Page 273 - Mathematical Techniques of Fractional Order Systems

262 Mathematical Techniques of Fractional Order Systems

FIGURE 9.4 FOFSMCPD controller block diagram.

TABLE 9.2 Input and Output MFs Terminology
Input MFs Output MFs
NB Negative big B Big
NM Negative medium M Medium
NS Negative small S Small
Z Zero VS Very small
PS Positive small
PM Positive medium
PB Positive big

FOFSMCPD controller. A single-input single-output FLC is used where
input is used as sliding surface. There are seven triangular input membership
functions (MFs) used for input whereas four output MFs are used out of
which two are triangular and the remaining two are considered as trapezoi-
dal. The terminology of these MFs is given in Table 9.2 whereas the input
and output MFs are shown in Figs. 9.5 and 9.6, respectively. Fuzzy logic
block diagram is shown in Fig. 9.7.
In the present work, the fuzzy rules are stated as:
R i :If s is S i then o is O i

where, E and k are defined as E 5 O i g E and k 5 O i g k . Here g E and g k are
taken as two different FLC output gains which are obtained from GA while
O i is the output of FLC. Here E and k supplies different values in run-time
due to different values of gains g E and g k . The used rule base is presented in
Table 9.3 which has been considered from Delavari et al. (2010a). The
design of rule base signifies that if the value of sliding surface tends to zero,
E and k should be minimum, whereas if the value of sliding surface tends to
1or 11, E and k should be maximum. Mamdani type min max inference