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Design of Fractional Order Fuzzy Sliding Mode Controller Chapter | 9 275

1.5
Reference
IOSMCPD
1
FOFSMCPD
Y-position (radian) –0.5 0 1.028
1.032
0.5
1.03
1.026
1.024
1.022
–1 0.586 0.5862

–1.5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
X–position (radian)
FIGURE 9.25 Corresponding X Y curve.

TABLE 9.8 IAE Values and Objective Functions for Length Uncertainty in
Both Links

IAE Link-1 IAE Link-2 Objective function
IOSMCPD 0.0015 0.0013 0.0031
FOFSMCPD 0.0013 0.0007 0.0022

9.7.3 Robustness Testing: Uncertainty in Length
To test the robustness of IOSMCPD and FOFSMCPD controllers, the length
of both the links of the manipulator system is increased by 10%. Although
the controllers have been tuned for the length of both links as 0.8 m for link-
1 and 0.4 m for link-2, for robustness testing the length of both links are con-
sidered as 0.88 m and 0.44 m for link-1 and link-2, respectively. The
obtained values of IAE and objective functions are listed in Table 9.8 where
it can be easily observed that a 29.03% improvement in objective function is
observed by FOFSMCPD over the IOSMCPD controller. Improvements of
13.33% and 46.15% in IAE values are also obtained by FOFSMCPD over
the IOSMCPD controller for link-1 and link-2, respectively.

9.8 ROBUSTNESS TESTING: UNCERTAINTY IN MASS

Another robustness testing is carried out by increasing the mass of both the
links by 10%. Although the controllers have been tuned for the mass of both
links as 0.1 kg, for robustness testing the mass of both links are considered
as 0.11 kg. Table 9.9 indicates the obtained values of IAE and objective