2. Fuzzy Logic
Fuzzy Control
Solution: Homework 12

3. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)
FC with 5 Rules
Rule 1: IF error is zero, THEN valve is no change.
Rule 2: IF error is positive,THEN valve is open fast.
Rule 3: IF error is negative,THEN valve is close fast.
Rule 4: IF error is zero AND error rate is positive, THEN valve is open slow.
Rule 5: IF error is zero AND error rate is negative, THEN valve is close slow.
Rule 1: IF level is okay, THEN valve is no change.
Rule 2: IF level is low, THEN valve is open fast.
Rule 3: IF level is high, THEN valve is close fast.
Rule 4: IF level is okay AND rate is negative, THEN valve is open slow.
Rule 5: IF level is okay AND rate is positive, THEN valve is close slow.
error = reference – level
rate of error = – rate of level

4. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)
1st Set of Membership Functions
zero
positive
negative
–5 – 1
zero
positive
negative
– – 1
Level error [cm]
Rate of level error [cm/s]
no change
open fast
close fast
–30 –20 – 1
open slow
close slow
Valve control signal [%/s]

5. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)

6. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)
2nd Set of Membership Functions
zero
positive
negative – 1
zero
positive
negative
– – 1
Level error [cm]
Rate of level error [cm/s]
no change
open fast
close fast
–30 –20 – 1
open slow
close slow
Valve control signal [%/s]

7. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)

8. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)
3rd Set of Membership Functions
zero
positive
negative
– –? ? 1
zero
positive
negative
– – 1
Level error [cm]
Rate of level error [cm/s]
no change
open fast
close fast
–30 –20 – 1
open slow
close slow
Valve control signal [%/s]

9. Solution: Homework 12 (Cont.)
Fuzzy Logic
Fuzzy Control
Solution: Homework 12 (Cont.)

10. PID-like Fuzzy Controllers
Fuzzy Logic
Fuzzy Control
PID-like Fuzzy Controllers u + – e r y
Fuzzy P Controller

11. PID-like Fuzzy Controllers
Fuzzy Logic
Fuzzy Control
PID-like Fuzzy Controllers u + – e r y
Fuzzy PD Controller

12. PID-like Fuzzy Controllers
Fuzzy Logic
Fuzzy Control
PID-like Fuzzy Controllers u e r y + –
Fuzzy PID Controller
Weakness: too many rules

13. PID-like Fuzzy Controllers
Fuzzy Logic
Fuzzy Control
PID-like Fuzzy Controllers r + – e y Du
Fuzzy PD+I Controller

14. PID-like Fuzzy Controllers
Fuzzy Logic
Fuzzy Control
PID-like Fuzzy Controllers r u + – e y Du
Fuzzy PD+I Controller

15. PID-like Fuzzy Controllers
Fuzzy Logic
Fuzzy Control
PID-like Fuzzy Controllers r u + – e y
Fuzzy PD+I Controller

16. Fuzzy Logic
Fuzzy Control
End of the Lecture