eee-8005 industrial automation sdl module leader: dr. damian giaouris email:...
TRANSCRIPT
![Page 1: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/1.jpg)
EEE-8005 Industrial automation SDL
Module leader: Dr. Damian Giaouris
Email: [email protected]
Room: E3.16
Phone: 0191 222 -7327
Module Leader of: Digital Control (EEE 8007)Degree Program Director of MSc: Automation and Control
![Page 2: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/2.jpg)
Scopes / Objectives
Lecture Scope: • To give a mathematical background on set theory
Lecture Outcomes: • Syllabus outline• Explain the SDL part of the course• Boolean set theory – definition, intersection, union…• Need for fuzzy logic• Fuzzy logic set theory – membership functions: form, domain,
image• Logical operators OR AND Min Max…• Linguistic variables
![Page 3: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/3.jpg)
Module Structure
Student Directed LearningStudent Directed Learning
Some lectures => Trigger further individualindividual study
Normal Lectures: 2hs/week
1h session/week: SDL
![Page 4: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/4.jpg)
Provisional syllabus
Artificial IntelligenceFuzzy Logic
Theory Matlab
Neural NetworksGenetic algorithms
![Page 5: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/5.jpg)
Provisional syllabus
Week 1: Intro – Basic set theoryWeek 2: Design of fuzzy logic controllersWeek 3: Design of fuzzy logic controllers IIWeek 4: TS Fuzzy Logic Weeks 5 - 7: Matlab programming Week 8: ANN – Matlab Week 9: ANN – Matlab IIWeek 10: Genetic AlgorithmsWeek 11: RevisionWeek 12: ???
![Page 6: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/6.jpg)
Control strategy
Conventionalcontrol Model of the actual plant
Deterministic Stochastic
Inaccurate
Complex methods
![Page 7: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/7.jpg)
Human reasoning and experience
Complicated processes Controlled by experiencedpractical engineers
Have no ideaabout the model
Use their knowledge &experience
Human reasoningNo model neededSatisfactory performance
Artificial Intelligence
![Page 8: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/8.jpg)
Artificial Intelligence
•Expert Systems (ES)•Fuzzy Logic (FL)•Artificial Neural Networks (ANN)•Genetic Algorithms (GAs)•A combination of all these
![Page 9: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/9.jpg)
Set theory I
Shape A Shape B Shape C Shape D
Shape E Shape F Shape G Shape H
H Shape F, Shape D, Shape C, ShapeA
G Shape E, Shape B, Shape A, ShapeB
H Shape G, Shape F, Shape E, Shape D, Shape C, Shape B, Shape A, ShapeC
![Page 10: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/10.jpg)
Set theory II
H Shape F, Shape D, Shape C, ShapeA
G Shape E, Shape B, Shape A, ShapeB
H Shape G, Shape F, Shape E, Shape D, Shape C, Shape B, Shape A, ShapeC
Subset: A set that has some elements from another set
G Shape B, Shape A, ShapeD BD Union: A set that has all the elements of two other sets
G Shape B, Shape A, Shape H, Shape F, Shape D, Shape C, Shape AD
DAAD
Intersection: A set that has all the common elements of two other sets
G ShapeEB H Shape G, ShapeEwhere
BEEB
![Page 11: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/11.jpg)
Boolean Logic
esTemperaturA HotesTemperaturBAB ,
25 esTemperaturesTemperaturB
25 Temperature
MembershipFunction
100%
0%
![Page 12: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/12.jpg)
Boolean and Fuzzy Logic (FL)
Temperature=24.99 ??? Not so HotNot so Hot
Temperature=25 100 %
Temperature=24 90 %Temperature=15 0 %
Element Membership function, I.e. How much an element belongs to a set
HotMuchHowesTemperaturC ,
![Page 13: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/13.jpg)
Fuzzy Logic
25 Temperature
MembershipFunction
15
100%
0%
25 Temperature
MembershipFunction
100%
0%
![Page 14: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/14.jpg)
Fuzzy Sets I
Triangular
Trapezoidal
![Page 15: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/15.jpg)
Fuzzy Sets II
Gaussian
Sigmoidal
![Page 16: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/16.jpg)
Polynomial
Fuzzy Sets III
![Page 17: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/17.jpg)
Logical Operators
