Design & Technology Foundation - Electronic Control (II) (Fuzzy Control Technology)

1. Design & TechnologyFoundation - Electronic Control (II)(Fuzzy Control Technology) By Jasper Wong email: icjwong@polyu.edu.hk fuzz/jw

2. Fuzzy Control Technology • A Simple Temperature Control System • Gas Flow is regulated by a knob in 10 notches • Fuzzy controller samples temperature, then based on a set of rules, adjust the gas knob up & down fuzz/jw

3. Fuzzy Control Technology • Define Input temperature conditions (Fuzzy Sets) : warm, medium & cool • For humans: 70 degree is the most comfortable temperature • Fuzzy sets overlap (e.g. between 60 degree & 66 degree) • 64 degree is “little bit cool” and “somewhat medium” fuzz/jw

4. Fuzzy Control Technology • Define output number of notches (Fuzzy sets): gas down, gas ok & gas up • Gas down corresponds to turning gas knob towards off fuzz/jw

5. Fuzzy Control Technology • The fuzzy controller operates a set of rules: • Rule 1: if temp. is cool, then turn up the gas • Rule 2: if temp. is medium, then gas is OK • Rule 3: if temp. is warm, then turn down the gas • Temp sensor reports 64 degree • Rule 1 applies at 20% • Rule 2 applies at 40% • Rule 3 does not applies at all • The output of the fuzzy controller is the Union of these two sets fuzz/jw

6. Fuzzy Control Technology • The output of the Fuzzy controller is the Union of the two fuzzy sets • Defuzzy the output, i.e, average value to a specific command to control the gas knob • The point is 1.86 fuzz/jw

7. Fuzzy Control Technology • Two-input system, add second input “rate-of-temperature change” • Define T: Lowering, Steady & Raising • e.g. Lowering is defined a temp falling rate from 0.2 to 1 deg. per minute fuzz/jw

8. Fuzzy Control Technology • Fuzzy rules for the two-input controller • Rule1: if T is cool & lowering, then increase the gas sharply • Rule2: if T is cool & steady, then increase the gas • Rule3: if T is cool & raising, then the gas OK • Rule4: if T is medium and lowering, then increase the gas • Rule5: if T is medium and steady, then the gas is OK • Rule6: if T is medium and raising, then decrease the gas • Rule7: if T is warm and lowering, then gas is OK • Rule8: if T is warm and steady, then decrease the gas • Rule9: if T is warm and raising, then decrease the gas sharply fuzz/jw

9. Fuzzy Control Technology • Assign values to the output conditions of “increase gas, “gas is OK” and “decrease gas”and in a table fuzz/jw

10. Fuzzy Control Technology • Assume temp. sensor reports 64 degree & temp. is rising at 0.6 degree per minute • From Temp. Graph: 64 degree corresponds to 20% cool & 40% medium • From T graph: 0.6 per min. corresponds to 10% steady & 50% raising • Out of 9 rules, only four rules apply: • Rule 2: if T is cool steady , then increase the gas • Rule 3: if T is cool raising , then gas is OK • Rule5: if T is medium and steady, then the gas is OK • Rule6: if T is medium and raising, then decrease the gas • As variables are fuzzy, each rule contributes to different degree. A measure of influence of Rule i is the product of the two probabilities in the rule. • Influence of Rule i = Wi =Ai1 x Ai2 i=1,2,... fuzz/jw

11. Fuzzy Control Technology • Wi = influence of Rule I, Ai1= probability of T, Ai2=probability of T • Applying the rules: w2 = 0.2 x0.1 = 0.02 w3 = 0.2 x 0.5 = 0.1 w5 = 0.4 x 0.1 = 0.04 w6 = 0.4 x 05 = 0.2 • Output Component for each rule: yi = wi x Bi • yi = output from a rule, Bi= approx. value from output table • Applying this: y2 = w2 x B2 = 0.02 x 2 = 0.04 y3 = w3 x B3 = 0.1 x 0 = 0 y5 = w5 x B5 = 0.04 x 0 = 0 y6 = w6 x B6 = 0.2 x -2 = -0.4 fuzz/jw

12. Fuzzy Control Technology • Defuzzify the four outputs from the rules into a single command for the gas knob • Weighted mean approach: • ytot = ( w2y2 + w3y3 + w5y5 + w6y6) / (w2 + w3 + w5 + w6) • =[(0.02x0.04)+(0.1x0)+(0.04x0)+(0.2x -0.4)] / (0.02 +0.1 + 0.04 + 0.2) • = - 0.22 notch • Final output of the fuzzy control should the gas knob down slightly 0.22 notch fuzz/jw

13. Fuzzy Control Technology • A Fuzzy Vacuum Cleaner fuzz/jw

14. Fuzzy Control Technology • The controller should regulate the force of sucking dust from a surface being cleaned • The force can be very strong, strong, ordinary, weak, very weak • The surface can be very dirty, dirty, rather dirty, almost clean, clean • Controller changes force depending on the how dirty the surface is • Rules : • if surface is very dirty then force is very strong, • if surface is dirty then force is strong, • if surface is rather dirty then force is ordinary, • if surface is almost clean then force is weak, • if surface is clean then force is very weak. fuzz/jw

