Rockwell Automation RSLogix 5000 Fuzzy Designer - Manual (Page 50)

Publication LOGIX-UM004A-EN-P - March 2007
50 FuzzyDesigner Component Library
You can also formulate the rule base schematically:
• (small, negative) → (medium [0.9] , positive [1.0]).
• (large, negative) → (small [0.8] , ).
• ( , positive) → (small [1.0] , positive [1.0]).
In the following example, some premise variable DOFs are supposed.
• Temperature: DOFtemp(small) = 0.4 , DOFtemp(large) = 0.8
• Pressure: DOFpress(negative) = 0.1 , DOFpress(zero) = 0.9 ,
DOFpress(positive) = 0.5
EXAMPLE
Step 1: DOFs of all rules are computed.
Rule 1: DOF
rule1
= min (DOF
temp
(small), DOF
press
(negative)) = min(0.4, 0.1) = 0.1
Rule 2: DOF
rule2
= min (DOF
temp
(large), DOF
press
(negative)) = min(0.8, 0.1) = 0.1
Rule 3: DOF
rule3
= min (DOF
press
(positive)) = min(0.5) = 0.5
Step 2: DOFs of all consequent variables for every rule terms are computed.
Rule 1: DOF
volt
(medium) = DOF
rule1
· Weight
volt
= 0.1 · 0.9 = 0.9, DOF
curr
(positive) = DOF
rule1
· Weight
curr
= 0.1 · 1.0 =
0.1
Rule 2: DOF
volt
(small) = DOF
rule2
· Weight
volt
= 0.1 · 0.8 = 0.8
Rule 3: DOF
volt
(small) = DOF
rule1
· Weight
volt
= 0.5 · 1.0 = 0.5
DOF
curr
(positive) = DOF
rule1
· Weight
curr
= 0.5 · 1.0 = 0.5
Step 3: DOFs of all consequent variables terms for overall fuzzy system are computed.
DOF
volt
(small) = max (DOF
volt
(small) for all rules) = max (0.08, 0.5) = 0.5
DOF
volt
(medium) = max (DOF
volt
(medium) for all rules) = max (0.09) = 0.09
DOF
volt
(large) = 0
DOF
curr
(zero) = 0
DOF
curr
(positive) = max (DOF
curr
(positive) for all rules) = max (0.1, 0.5) = 0.5
These steps are schematically shown on the following figures.