6 4, 2, 1,A
1 2 3 4 5 6
Set A
Union•For element 1: Is 1 a member of set A OR set BIntersection•For element 1: Is 1 a member of set A AND set B
6 5, 2,3, B
1 2 3 4 5 6
Set B
![Page 18: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/18.jpg)
Logical Operators Discrete Sets
6 3,4,5, 2, 1,BA
1 2 3 4 5 6
UnionA B AND OR
1 0 0 1
0 1 0 1
1 1 1 1
0 0 0 0
6 2,BA
1 2 3 4 5 6
Intersection
![Page 19: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/19.jpg)
Logical Operators Continuous Sets
25 esTemperaturesTemperaturA
30 eTemperatureTemperaturInter
25 etemperaturetemperaturUnion
25 Temperature30 25 Temperature30
03 esTemperaturesTemperaturB
![Page 20: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/20.jpg)
Fuzzy sets & Logical Operators I
OR=MAXAND=MIN
A B Min(A, B)and
Max(A, B)or
1 0 0 1
0 1 0 1
1 1 1 1
0 0 0 0
![Page 21: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/21.jpg)
Fuzzy sets & Logical Operators II
![Page 22: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/22.jpg)
Example – Matlab Exercise
Two fuzzy sets have the following membership functions
35,30,75
1
30,25,55
1
3525,0
xxx
xxx
xorxx
A
40,35,85
1
35,30,65
1
4030,0
xxx
xxx
xorxx
B
Plot the two setsFind the union and the intersection of them, and explain the results through the min, max operator
![Page 23: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/23.jpg)
Linguistic variables
The room is cold lets switch on the heaterNot The temperature is 17.5 degrees
)(x
esTemperatur
1
1510 20
cold
Lecture 1
![Page 24: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/24.jpg)
Lecture scope
Lecture Scope: • To define advanced concepts on FL set theory• Connection between classical and FS theory
Lecture Outcomes: • Notation• Definitions like support, height…• Union, intersection, max and min• Negation, bounded sums• Cartesian products on crisp and FS• Extension principle• Fuzziness
![Page 25: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/25.jpg)
Lecture Outcomes
Lecture Scope: • Basic steps in the design of a Fuzzy Logic Controller
Lecture Outcomes:
• Basic Control strategy• Fuzzification• Fuzzy Inference System• Multiple Inputs – And/Or operators• Overlapping Fuzzy Sets• Defuzzyfication
![Page 26: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/26.jpg)
Design of a FLC - Basic Concept
FL mimics Human Reasoning:
If … Then…
IF THEN RULES
R1: If the room is very cold then switch on the heater to fullR2: If the room is cold then switch on the heater to mediumR3: If the room is normal then switch off the heater
If part: premise - Then part: conclusion
![Page 27: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/27.jpg)
Design of a FLC - Fuzzification I
)(x
Temperatures
1
1510 20
VeryCold
Cold Warm Hot
1. Cover I/O the universe of discourse with FS2. Assign to every real input a membership function at each set This process is called Fuzzyfication
![Page 28: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/28.jpg)
Design of a FLC - Fuzzification II
)(x
Temperatures
1
1510 20
VeryCold
Cold Warm Hot
11
0.7
0.5
With this way every real input is mapped to a fuzzy setThe value of the membership function that will be assigned dependson the shape of the membership function
![Page 29: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/29.jpg)
Design of a FLC – If… Then…
1. If … Then … Rules2. Input Fuzzy Sets (Fuzzification)3. Output Fuzzy Sets
Associate
If Then Rules
Input Linguistic Variable
Output Linguistic Variable
If … Then … Rules associate the input fuzzy sets to the output fuzzy setsIf … Then … Rules associate the input fuzzy sets to the output fuzzy sets
![Page 30: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/30.jpg)
Design of a FLC – If… Then…
)(x
eTemperatur0
Very Cold Cold Normal
35 10050 80
)(x
%
Heater0
MaxMedOff
35 10050 80
R1: If temp is Very Cold Then Heater is MaxR2: If temp is Cold Then Heater is MedR3: If temp is Normal Then Heater is Off
![Page 31: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/31.jpg)
Design of a FLC - Degree of Support Boolean sets
Assume an IF THEN rule with Boolean sets:R1: IF student fails THEN his/her parents are Sad
Hence if a student x fails 100% then his/her parentswill be 100% sad.
