This document summarizes a lecture on neural networks and fuzzy logic. It discusses fuzzy control systems and different methods for fuzzy control, including using fuzzy logic to mimic proportional-integral-derivative controllers. Various membership functions are presented and it is noted that using different membership functions can result in different control system behaviors. PID-like fuzzy controllers are explored, including fuzzy proportional, fuzzy proportional-derivative, and fuzzy proportional-derivative-integral controllers.

1. Lecture 6
Introduction to Neural Networks
and Fuzzy Logic
President University Erwin Sitompul NNFL 6/1
Dr.-Ing. Erwin Sitompul
President University
http://zitompul.wordpress.com
2 0 2 1

2. President University Erwin Sitompul NNFL 6/2
Solution: Homework 5
Fuzzy Control
Fuzzy Logic

3. President University Erwin Sitompul NNFL 6/3
Solution: Homework 5
Fuzzy Control
Fuzzy Logic
r = 5 cm
y = 7 cm
e = –2 cm
y = 1 cm
e = +4 cm
level is too high
error is negative
level is too low
error is positive

4. President University Erwin Sitompul NNFL 6/4
FC with 5 Rules
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
 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.
 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.
error = reference – level
rate of error = – rate of level
e = r – y
e = r – y
e = – y

5. President University Erwin Sitompul NNFL 6/5
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
Valve control signal [%/s]
–30 –20 –10 0 10 20 30
1
Rate of level error [cm/s]
zero positive
negative
–4 –0.5 0 0.5 4
1
Level error [cm]
zero positive
negative
–5 –4 0 4 5
1
1st Set of Membership Functions

6. President University Erwin Sitompul NNFL 6/6
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
 Different
membership
functions will
result
different
control
results.

7. President University Erwin Sitompul NNFL 6/7
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
Level error [cm]
zero positive
negative
–5 -1 0 1 5
1
2nd Set of Membership Functions
Valve control signal [%/s]
–30 –20 –10 0 10 20 30
1
Rate of level error [cm/s]
zero positive
negative
–4 –0.5 0 0.5 4
1

8. President University Erwin Sitompul NNFL 6/8
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
 Different
membership
functions will
result
different
control
results.

9. President University Erwin Sitompul NNFL 6/9
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
Level error [cm]
zero positive
negative
–10 –? 0 ? 10
1
3rd Set of Membership Functions
Valve control signal [%/s]
–30 –20 –10 0 10 20 30
1
Rate of level error [cm/s]
zero positive
negative
–4 –0.5 0 0.5 4
1

10. President University Erwin Sitompul NNFL 6/10
Solution: Homework 5 (Cont.)
Fuzzy Control
Fuzzy Logic
 Different
membership
functions will
result
different
control
results.

11. President University Erwin Sitompul NNFL 6/11
PID-like Fuzzy Controllers
Fuzzy P Controller
u
+
–
e
r y
Fuzzy Control
Fuzzy Logic
 There are many possible realization of fuzzy controllers, as
presented in the following slides.

12. President University Erwin Sitompul NNFL 6/12
PID-like Fuzzy Controllers
Fuzzy PD Controller
u
+
–
e
r
y
Fuzzy Control
Fuzzy Logic

13. President University Erwin Sitompul NNFL 6/13
PID-like Fuzzy Controllers
Fuzzy PID Controller
u
e
r y
+
–
• Weakness: too many rules
Fuzzy Control
Fuzzy Logic

14. President University Erwin Sitompul NNFL 6/14
PID-like Fuzzy Controllers
Fuzzy PD+I Controller
r
+
–
e
y
Du
Fuzzy Control
Fuzzy Logic

15. President University Erwin Sitompul NNFL 6/15
PID-like Fuzzy Controllers
r u
+
–
e y
++
Du
Fuzzy PD+I Controller
Fuzzy Control
Fuzzy Logic

16. President University Erwin Sitompul NNFL 6/16
PID-like Fuzzy Controllers
Fuzzy PD+I Controller
r u
+
–
e y
++
Fuzzy Control
Fuzzy Logic

17. President University Erwin Sitompul NNFL 6/17
End of the Lecture
Fuzzy Control
Fuzzy Logic