Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

The frequency response functions from disturbance inputs to the performance are
computed from the state-space matrices as follows:
Gzw (s) =C (sI − A) −1 B (2.10)
where s = jω and, Gzw is a matrix of transfer functions. The resulting transfer
functions from the SCI model are plotted in Figure 2-2. The transfer function from
Fx and Tz to OPD are drawn in solid and dash-dotted lines, respectively. The transfer
function from Fy to OPD does not appear on the plot because the force in this
direction does not couple to the output due to the symmetry in the model. Forcing
the structure at the center node in the y-direction only excites the symmetric bending
modes. It is seen from Equation 2.9 that symmetric y motion of the two collector
nodes results in zero OPD. The dominant transfer function is that from torque at the
FRF Magnitude
10 0
10 −5
10 −1
10 0
10 1
Frequency [Hz]
F x [µm/N]
T z [µm/Nm]
Figure 2-2: Frequency response functions (FRF) of SCI: disturbance input to performance.
center to OPD. The first flexible mode is the first asymmetric bending mode at 0.708
Hz, followed by the higher order asymmetric bending modes. In contrast, the Fx
transfer function has no low-frequency modes because the beam elements are much
stiffer axially than in bending. The first observable axial mode is at 80.2 Hz.
45
10 2