Therefore how much truth is the premise defines how much truth is the conclusion
The value of 100% or 0% is called degree of support of R1
![Page 32: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/32.jpg)
Design of a FLC - Degree of Support Fuzzy sets I
Exactly the same stands for fuzzy setsR1: If temp is Cold Then Heater is Med
)(x
1
5030 80
Cold)(x
1
50%35% 80%
Med
Assume temp=35oC
![Page 33: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/33.jpg)
Design of a FLC - Degree of Support Fuzzy sets II
So the degree of support is 0.7So the output “Med” is true 0.7
)(x
1
5030 80
Cold
35
0.7
???
R1: If temp is Cold Then Heater is Med
![Page 34: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/34.jpg)
Design of a FLC - Degree of Support Fuzzy sets III
I have to take 70% of the output
)(x
1
5030 80
Cold
35
0.7
)(x
1
50%35% 80%
Med
0.7
![Page 35: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/35.jpg)
Design of a FLC - Degree of Support Fuzzy sets IV
)(x
1
50%35% 80%
Med
0.7
)(x
1
50%35% 80%
Med
0.7
Min method Product method
![Page 36: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/36.jpg)
Design of a FLC - 2nd example
)(x
hour
milesSpeed0
Slow Normal Fast
35 10050 80
)(x
%
LevelBrake0
Min Med Max
35 10050 80
R1: If speed is Slow Then Brake is MinR2: If speed is Normal Then Brake is MedR3: If speed is Fast Then Brake is Max
![Page 37: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/37.jpg)
Design of a FLC - Degree of Support Fuzzy sets II
85 miles/hour -> Input: Max 0.5Hence Output: 0.5
)(x
hourmilesSpeed
0.5
9080 100
Fast
85
)(x
0.5
90%80% 100%
Maximum
Brake level
![Page 38: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/38.jpg)
Design of a FLC - Degree of Support Fuzzy sets III
85 miles/hour -> Input: High 0.5Hence Output: 0.5
)(x
0.5
90%80% 100%
High
Brake level
)(x
hourmilesSpeed
0.5
9080 100
Fast
85
![Page 39: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/39.jpg)
Design of a FLC – Number of Inputs
Has the previous controller a satisfactory performance?
No, what about if the speed is medium and there is a car in 5m
We need another input, the distance from the front car.
Hence the rules will have the following form:
R1: If Speed is High OR/AND the Distance is Small Then Brake is Max
Hence we have to use logical operators: Max & Min
![Page 40: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/40.jpg)
Design of a FLC – Or / AND I
The problem now is the degree of support of this rulesince there are two fuzzy sets that are activated
High Speed and Small Distance
)(x
hkmSpeed /,
1
9080 100
High)(x
m,distance
1
2010 30
Close
![Page 41: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/41.jpg)
Design of a FLC – Or / AND II
Assume that the actual speed is 85 and the actual distance is 18 meters:
)(x
hkmSpeed /,
1
9080 100
High
85
0.5
)(x
m,distance
1
2010 30
Close
0.6
18
Degree from input 1=0.5Degree from input 2=0.6
![Page 42: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/42.jpg)
Design of a FLC – Or / AND III
Since the OR operator was used then the overall degree of support is found by the max operation:Degree of Support for rule 1: max(0.5,0.6)=0.6
If the operator was the AND then we would use min:Degree of Support for rule 1: min(0.5,0.6)=0.5
)(x
0.6
90%80% 100%
Maximum
Brake level
)(x
0.6
90%80% 100%
High
Brake level
Maximum
![Page 43: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/43.jpg)
Design of a FLC – Multiple Input FS I
The universe of discourse must be fully covered by FSHence now the controller could be:
)(x
hkmSpeed /,
9080 100
High
60504030
MedLow
Input Output
)(x
scaleBrake
9080 100
Full
60504030
SomeLittle
If Speed==Low Then Brake==Little
If Speed==Some Then Brake==Some
If Speed==High Then Brake==Full
![Page 44: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/44.jpg)
Design of a FLC – Multiple Input FS II
Hence if input=35km/h:
Input Output
)(x
hkmSpeed /,
9080 100
High
60504030
MedLow
0.5
)(x
scaleBrake
9080 10060504030
Little
![Page 45: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/45.jpg)
Design of a FLC – Overlapping Input FS I
What about if speed is 50km/h?The controller will do nothing!!!
