Fuzzy Controller. Fuzzy Inference System. Basic Components of Fuzzy Inference System. Rule based system: Contains a set of fuzzy rules

Transcription

1 Fuzz Controller Fuzz Inference Sstem Basic Components of Fuzz Inference Sstem Rule based sstem: Contains a set of fuzz rules Data base dictionar: Defines the membership functions used in the rules base sstem Defuzzification sstem: A defuzzifier to provide a crisp result from the output membership functions 2

2 Sstem Basic Components of Fuzz Inference Sstem Knowledge Base Fuzz or Crisp Input Fuzzification Defuzzification Crisp Output Fuzz Decision-Making Logic (Decision Rules) Fuzz 3 Fuzz Controller Step1: Values of the input variables Step4: Determine the consequence of each rule Step2: Fuzzif inputs Step5: Aggregate the consequences Step3: Calculate the firing strength Step6: Defuzzif the output 4

3 Fuzz Controller Basic Components of Fuzz Inference Sstem 1 Input vocabular, fuzzification (creating fuzz sets) 2 Fuzz propositions IF X is Y THEN Z (or Z is A) there are four tpes of propositions 3 Combination and evaluation computation of the results given the inputs 4 Action - defuzzification 5 Fuzz Controller Fuzzification Transforming measurement (input) data into valuation of subjective values (It is mapping from an observed input space to labels of fuzz sets) Input data are usuall crisp; or it might be fuzz sets A A A µ µ 6

4 Fuzz Rule-Base It is the collection of fuzz IF-THEN rules in which the preconditions and consequences are linguistic terms Fuzz rules relate inputs to outputs (control logic) Rules are formed using linguistic variables, so it is not precise Output is also a linguistic value representing a fuzz set Determine degree of match of fuzz input with rule antecedent and assign this to the rule conclusion Antecedent is the intersection or union of fuzz inputs It is also called the degree of truth 7 Fuzz Rule-Base Eample Assume two fuzz linguistic variables Speed and Position Speed (fast, 065 and Medium, 035) Position (centered, 04 and right, 06) Find the membership for the conclusion of the rules: If Speed = Fast and Position = Centered then Change in speed = Faster If Speed = Fast and Position = Right then Change in speed = Zero If Speed = Medium and Position = Centered then Change in speed = Faster 8

5 Fuzz Rule-Base Eample If Speed = Fast (065) and Position = Centered (04) then Change in speed = Faster (04) If Speed = Fast (065) and Position = Right (06) then Change in speed = Zero (06) If Speed = Medium (035) and Position = Centered (04) then Change in speed = Faster (035) Appl Union or Intersection according to And or Or 9 Fuzz Rule-Base Eample If rules have the same conclusion with different degree of truth, then take the maimum for the degree of truth for the conclusions (union of results) Appl this for the previous eample ields: If Speed = Fast (065) and Position = Centered (04) then Change in speed = Faster (04) If Speed = Medium (035) and Position = Centered (04) then Change in speed = Faster (035) Change in Speed: Faster = ma (04, 035) = 04 10

6 Combining and Decomposition of Fuzz Sets If is A then is B Fact rule is A If is A then is B Consequence is B Given an input of A fuzz set or crisp value A Fact is A rule If is A then is B Consequence is B 11 Fuzz Inference Single Rule with Single Antecedent µ B () = U [µ A () ^µ A () ] ^ µ B () = ω ^ µ B () ω is called the rule firing strength B A A B ω 12

7 Single Rule with Single Antecedent Assume crisp input (fuzzification) µ B () = ω ^ µ B () B A B ω A 13 Fuzz Inference Single Rule with Multiple Antecedent Rule: If is A and is B then z is C Fact: is A and is B Conclusion: z is C µ C (z) = {U [µ A ()^ µ A ()]} ^ {U [ µ B ()^ µ B () ]}^µ C (z) = (ω1 ^ ω2) ^ µ C (z) (ω1 ^ ω2) is called the rule firing strength 14

8 Single Rule with Multiple Antecedent A A B B C ω1 ω2 C z 15 Fuzz Inference 16

9 Multiple Rules with Multiple Antecedent Rule: If is A1 and is B1 then z is C1 If is A2 and is B2 then z is C2 Fact: is A and is B Conclusion: z is C C = [(A B ) o R1] U [(A B ) o R2] = C1 U C2 17 Fuzz Inference Multiple Rules with Multiple Antecedent A1 A1 B1 B1 ω2 ω1 A2 A2 B2 B2 ω3 ω4 C1 C1 C2 C2 z z C2 C1 18

10 19 Fuzz Inference 20

11 Combining and Decomposition of Fuzz Sets 21 Fuzz Inference Combining and Decomposition of Fuzz Sets 22

12 User input Value of variable 1 WF = 90 Value of variable 2 SE = 3 Value of variable 3 UP = 6 Value of output R =? Rule 1 Rule 6 Rule L ω1= Area1 10 M 10 H 10 I ω2=67 Area6 ω3= Area27 23 Fuzz Inference Overall Membership Function Envelop enclosing all areas (area1 to area27) Area Overall output = Center of Area=

13 Defuzzification Defuzzification represents the wa a crisp value is etracted from a fuzz set as a representative value 25 Fuzz Inference Defuzzification Z COA = µ A (z)z dz / µ A (z) dz µ A (z) is the aggregated membership function 26

14 Defuzzification Mean of maimum Z mom = (Z 1 + Z 2 ) /2 Smallest of maimum Z som is the minimum of the maimums of Z = Z 1 Largest of maimum Z 1 Z 2 Z Lom = Z 2 27 Fuzz Controller Eample H Fuzz logic controller T Cooling rate C Air conditioner Temperature Humidit sensor sensor Room 28

15 Fuzz Controller Eample Low (LW) High (HG) Low (LW) High (HG) Temperature T Humidit H Negative high Negative low Positive low Positive high (NH) (NL) (PL) (PH) C Cooling Rate 29 Fuzz Controller Eample: If-then rules Rule 1: If T is HG and H is HG then C is PH Rule 2: If T is HG and H is LW then C is PL Rule 3: If T is LW and H is HG then C is NL Rule 4: If T is LW and H is LW then C is NH 30

16 Fuzz Controller Eample High High Positive high T H C High Low Positive low T H C Low High Negative low Low T Low H Negative high C T H C 31 Fuzz Controller Eample: Overall Output Membership Function C 32