25 points between 5 and 20 rad/s. The results are presented in figures 10.3 and 10.4. The value of the upper bound of Umax is 1.97 (between 9.93 and 10.00 rad/s): the flight control system can thus toler­ate an uncertainty of 5.1 % (~ 10/1.97) in the stability derivatives and an uncertainty of 10.2 % (и 20/1.97) in the frequencies of the bending modes. The value of the lower bound provided by (Magni and Doll, 1997) is 1.94 at 9.97 rad/s (this lower bound is represented as a "*" in figures

10.3 and 10.4). The gap between the /і bounds is consequently less than 2 %. The computations were done in 1700 s (about half an hour) on an efficient Sun SPARCstation.

A lower bound of the maximal s. s.v. over the frequency range is com­puted with the method of section 3. of chapter 5 (see subsection 6.4 for details). The frequency gridding is simply chosen as 20 points between 9.93 and 10.00 rad/s, since the maximal value of the upper bound of цтах was found inside this interval. The value of the lower bound is 1.966 at 9.95 rad/s (this lower bound is represented as a "o" in figures 10.3 and 10.4). The result is thus even more accurate than the one provided by (Magni and Doll, 1997).

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