For this reason we overlap the FS:
)(x
hkmSpeed /,
9080 1007050403020100 60
VeryLow
Low HighVeryHigh
)(x
hkmSpeed /,
9080 1007050403020100 60
Nothing Little Some Full
Brake scale %
![Page 46: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/46.jpg)
Design of a FLC – Overlapping Input FS II
1. If Speed==Very Low Then Brake==Nothing2. If Speed==Low Then Brake==Little3. If Speed==High Then Brake==Some 4. If Speed==Very High Then Brake==Full
Speed=25 km/h Very Low 0.8 Low 0.2
Hence degree of support for R1 is 0.8 and for R2 is 0.2
![Page 47: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/47.jpg)
Design of a FLC – Overlapping Input FS III
)(x
hkmSpeed /,
9080 1007050403020100 60
Nothing
Brake scale%
)(x
hkmSpeed /,
9080 1007050403020100 60
Little
Brake scale%
![Page 48: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/48.jpg)
Aggregation MethodAggregation Method
1. Max (Maximum) 2. Prodor (Probabilistic Or) 3. Sum
)(x
hkmSpeed /,
9080 1007050403020100 60
Nothing
Brake scale %
![Page 49: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/49.jpg)
Design of a FLC – Overlapping Input FS V
Brake scale %
)(x
hkmSpeed /,
9080 1007050403020100 60
Nothing
Brake scale %
)(x
hkmSpeed /,
9080 1007050403020100 60
Nothing)(x
hkmSpeed /,
9080 1007050403020100 60
Nothing
![Page 50: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/50.jpg)
Design of a FLC – Defuzzification
)( x
0.5
90%80% 100%
Maximum
)( x
0.5
90%80% 100%
Mean Of Maxima
Max Of Maxima
Least Of Maxima
)( x
0.5
90%80% 100%
Centre of area (COA)
![Page 51: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/51.jpg)
Design of a FLC – Defuzzification
max: yyout Maximum
Mean Of Maxima (MOM) max:1
1
j
m
jj yy
mout
Centre of area (COA)
m
ij
m
ijj
y
yyout
1
1
Largest of maximumSmallest of maximum
![Page 52: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/52.jpg)
Design of a FLC – Summary
The first step is to Fuzzify the real inputs:Appropriate cover the universe of discourse with FS
The second step is to create the FIS:Create the IF THEN rules using AND/OR operatorAggregate all the FLR to get the final output FS
Initially choose the number of inputs/outputs and their universe of discourse
The last step is to defuzzify the output fuzzy sets to a real value
Lecture 3
![Page 53: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/53.jpg)
Artificial Neural Networks (ANNs)
Human Brain:
Memory Processor
Small “computing” element: Neuron
NucleusCell bodyAxon/Nuerous dendritic links Synapses
1010 to 1012
Adaptive connections
![Page 54: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/54.jpg)
Structure of ANNs
Σ f(net)net y
w1
w2
w3
w n
x1
x2
x3
xn
Activationfunction
Inputs
1
b
Inputs: x1 ,x2,x3,…,xn Weights w1 ,w2,w3,…,wn
bxwxwxwxwbxwnet nn
n
iii
.......332211
1
bxwfnetfy
n
iii
1
![Page 55: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/55.jpg)
Activation function
bxwfnetfy
n
iii
1
Linear activation function
y
net
Threshold activation function
y
net
+1
-1
![Page 56: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/56.jpg)
