Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

method are shown with dashed lines. The transfer functions from axial force and
torque to the output do not show much change between the two models. However,
there is a significant increase in FRF magnitude between the nominal and worst-
case designs for the y-direction force input. Recall, that in the PT configuration,
the design is nearly symmetric and that the y-force disturbance has little effect on
the output. When the system asymmetry is increased the symmetric modes become
asymmetric and are observable in the OPD.
The normalized cumulative variance and output PSD plots are shown in Fig-
ure 3-2(d). It is clear from this plot that nearly all of the RMS in the worst-case
PT model is attributed to one mode. This mode is the first bending mode at 0.023
Hz, and does not contribute significantly to the output in the nominal PT design,
as evidenced by the modal energy distributions plotted and tabulated in Figure 3-3.
The modal energy breakdown for the nominal uncertainty PT system is repeated here
for comparison. In the nominal PT model the first bending mode contributes only
3.50µm to the total RMS performance. However, at the worst-case uncertainty vertex
this mode accounts for 99.1% (1343µm) of the output energy.
The reason for the dramatic degradation in performance is found by comparing
the shape of the first bending modes of the two systems (Figure 3-4). Note that the
nominal PT mode shape (solid line) is nearly symmetric about the center so that
there is no discernible relative y-motion between the collectors and no resulting OPD
contribution. However, at the worst-case uncertainty vertex the system is highly
asymmetric, and this bending mode is not symmetric about the center of the array
(dotted line). In that case, the collector nodes do not move the same amount and
OPD results. The addition of this mode to the output is significant since it is excited
by both the force in the y-direction and torque about the z-axis.
The uncertainty propagation analysis of the PT optimized design shows that this
design is only optimal if the model represents the physical system exactly. Small
changes in the model parameters have drastic effects on the performance. This result
is common in optimization problems as the design is often pushed to sensitive areas
of the solution space in order to achieve maximum performance. In order to increase
80