15. Fuzzy Control Technology • How about for different surface texture and fabric ? • Rule table for surface type and dust amount Clean Almost clean Rather dirty Dirty Very dirty Wood Very weak Very weak Weak Ordinary Strong Tatami very weak Weak Ordinary Strong Strong Carpet weak Ordinary Ordinary Strong Strong fuzz/jw

16. Fuzzy Control Technology • Practical Implementation: • Dust Sensor • Phototransistor mounted opposite an infrared light -emitting diode • Infrared rays is blocked by dust, causing lose of ray intensity • Change in dust density will vary ray intensity • Amount of dust on the surface can be evaluated. • Surface type • The surface type will effect the speed of removing dust • Smooth surface will be cleaned fast • Wool carpet will be cleaned slowly • Surface type can be determined by the amount of dust collected in a time unit. fuzz/jw

17. Fuzzy Control Technology • Lighting Control fuzz/jw

18. Fuzzy Control Technology • Basic Fuzzy Control Concepts • Definition of Crisp Sets • List method: List the members of the set Universe Set 1,2,3,4,5,6,…….,1000, ….. 3,4,5,6 fuzz/jw

19. Fuzzy Control Technology • Rule method: Take only the members which satisfy the rule • Rule: Take only the houses higher than 15m • Rule : Choose all and only real numbers X for which abs(x) < 3 fuzz/jw

20. Fuzzy Control Technology • Definition of Fuzzy set • List method: List the members of the set Universe Fuzzy set 1,2,3,4,5,6,….,1000.. 10/0.1, 2/0.2,3/0.3, 4/0.95, 5/0.9, 6/0.85, 7/0.75 fuzz/jw

21. Fuzzy Control Technology • Rule method: Take only the members which satisfy to the rule • Rule: Take only the high of the houses • Rule: Choose all and only small real number X fuzz/jw

22. Fuzzy Control Technology • In a fuzzy set, we name all elements of the Universe and supplement to them a number between 0 and 1 • This number constitutes the membership degree of the element • The element and membership degree determines a membership function • Common membership functions: fuzz/jw

23. Fuzzy Control Technology • Terms in a Membership function fuzz/jw

24. Fuzzy Control Technology • Basic Structure of a Fuzzy Controller fuzz/jw

25. Fuzzy Control Technology • Operation of a Fuzzy Controller fuzz/jw

26. Fuzzy Control Technology • Fuzzy Rules Formulation fuzz/jw

27. Fuzzy Control Technology • Limitations of conventional controllers • Linearity models are too restrictive, nonlinear models are computationally intensive • Plant uncertainty, lack of perfect knowledge • Multivariables, multiloops and environment constraints • Uncertainty in measurements • Plants, controllers, environments and their constraints vary with time. Difficult to model time delays fuzz/jw

28. Fuzzy Control Technology • Benefits of Fuzzy Controllers • More robust than PID controllers, wide range of operating conditions • Cheaper in development • Fuzzy controllers are customizable, easy to understand the rules, expressed in natural linguistic terms • easy to operate and apply fuzz/jw

29. Fuzzy Control Technology • Typical Fuzzy Control Applications • Washing Machine • Optimum wash conditions by analyzing water temperature, load size, and water level. • Type of dirt and detergent for ideal wash • Dryer • Monitors load size, fabric type, and air flow to determine the optimum drying time • Vacuum Cleaner • Optimum suction power and beater-bar speed by sensing the amount of dirt and type of floor. • Even monitor the type dirt for more efficient cleaning fuzz/jw

30. Fuzzy Control Technology • Microwave Oven • Monitor temperature of the food and oven and the amount of steam generated • Calculate remaining time • Refrigerator • determine the most efficient time to defrost • use learned consumer usage patterns for optimum defrost and temperature control • Air Conditioner • Sense temperature, humidity and the number of people present and then cools the room accordingly • Defrosts outside at the most efficient time • Dishwasher • detect the amount of dishes loaded, type of food, and cleanliness level of the dishes and the correct cleaning cycle fuzz/jw

31. Fuzzy Control Technology • Rice Cooker • Monitor steam, temperature, and the volume of rice and calculate the remaining cooking time based on the programmed rice types • Toaster • adjust toasting time based on sensed bread type and learned preferences • Television • stabilize volume based on viewer location • adjust picture brightness and contrast in low-ambient-lighting conditions • Shower Carpet • stabilize water temperature regardless of water pressure fuzz/jw

32. Fuzzy Control Technology • Definition of key terms • Fuzzification • the process by which inputs can be transformed into fuzzy subsets • Defuzzification • the process of converting fuzzy outputs into crip control actions • Inference engine • a process of transforming fuzzy inputs into a fuzzy outputs by dealing with fuzzy rules. fuzz/jw