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 of: Digital Control (EEE 8007) Degree Program Director of MSc: Automation and Control

2. 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

3. Module Structure Student Directed Learning Some lectures => individual Trigger further individual study Normal Lectures: 2hs/week 1h session/week: SDL

4. Provisional syllabus Artificial Intelligence Fuzzy Logic TheoryMatlab Neural Networks Genetic algorithms

5. Provisional syllabus Week 1:Intro – Basic set theory Week 2: Design of fuzzy logic controllers Week 3: Design of fuzzy logic controllers II Week 4: TS Fuzzy Logic Weeks 5 - 7: Matlab programming Week 8: ANN – Matlab Week 9: ANN – Matlab II Week 10: Genetic Algorithms Week 11:Revision Week 12:???

6. Control strategy Conventional control Model of the actual plant DeterministicStochastic Inaccurate Complex methods

7. Human reasoning and experience Complicated processes Controlled by experienced practical engineers Have no idea about the model Use their knowledge & experience Human reasoning No model needed Satisfactory performance Artificial Intelligence

8. Expert Systems (ES) Fuzzy Logic (FL) Artificial Neural Networks (ANN) Genetic Algorithms (GAs) A combination of all these

9. Set theory I

10. Set theory II Subset: A set that has some elements from another set Union: A set that has all the elements of two other sets Intersection: A set that has all the common elements of two other sets

11. Boolean Logic

12. Boolean and Fuzzy Logic (FL) Temperature=24.99 ??? Not so Hot Temperature=25 100 % Temperature=24 90 % Temperature=15 0 % Element Membership function, I.e. How much an element belongs to a set

13. Fuzzy Logic

14. Fuzzy Sets I Triangular Trapezoidal

15. Fuzzy Sets II Gaussian Sigmoidal

16. Polynomial Fuzzy Sets III

17. Logical Operators Union For element 1: Is 1 a member of set A OR set B Intersection For element 1: Is 1 a member of set A AND set B

18. Logical Operators Discrete Sets ABANDOR 1001 0101 1111 0000

19. Logical Operators Continuous Sets

20. Fuzzy sets & Logical Operators I OR=MAX AND=MIN ABMin(A, B) and Max(A, B) or 1001 0101 1111 0000

21. Fuzzy sets & Logical Operators II

22. Example – Matlab Exercise Two fuzzy sets have the following membership functions Plot the two sets Find the union and the intersection of them, and explain the results through the min, max operator

23. Linguistic variables The room is cold lets switch on the heater Not The temperature is 17.5 degrees Lecture 1

24. 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

25. 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

26. 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 full R2: If the room is cold then switch on the heater to medium R3: If the room is normal then switch off the heater If part: premise - Then part: conclusion

27. Design of a FLC - Fuzzification I 1.Cover I/O the universe of discourse with FS 2.Assign to every real input a membership function at each set This process is called Fuzzyfication

28. Design of a FLC - Fuzzification II With this way every real input is mapped to a fuzzy set The value of the membership function that will be assigned depends on the shape of the membership function

29. Design of a FLC – If… Then… 1.If … Then … Rules 2.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 sets

30. Design of a FLC – If… Then… R 1 : If temp is Very Cold Then Heater is Max R 2 : If temp is Cold Then Heater is Med R 3 : If temp is Normal Then Heater is Off

31. Design of a FLC - Degree of Support Boolean sets Assume an IF THEN rule with Boolean sets: R 1 : IF student fails THEN his/her parents are Sad Hence if a student x fails 100% then his/her parents will 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 R 1

32. Design of a FLC - Degree of Support Fuzzy sets I Exactly the same stands for fuzzy sets R 1 : If temp is Cold Then Heater is Med Assume temp=35 o C

33. Design of a FLC - Degree of Support Fuzzy sets II So the degree of support is 0.7 So the output “Med” is true 0.7 ??? R 1 : If temp is Cold Then Heater is Med

34. Design of a FLC - Degree of Support Fuzzy sets III I have to take 70% of the output

35. Design of a FLC - Degree of Support Fuzzy sets IV Min method Product method

36. Design of a FLC - 2 nd example R 1 : If speed is Slow Then Brake is Min R 2 : If speed is Normal Then Brake is Med R 3 : If speed is Fast Then Brake is Max

37. Design of a FLC - Degree of Support Fuzzy sets II 85 miles/hour -> Input: Max 0.5 Hence Output: 0.5

38. Design of a FLC - Degree of Support Fuzzy sets III 85 miles/hour -> Input: High 0.5 Hence Output: 0.5

39. 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: R 1 : If Speed is High OR/AND the Distance is Small Then Brake is Max Hence we have to use logical operators: Max & Min

40. Design of a FLC – Or / AND I The problem now is the degree of support of this rule since there are two fuzzy sets that are activated High Speed and Small Distance

41. Design of a FLC – Or / AND II Assume that the actual speed is 85 and the actual distance is 18 meters: Degree from input 1=0.5 Degree from input 2=0.6

42. 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 Maximum

43. Design of a FLC – Multiple Input FS I The universe of discourse must be fully covered by FS Hence now the controller could be: InputOutput If Speed==Low Then Brake==Little If Speed==Some Then Brake==Some If Speed==High Then Brake==Full

44. Design of a FLC – Multiple Input FS II Hence if input=35km/h: InputOutput

45. 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: Brake scale %

46. Design of a FLC – Overlapping Input FS II 1.If Speed==Very Low Then Brake==Nothing 2.If Speed==Low Then Brake==Little 3.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

47. Design of a FLC – Overlapping Input FS III Brake scale %

48. Aggregation Method 1.Max (Maximum) 2.Prodor (Probabilistic Or) 3.Sum Brake scale %

49. Design of a FLC – Overlapping Input FS V

50. Design of a FLC – Defuzzification Maximum Mean Of Maxima Max Of Maxima Least Of Maxima Centre of area (COA)

51. Design of a FLC – Defuzzification Maximum Mean Of Maxima (MOM) Centre of area (COA) Largest of maximum Smallest of maximum

52. 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 operator Aggregate 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

53. Artificial Neural Networks (ANNs) Human Brain: Small “computing” element: Neuron Nucleus Cell body Axon/Nuerous dendritic links Synapses 10 10 to 10 12 Adaptive connections

54. Structure of ANNs Inputs: x 1,x 2,x 3,…,x n Weights w 1,w 2,w 3,…,w n

55. Activation function Linear activation function Threshold activation function

56. Activation function… cont Sigmoid function Tansigmoid function

57. Architecture of ANNs Combinations of ANNs Multi-layer feedforward 3 inputs x 4 outputs from o 3 outputs y

58. Multi-layer feedforward 1 st Layer Hidden Layer

59. R ecurrent neural networks

60. Classification of ANN Supervised Learning: Unsupervised Learning Teacher Input/ Target data Network weight correction Learning algorithm Minimize an error function Mean-squared errorMean-squared error (MSE)

61. Learning algorithm Back propagation n: Learning Rate

62. ANNs Strategy 1.Assemble the suitable training data 2.Create the network object 3.Train the network 4.Simulate the network response to new inputs

63. Application of ANNs 1.Classification and diagnostic 2.Pattern recognition 3.Modelling 4.Forecasting and prediction 5.Estimation and Control

64. Revision

65. Matlab net= newff ([-4 3; -5 5], [4,1], {‘tansig’,’purelin’},’traingda’ ) net.trainParam.lr net.trainParam.epochs net.trainParam.goal 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)