Question 12 (20 marks) You will be able to answer this question after you have studied Week 16. This question asks you to calculate the output of a fuzzy logic controller that is used in a washing machine. You are advised to use no more than 500 words in your answer to this question. When clothes are placed in a washing machine and water added, an optical sensor is used to detect the dirtiness of the clothes and the type of dirt. In particular, greasy clothes, for example, take longer to wash. A fuzzy controller is used to determine the wash time. A set of rules are produced as follows: 1. If dirtiness of clothes is LARGE and type of dirt is GREASY, then wash time is LONG. 2. If dirtiness of clothes is MEDIUM and type of dirt is GREASY, then wash time is LONG. 3. If dirtiness of clothes is SMALL and type of dirt is GREASY, then wash time is LONG. 4. If dirtiness of clothes is LARGE and type of dirt is MEDIUM, then wash time is LONG. 5. If dirtiness of clothes is MEDIUM and type of dirt is MEDIUM, then wash time is MEDIUM. 6. If dirtiness of clothes is SMALL and type of dirt is MEDIUM, then wash time is MEDIUM. 7. If dirtiness of clothes is LARGE and type of dirt is NOT GREASY, then wash time is MEDIUM. 8. If dirtiness of clothes is MEDIUM and type of dirt is NOT GREASY, then wash time is SHORT. 9. If dirtiness of clothes is SMALL and type of dirt is NOT GREASY, then wash time is SHORT. The membership functions for dirtiness, type of dirt and wash time are all triangular with three functions running from 0 to 100%. For dirtiness the sets are: SMALL MEDIUM LARGE. Membership 1 0 50 100 Dirtiness (%) SMALL membership MEDIUM membership LARGE membership || Figure 3 Dirtiness For type of dirt the sets are: NOT GREASY III MEDIUM GREASY. Membership 1 O 50 100 Type of dirt (%) NOT GREASY membership MEDIUM membership GREASY membership Figure 4 Type of dirt For wash time the sets are: SHORT MEDIUM III LONG. Membership 1 0 50 100 Wash time (%) SHORT membership MEDIUM membership LONG membership ||| Figure 5 Wash time a. Using these membership functions, estimate the membership values of the fuzzy logic controller in the washing machine when the dirtiness is 30% and the type of dirt is 65%. (6 marks) b. Using the rules, find the values of the membership functions of the wash time. Do this by completing the following two tables. (4 marks) Table 2 Minimum values of the two input conditions Dirtiness Type of dirt NOT GREASY MEDIUM GREASY SMALL MEDIUM LARGE Table 3 Maximum values for the membership functions of wash time Rule Rule Rule Rule R Wash time membership 1 2 3 4 5 SHORT MEDIUM LONG C. Redraw the membership functions of wash time using the values form (c). Replace the triangles with singletons and then, using 'centre of area' defuzzification, find the final value of the wash time. III (8 marks) Question 12 (20 marks) You will be able to answer this question after you have studied Week 16. This question asks you to calculate the output of a fuzzy logic controller that is used in a washing machine. You are advised to use no more than 500 words in your answer to this question. When clothes are placed in a washing machine and water added, an optical sensor is used to detect the dirtiness of the clothes and the type of dirt. In particular, greasy clothes, for example, take longer to wash. A fuzzy controller is used to determine the wash time. A set of rules are produced as follows: 1. If dirtiness of clothes is LARGE and type of dirt is GREASY, then wash time is LONG. 2. If dirtiness of clothes is MEDIUM and type of dirt is GREASY, then wash time is LONG. 3. If dirtiness of clothes is SMALL and type of dirt is GREASY, then wash time is LONG. 4. If dirtiness of clothes is LARGE and type of dirt is MEDIUM, then wash time is LONG. 5. If dirtiness of clothes is MEDIUM and type of dirt is MEDIUM, then wash time is MEDIUM. 6. If dirtiness of clothes is SMALL and type of dirt is MEDIUM, then wash time is MEDIUM. 7. If dirtiness of clothes is LARGE and type of dirt is NOT GREASY, then wash time is MEDIUM. 8. If dirtiness of clothes is MEDIUM and type of dirt is NOT GREASY, then wash time is SHORT. 9. If dirtiness of clothes is SMALL and type of dirt is NOT GREASY, then wash time is SHORT. The membership functions for dirtiness, type of dirt and wash time are all triangular with three functions running from 0 to 100%. For dirtiness the sets are: SMALL MEDIUM LARGE. Membership 1 0 50 100 Dirtiness (%) SMALL membership MEDIUM membership LARGE membership || Figure 3 Dirtiness For type of dirt the sets are: NOT GREASY III MEDIUM GREASY. Membership 1 O 50 100 Type of dirt (%) NOT GREASY membership MEDIUM membership GREASY membership Figure 4 Type of dirt For wash time the sets are: SHORT MEDIUM III LONG. Membership 1 0 50 100 Wash time (%) SHORT membership MEDIUM membership LONG membership ||| Figure 5 Wash time a. Using these membership functions, estimate the membership values of the fuzzy logic controller in the washing machine when the dirtiness is 30% and the type of dirt is 65%. (6 marks) b. Using the rules, find the values of the membership functions of the wash time. Do this by completing the following two tables. (4 marks) Table 2 Minimum values of the two input conditions Dirtiness Type of dirt NOT GREASY MEDIUM GREASY SMALL MEDIUM LARGE Table 3 Maximum values for the membership functions of wash time Rule Rule Rule Rule R Wash time membership 1 2 3 4 5 SHORT MEDIUM LONG C. Redraw the membership functions of wash time using the values form (c). Replace the triangles with singletons and then, using 'centre of area' defuzzification, find the final value of the wash time. III (8 marks)