A First Course in FUZZY and NEURAL CONTROL

4.1. A FUZZY CONTROLLER FOR AN INVERTED PENDULUM 135

ANGULAR VELOCITY

B 1 =NB B 2 =NM B 3 =NS B 4 =PS B 5 =PM B 6 =PB

Fuzzy setsBjfor ìangular velocityî

FORCE

C 1 =NB C 2 =NM C 3 =NS C 4 =PS C 5 =PM C 6 =PB

Fuzzy setsCjfor ìforceî

The particular choice of membership functions chosen to represent the lin-
guistic labels is somewhat arbitrary. One of the adjustments made during testing
of the control system will be experimenting with different membership functions,
that is, changing the parameters of these triangular functions. This process is
calledtuning.

Therulesarethenoftheform

1. Ifangleis negative medium andvelocityis positive small thenforceis
   negative small.


2. Ifangleis negative medium andvelocityis positive medium thenforceis
   positive small.


3. Ifangleis negative small andvelocityis positive medium thenforceis
   positive small.

and so forth. With six membership functions for each ofXandY,we can have
36 rules of the form

Rj:If θisAjandθ^0 isBjthenuisCj

where Aj,Bj,andCjare the fuzzy subsets ofX,Y andUdepicted above.