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Force sensing in compact concentric tube mechanism with optical fibers 339

14.5.2 Proportional integral derivative tuning

The PID controller in the motor driver had to be tuned for optimal performance. We used
Agilent HEDS 5540s incremental quadrature encoders, with a resolution of 0.18 degrees
with 500 cycles per revolution, and output pulses resolution set to 4X for directional and
position control.

The PID parameters were tuned using trial and error. Initially increasing K p excessively
caused the motor to start vibrating, whereas increasing K d reduced the vibrations. Therefore
the right balance had to be struck between the K p and K d constants. Furthermore, including
the integral constant K i improved error tracking considerably from 6 11 to 6 1 ticks of the
optical encoder. This is a 0.0015259% error rate for an optical encoder with an output range
of 0 65,535 ticks per revolution.

The final tuning parameters chosen were K p : 400, K i : 5, and K d : 100, which gave a constant
speed waveform and minimized error resulting from jerk when changing the direction of
revolution.

14.6 Force sensing tip

To integrate force sensing into the CTR, two FBGs were attached to the distal tip on both sides
using an epoxy adhesive shown in Fig. 14.11. Both FBGs were aligned flush to the end of the
distal tip (Fig. 14.12). This allowed the FBGs to sense transverse forces exerted on the
concentric tube in the x-direction by the surface strain as well as forces in the y-direction.

The FBGs were connected to an optical interrogator, OPT-T1620, from MChlight, for
monitoring of their wavelength shifts. Fig. 14.13 shows a snapshot of the entire
experimental setup.

FBG1 and FBG2 have center wavelengths of 1540.286 and 1540.354 nm, respectively.
Fig. 14.14 shows the reflection spectrum of the FBGs.

As shown in Fig. 14.14, the two FBGs have peak signal strengths close to 1540 nm, and
FBG2 clearly has less noise and displays a more consistent and stable signal.

y y

x FBG2
FBG1 z
FBG2

Figure 14.11
Placement of FBGs with respect to coordinate planes.