FUZZY LOGIC T.C.Kanish Assistant Professor (Sr.) VIT University
OVERVIEW
What is Fuzzy Logic?
Where did it begin?
What is MatLab Fuzzy Logic Toolbox For?
Fuzzy Logic in Control Systems
Overview: Fuzzy Inference Systems
Fuzzy Set Concept
Fuzzy Rules
Membership functions
How it works
Building Systems: An Example
Demo
Discussion
WHAT IS FUZZY LOGIC?
Definition of fuzzy
Fuzzy – “not clear, distinct, or precise; blurred”
Definition of fuzzy logic
A form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts.
FUZZY LOGIC
As complexity rises, precise statements lose meaning and meaningful statements lose precision “
”
- Lotfi Zadeh
FUZZY LOGIC COME FROM
Concept of Fuzzy Logic (FL) was conceived by Lotfi Zadeh, a professor at the University of California at Berkley, and presented not as a control methodology,
But as a way of processing data by allowing partial set membership rather than crisp set membership or nonmembership
This approach to set theory was not applied to control systems until the 70's due to insufficient small-computer capability prior to that time.
ORIGINS OF FUZZY LOGIC
Traces back to Ancient Greece
Lotfi Asker Zadeh ( 1965 )
First to publish ideas of fuzzy logic.
Professor Toshire Terano ( 1972 )
Organized the world's first working group on fuzzy systems.
F.L. Smidth & Co. ( 1980 )
First to market fuzzy expert systems.
FUZZY LOGIC
FL is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded microcontrollers to large, networked, multi-channel PC or workstation-based data acquisition and control systems.
It can be implemented in hardware, software, or a combination of both. FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. FL's approach to control problems mimics how a person would make decisions, only much faster.
FUZZY LOGIC (Cont..)
Fuzzy logic provides a method to formalize reasoning when dealing with vague terms.
Traditional computing requires finite precision which is not always possible in real world scenarios. Not every decision is either true or false, or as with Boolean logic either 0 or 1.
Fuzzy logic allows for membership functions, or degrees of truthfulness and falsehoods. or as with Boolean logic, not only 0 and 1 but all the numbers that fall in between.
TRADITIONAL REPRESENTATION OF LOGIC
Slow
Fast
Speed = 0
Speed = 1
bool speed; get the speed if ( speed == 0) { // speed is slow } else { }
//
speed is fast
FUZZY LOGIC REPRESENTATION
For every problem must represent in terms of fuzzy sets.
Slowest [ 0.0 – 0.25 ]
Slow [ 0.25 – 0.50 ]
Fast [ 0.50 – 0.75 ]
Fastest [ 0.75 – 1.00 ]
FUZZY LOGIC REPRESENTATION CONT.
Slowest
Slow
Fast
float speed; get the speed if ((speed >= 0.0)&&(speed < 0.25)) { // speed is slowest } else if ((speed >= 0.25)&&(speed < 0.5)) { // speed is slow } else if ((speed >= 0.5)&&(speed < 0.75)) { // speed is fast } else // speed >= 0.75 && speed < 1.0 { // speed is fastest }
Fastest
FUZZY MATHEMATICS
Fuzzy Numbers – almost 5, or more than 50
Fuzzy Geometry – Almost Straight Lines
Fuzzy Algebra – Not quite a parabola
Fuzzy Calculus
Fuzzy Graphs – based on fuzzy points
FUZZY LOGIC VS. NEURAL NETWORKS
How does a Neural Network work?
Both model the human brain.
Fuzzy Logic
Neural Networks
Both used to create behavioral systems.
FUZZY OPERATIONS
A
A
B
B
A
B
¬
A
CONTROLLER STRUCTURE
Fuzzification
Scales and maps input variables to fuzzy sets
Inference Mechanism
Approximate reasoning
Deduces the control action
Defuzzification
Convert fuzzy output values to control signals
SIMPLE FUZZY CONTROLLER
FUZZY LOGIC IN CONTROL SYSTEMS
Fuzzy Logic provides a more efficient and resourceful way to solve Control Systems.
Some Examples
Temperature Controller
Anti – Lock Break System ( ABS )
SIMPLE TEMPARTURE CONTROL
Fuzzy based Temperature controller
RULE BASE
Air Temperature Set cold {50, 0, 0}
Fan Speed o Set stop {0, 0, 0}
Set cool {65, 55, 45}
Set just right {70, 65, 60}
o Set medium {60, 50, 40}
Set warm {85, 75, 65}
o Set fast {90, 70, 50}
Set hot {∞, 90, 80}
o Set blast {∞, 100, 80}
o Set slow {50, 30, 10}
RULES Air Conditioning Controller Example:
IF Cold then Stop
If Cool then Slow
If OK then Medium
If Warm then Fast
IF Hot then Blast
FUZZY AIR CONDITIONER 0 100 90
80
If Hot then Blast
st Bla
Fast
If Warm then Fast
70 60 Med iu
50 40
Sl o
If Just Right then Medium
m
IF Cool then Slow
w
30 if Cold then Stop
20 10
S
to p
0
1 C
ol Co
o ld
t Ho
m ar W
st ht Ju ig R
0 45
50
55
60
65
70
75
80
85
90
MAPPING INPUTS TO OUTPUTS 1 0 100 90 80
s Bla
t
t
Fa st
70 60 50
Med ium
40 Sl ow
30 20 10
S to p
0
1
ol Co
C ol d
W
st ht Ju ig R
t Ho
m ar
0 45
50
55
60
65
70
75
80
85
90
TEMPERATURE CONTROLLER
The problem
A temperature control system has four settings
Cold, Cool, Warm, and Hot
Humidity can be defined by:
Change the speed of a heater fan, based off the room temperature and humidity.
Low, Medium, and High
Using this we can define the fuzzy set.
BENEFITS OF USING FUZZY LOGIC
ANTI LOCK BREAK SYSTEM ( ABS )
Nonlinear and dynamic in nature
Inputs for Intel Fuzzy ABS are derived from
Brake
4 WD
Feedback
Wheel speed
Ignition
Outputs
Pulsewidth
Error lamp
FUZZY LOGIC IN OTHER FIELDS
Business
Hybrid Modeling
Expert Systems
FUZZY LOGIC USING MATLAB
PRIMARY GUI Tools We can use five primary GUI tools for building, editing, and observing fuzzy inference systems in the toolbox
Fuzzy Inference System (FIS) Editor
Membership Function Editor
Rule Editor
Rule Viewer Surface Viewer
PRIMARY GUI TOOLS
User Interface Layout: Getting Started
User Interface Layout: FIS Editor
UI Layout: MF Editor - Service
UI LAYOUT: MF EDITOR -FOOD
UI Layout: MF Editor - Tip
User Interface Layout: Rule Editor
User Interface Layout: Rule Viewer
User Interface Layout: Surface Viewer
CONCLUSION
Fuzzy logic provides an alternative way to represent linguistic and subjective attributes of the real world in computing.
It is able to be applied to control systems and other applications in order to improve the efficiency and simplicity of the design process.