Page 274 - Mathematical Techniques of Fractional Order Systems

Design of Fractional Order Fuzzy Sliding Mode Controller Chapter | 9 263

NB NM NS z PS PM PB
1
0.8
Degree of membership 0.6

0.4

0.2

0
–1 –0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1
Sliding surface (S)
FIGURE 9.5 Input MFs.

VS S M B
1

0.8
Degree of membership 0.6

0.4

0.2

0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Output
FIGURE 9.6 Output MFs.

TABLE 9.3 Rule Bases for FLC Design
Input (sliding surface) NB NM NS Z PS PM PB
Output B M S VS S M B

and the center of gravity defuzzification method have been used in the pres-
ent work. A V-shape input output profile is shown in Fig. 9.8 as the result-
ing control action which implies the rule base design. It can also be seen that
for any value of sliding surface, the output of FLC is positive as expected
from the definition of exponential law because E and k should be positive as
required by this law.