Activation function…cont
bxwfnetfy
n
iii
1
net
+1
0.5
y
Sigmoid function
Tansigmoid function
y
net
+1
-1
![Page 57: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/57.jpg)
Architecture of ANNs
Combinations of ANNs
y1
x2
x3
x1
y2
y3
+1 +1
Threshold Threshold
b11
b12
w111
w112
w431 w34
2
InputLayer
OutputLayer
HiddenLayer
o1
o2
o3
o4
Multi-layer feedforward
Σ f(net)net y
w1
w2
w3
w n
x1
x2
x3
xn
Activationfunction
Inputs
1
b
3 inputs x 4 outputs from o 3 outputs y
T
T
T
yyy
oooo
xxx
321
4321
321
y
o
x
![Page 58: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/58.jpg)
Multi-layer feedforward
T
T
T
yyy
oooo
xxx
321
4321
321
y
o
x
14
13
12
11
143
142
141
133
132
131
123
122
121
113
112
111
,
b
b
b
b
www
www
www
www
11 bw
y1
x2
x3
x1
y2
y3
+1 +1
Threshold Threshold
b11
b12
w111
w112
w431 w34
2
InputLayer
OutputLayer
HiddenLayer
o1
o2
o3
o4
1st Layer
Hidden Layer
113
1132
1121
111
11 bxwxwxwfo
214
2143
2132
2121
211
21 bowowowowfy
![Page 59: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/59.jpg)
Recurrent neural networks
y1
x2
x1
y2
y3
w111
w112
w431 w34
2
Delay
ExternalInputs
Delay
![Page 60: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/60.jpg)
Classification of ANN
Supervised Learning:
Unsupervised Learning
Teacher Input/ Target data
Network weight correction Learning algorithm
Minimize an error function
Mean-squared error (MSE)
![Page 61: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/61.jpg)
Learning algorithm
Back propagationNon-LinearFunction
NeuralNetwork
Learning Algorithm
x
Input
y
y
+
-
error )(1 kwkwkw ijijij
ijij w
Ew
n: Learning Rate
)1(
)(1
kw
kwkwkw
ij
ijijij
![Page 62: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/62.jpg)
ANNs Strategy
1.Assemble the suitable training data2.Create the network object
3.Train the network 4.Simulate the network response to new inputs
![Page 63: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/63.jpg)
Application of ANNs
1. Classification and diagnostic2. Pattern recognition 3. Modelling 4. Forecasting and prediction5. Estimation and Control
![Page 64: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/64.jpg)
Revision
Σ f(net)net y
w1
w2
w3
w n
x1
x2
x3
xn
Activationfunction
Inputs
1
b
y1
x2
x3
x1
y2
y3
+1 +1
Threshold Threshold
b11
b12
w111
w112
w431 w34
2
InputLayer
OutputLayer
HiddenLayer
o1
o2
o3
o4Non-Linear
Function
NeuralNetwork
Learning Algorithm
x
Input
y
y
+
-
error
![Page 65: EEE-8005 Industrial automation SDL Module leader: Dr. Damian Giaouris Email: Damian.Giaouris@ncl.ac.uk Room: E3.16 Phone: 0191 222 -7327 Module Leader](https://reader030.vdocuments.us/reader030/viewer/2022032703/56649d205503460f949f5204/html5/thumbnails/65.jpg)
Matlab
net= newff ([-4 3; -5 5], [4,1], {‘tansig’,’purelin’},’traingda’ )
net.trainParam.lr
net.trainParam.epochs
net.trainParam.goal
562.003.0 23 xxxxfy x=0-20 input=x
target=f(x)
>> net=newff([0,20],[10,1],{'tansig','purelin'},'trainlm');>> net.trainParam.goal=1e-5;>> net.trainParam.epochs=500;
>> [net,tr]=train(net,p,t);
>> a=sim(net,x)