Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Y−coordinate [m] 0.04 0.03 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 not tuned tuned −15 −10 −5 0 5 10 15 X−coordinate [m] (a) Y−coordinate [m] 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −15 −10 −5 0 5 10 15 X−coordinate [m] Figure 4-6: Mode shape comparisons, worst-case RPT AO untuned (blue solid) and tuned (green dashed): (a) Mode #2, first bending (b) Mode #3, second bending. increase in OPD in this mode. 4.1.2 Design Regimes In order to assess the impact of tuning on the design space it is applied to the worst- case PT and RPT AO models across a range of uncertainty values. The results are shown in Figure 4-7, a further evolution of the design regimes plot introduced at the end of Chapter 3. The y-axis represents the performance requirement of the system and the x-axis is the level of uncertainty in the parameters. It is assumed that the uncertainty levels range ±∆ about the nominal parameter value and are the same for both uncertainty parameters. The design regimes are the numbered areas, and the design methods that are successful in each regime are listed in the legend. The addition of hardware tuning to the design process changes the design regimes significantly from those observed with PT and RPT alone (Figure 3-12). There are now six separate regimes instead of only two due to intersecting regions, where more than one technique is applicable. Consider, for example, a performance requirement of 200µm. PT is adequate for this level of performance if the uncertainty is under 120 (b)
Performance Requirement [µm] 400 350 300 250 200 150 100 50 1 5 3 4 1: PT, RPT 2: PT tuned, RPT 3: PT tuned, RPT tuned 4: PT tuned 5: RPT 6: RPT tuned 0 0 5 10 15 20 25 Uncertainty (%) Figure 4-7: Requirement vs uncertainty for PT and RPT designs with tuning: design regimes are numbered and labelled on plot. 2%. Tuning the PT design increases the tolerated uncertainty level to just about 7%. It is interesting to note that the RPT AO method is only applicable up to 3% uncertainty at this perfomrance, and that this range is only increased to 5% by the addition of tuning. Therefore there is a regime, Region 4 in the figure, in which tuning the PT design is the only successful method. This result indicates that for this problem tailoring the system to be robust actually reduces the tuning authority available for later adjustments on the hardware. At the more stringent performance requirements it is better to performance tailor the design and then compensate for the uncertainty with tuning. This approach is somewhat worrisome because the success of the mission relies heavily on the ability to tune the hardware since the predicted worst case of the PT design is many times that of the nominal performance even at the low uncertainty levels. As the requirement is relaxed the RPT and tuned RPT designs have a great effect on the design space. At a requirement of 280µm, PT is only adequate up to 121 6 2
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<strong>Performance</strong> Requirement [µm]<br />
400<br />
350<br />
300<br />
250<br />
200<br />
150<br />
100<br />
50<br />
1<br />
5<br />
3<br />
4<br />
1: PT, RPT<br />
2: PT tuned, RPT<br />
3: PT tuned, RPT tuned<br />
4: PT tuned<br />
5: RPT<br />
6: RPT tuned<br />
0<br />
0 5 10 15 20 25<br />
Uncertainty (%)<br />
Figure 4-7: Requirement vs uncertainty for PT and RPT designs <strong>with</strong> tuning: design<br />
regimes are numbered and labelled on plot.<br />
2%. <strong>Tuning</strong> the PT design increases the tolerated uncertainty level to just about<br />
7%. It is interesting to note that the RPT AO method is only applicable up to 3%<br />
uncertainty at this perfomrance, and that this range is only increased to 5% by the<br />
addition of tuning. Therefore there is a regime, Region 4 in the figure, in which<br />
tuning the PT design is the only successful method. This result indicates that for<br />
this problem tailoring the system to be robust actually reduces the tuning authority<br />
available for later adjustments on the hardware. At the more stringent performance<br />
requirements it is better to performance tailor the design and then compensate for the<br />
uncertainty <strong>with</strong> tuning. This approach is somewhat worrisome because the success<br />
of the mission relies heavily on the ability to tune the hardware since the predicted<br />
worst case of the PT design is many times that of the nominal performance even at<br />
the low uncertainty levels.<br />
As the requirement is relaxed the RPT and tuned RPT designs have a great<br />
effect on the design space. At a requirement of 280µm, PT is only adequate up to<br />
121<br />
6<br />
2
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