Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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are shown in Figure 5-4, the final 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. The numbered regions indicate areas in which particular design methodologies are successful for all possible uncertainty realizations as listed inthelegend. Forexample,inRegion1, PT, RPT and RPTT all produce designs that can meet the requirement within the uncertainty bounds, while in region 4 only PT tuned and RPTT designs are successful. Performance Requirement [µm] 400 350 300 250 200 150 100 50 1 5 3 4 1: PT, RPT, RPTT 2: PT tuned, RPT, RPTT 3: PT tuned, RPT tuned, RPTT 4: PT tuned, RPTT 5: RPT, RPTT 6: RPT tuned, RPTT 7: RPTT 0 0 5 10 15 20 25 Uncertainty [%] Figure 5-4: Performance requirement vs uncertainty: all designs. In Region 7, only RPTT can produce a successful design indicating that consider- ing tuning in the tailoring stage of the design further extends the uncertainty that can be tolerated at a given performance requirement. For example, at a requirement of σreq = 200µm the maximum uncertainty that can be tolerated without RPTT is 7% and is achieved through a combination of PT design and hardware tuning. However, if RPTT is applied to the system the uncertainty range is extended to 9% for the 166 7 6 2
same requirement. The effect becomes more dramatic as the requirement is relaxed slightly. At a requirement of 280µm the tuned RPT design can tolerate up to 11% uncertainty, but the RPTT design allows ≈ 16.3%. The entire 25% uncertainty range is covered for requirements of 320µm and higher with the RPTT design. This requirement is nearly 13% lower (more aggressive) than that which can be met by the tuned RPT design at the same uncertainty level. In addition to extending the reachable design space, RPTT is the only method that is successful in all of the design regions. As noted in the previous chapter, Region 4 is interesting because the tuned PT design is adequate, but RPT and RPT tuned are not. This result is concerning because the uncertainty is relatively low in this region and it is reasonable to assume that RPT or tuned RPT formulations are the correct approach here. However, the plot shows that, for this problem, tuning the PT design achieves a more aggressive performance requirement than tuning the RPT design at the same level of uncertainty. For example, at ∆ = 5.75% the tuned PT design can meet a requirement of 178µm, while the tuned RPT design can only meet a requirement of 218.62µm. In contrast, RPTT is able to meet the same requirement as tuned PT, and can go slightly further to 161.43µm if necessary. In fact, RPTT is the only method that is appropriate in all of the regions shown here. 5.3 RPTT Simulations In this section the RPTT design space is investigated more thoroughly through a series of simulations. First the trade between tuning authority and robustness is considered by varying the robustness weight, α. Then, the PT, RPT and RPTT designs are compared over a set of random hardware simulations to assess the methodology performance the entire uncertainty space. 5.3.1 Tuning Authority Recall from Equation 5.1 that the RPTT objective function includes weighted robustness and tuning authority costs allowing a trade of relative importance between the 167
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Dynamic Tailoring and Tuning for Sp
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Acknowledgments This work was suppo
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3.2 RPT Formulation . . . . . . . .
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List of Figures 1-1 Timeline of Ori
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List of Tables 1.1 Effect of simula
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Nomenclature Abbreviations ACS atti
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dk optimization search direction f
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1.1 Space-Based Interferometry NASA
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unfettered by the Earth’s atmosph
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the SCI, both the size and flexibil
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maybethatitbecomescertain that the
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Table 1.1: Effect of simulation res
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Table 1.2: Effect of simulation res
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has been found that structural desi
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precision telescope structure for m
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attractive, and more conservative a
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to solve the performance tailoring
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Chapter 2 Performance Tailoring A c
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ometer (SCI). In the following sect
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The equations of motion of the unda
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The frequency response functions fr
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the output covariance matrix, Σz,
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where the subscript indicates the i
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2.3.3 Design Variables The choice o
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and then, by inspection, the inerti
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algorithms begin at an initial gues
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at least locally optimal, and the s
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initial design variable state, x =
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and the RMS OPD is computed using E
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# Designs 25 20 15 10 5 Accepted, b
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does not provide information on why
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energy is distributed almost evenly
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also symmetric as seen in the figur
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Chapter 3 Robust Performance Tailor
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through careful and experienced mod
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described above. However, one can r
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ic, σz(�x, �p), that is depend
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Magnitude, OPD/F x [µm/N] Magnitud
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% Energy 100 90 80 70 60 50 40 30 2
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metric to the cost function. Note,
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tion: ∂hi (z,�x, �pi) ∂�x
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values are chosen from their statis
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Table 3.3: Algorithm performance: a
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Statistical Robustness The statisti
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Performance [µm] 1400 1200 1000 80
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(Figure 3-6(b)). The nominal perfor
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Norm. Cum. Var. [µm 2 ] PSD [µm 2
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energy by mode for easy comparison.
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Y−coordinate [m] Y−coordinate [
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RMS performance, [µm] 400 350 300
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The requirement chosen here is some
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Chapter 4 Dynamic Tuning Robust Per
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on a physical truss. Since tailorin
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Table 4.1: Tuning parameters for SC
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m 2 [kg] J ∗ # # time y ∗ [kg]
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Page 185 and 186: Table 6.1: RWA disturbance model pa
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Page 189 and 190: Y Z Z X Y (a) w (c) w Y h Z Figure
Page 191 and 192: Table 6.6: Primary mirror propertie
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- Consider uncertainty analysis too
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Appendix A Gradient-Based Optimizat
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such that the gradient direction is
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the descent direction. In some case
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Bibliography [1] Jpl planet quest w
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[24] Nightsky Systems Carl Blaurock
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[48] S. C. O. Grocott, J. P. How, a
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[74] M. Lieber. Development of ball
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AIAA/ASME/ASCE/AHS/ASC Structures,
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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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