EE509
Fuzzy
Logic and applications
Homework #3
Due: Monday,
1. Create a fuzzy toolbox using Matlab or other programming language. The toolbox should support the following functionally:
- Define
a fuzzy set (membership function).
- Define a linguistic variable, assign membership functions to linguistic term
- Fuzzify a crisp input
- Process an IF-THEN rule and combine output from multiple rules. A rule may contain up to 10 fuzzy premises and one consequent.
- Defuzzify the output (centroid is required, other methods are optional)
- Select max-min or max-product inference
Requirements
- You set your own requirements for particular implementation of functions!
- You cannot use any external library, such as Fuzzy Toolbox in Matlab.
- Fuzzy toolbox should be completely separate of the GUI, if such is present
2.Implement a
simple fuzzy controller. Demonstrate a particular solution and a graph
of the
control surface (output vs input).
Position: Left(0,0,10,35), LeftCenter(30,40,50), Center(45,50,55), RightCenter(50,60,70), Right(65,90,100,100)
Angle: RBelow(-90,-45,9), RUpper(-9,23,54), RVertical(36,63,90), Vertical(72,90,108), LVertical(90,117,144), LUpper(126,157,189), LBelow(171,225,270)
Output: NegBig(-30,-15), NegMed(-25,-15,-5), NegSm(-12,-6,0),
Zero(-5,0,5),
PosSm(0,6,12), PosMed(5,15,25), PosBig(15,30)
Rules:
|
|
if
position is … |
and
if angle is … |
then
output is .. |
|
1 |
Left |
RBelow |
PosSm |
|
2 |
LeftCenter |
RBelow |
PosMed |
|
3 |
Center |
RBelow |
PosMed |
|
4 |
RightCenter |
RBelow |
PosBig |
|
5 |
Right |
RBelow |
PosBig |
|
6 |
Left |
RUpper |
NegSm |
|
7 |
LeftCenter |
RUpper |
PosSm |
|
8 |
Center |
RUpper |
PosMed |
|
9 |
RightCenter |
RUpper |
PosBig |
|
10 |
Right |
RUpper |
PosBig |
|
11 |
Left |
RVertical |
NegMed |
|
12 |
LeftCenter |
RVertical |
NegSm |
|
13 |
Center |
RVertical |
PosSm |
|
14 |
RightCenter |
RVertical |
PosMed |
|
15 |
Right |
RVertical |
PosBig |
|
16 |
Left |
Vertical |
NegMed |
|
17 |
LeftCenter |
Vertical |
NegMed |
|
18 |
Center |
Vertical |
Zero |
|
19 |
RightCenter |
Vertical |
PosMed |
|
20 |
Right |
Vertical |
PosMed |
|
21 |
Left |
LVertical |
NegBig |
|
22 |
LeftCenter |
LVertical |
NegMed |
|
23 |
Center |
LVertical |
NegSm |
|
24 |
RightCenter |
LVertical |
PosSm |
|
25 |
Right |
LVertical |
PosMed |
|
26 |
Left |
LUpper |
NegBig |
|
27 |
LeftCenter |
LUpper |
NegBig |
|
28 |
Center |
LUpper |
NegMed |
|
29 |
RightCenter |
LUpper |
NegSm |
|
30 |
Right |
LUpper |
PosSm |
|
31 |
Left |
LBelow |
NegBig |
|
32 |
LeftCenter |
LBelow |
NegBig |
|
33 |
Center |
LBelow |
NegMed |
|
34 |
RightCenter |
LBelow |
NegMed |
|
35 |
Right |
LBelow |
MegSm |
Plot the control surface of Mamdani controller for the range of values:
-position
0
to 100
-angle
-90
to 270
Repeat for
Larsen controller.
Grading criteria:
1. Correctness of fuzzy
inference
2. Satisfaction of
the HW
requirements and
functionality
3. Stability
Note: this homework is essential for further studies. You must fully complete it to be able to work on the homeworks that follow.
Last Updated:
08/25/03
Contact the instructor at: esazonov@clarkson.edu