frequency in rad’s
Irequency in rad/s
Figure 9.2. Robust performance – upper subhgure: // analysis, mixed // upper and lower bounds m solid line, complex /і upper bound in dashed line – lower subhgure: и analysis, first and second mixed v upper bounds in solid and dashed lines, mixed и lower bound in solid line.
Robust performance is analyzed. A fictitious performance block is added to the model perturbation, which thus contains 4 non repeated real scalars and two full complex blocks. The template on the sensitivity function S is the same as in chapter 6 (subsection 1.3).
When applying the fj, tools to this robust performance problem ‘, the maximal s. s.v. is 0.86 at и = 10.8 rad/s (see Figure 9.2 – the result is nearly non conservative). The corresponding uncertainty in the stability derivatives is thus 5/0.86 « 5.8%. However, if the performance block and the bending mode are maintained inside their unit balls, the maximal uncertainty in the stability derivatives becomes 5/0.27 « 18.5% (see the bottom diagram of Figure 9.2). This illustrates that a brute application of d analysis can provide an overly conservative result in the context of a robust performance problem.
The skewed s. s.v. presents two peaks at ш = 2.5 rad/s and u; = 12 rad/s. When comparing the d upper and lower bounds at these frequencies, the result is nearly non conservative for the first peak and reasonably conservative (6 % between the two bounds) for the second one.