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Fuzzy Room temperature control
Abstract: This project paper describes the design of a room temperature controller using fuzzy logic. The proposed model consists of fuzzy logic controllers to control temperature. The controller accepts two input values- the current temperature as detected by temperature sensor and its deviation from user set-temperature, and controls the speed of heat-fan and cool-fan accordingly. This research work will increase the capability of fuzzy logic control systems in process automation with potential benefits. MATLAB-simulation is used to achieve the designed goal.
1 Introduction This proposed design work of room temperature controller can be used in a processing plant to maintain comfortable atmosphere in the room the basic model of the proposed structure consists of room temperature controller with fuzzy logic control system. The room atmosphere controller has a heating fan, a cooling fan to heat or cool the room according to user demand; temperature sensors used to monitor the environment of room are mounted in the room and are connected with the fuzzifiers of the fuzzy logic control system. The fuzzy controller is composed of the following four elements: 1. A rule-base (a set of If-Then rules), which contains a fuzzy logic quantification of the expert’s linguistic description of how to achieve good control 2.An inference mechanism (also called an “inference engine” or “fuzzy inference” module), which emulates the expert’s decision making in interpreting and applying knowledge about how best to control the plant. Group two
Page 1
Fuzzy Room temperature control 3.A fuzzification interface, which converts controller inputs into information that the inference mechanism can easily use to activate and apply rules.
4.A defuzzification interface, which converts the conclusions of the inference mechanism into actual inputs for the process
Figure 1: Fuzzy controller
Group two
Page 2
Fuzzy Room temperature control
e(t) FLC
Heater fan
Y(t)
Plant
Cooler fan Ce(t)
Figure 2: Block diagram of temperature control by fuzzy
2 Determining linguistic variables for the system. Input Variables:1 Current Temperature (error) It is the current temperature of the room as recorded by the temperature sensor mounted in the room 2. Deviation From Set Temperature(change in error) It gives the difference between the user preferred temperature and current temperature of the room as recorded by the temperature sensor in the room Output Variables 1.Heat-Fan-Speed
Group two
Page 3
Fuzzy Room temperature control The heat fan can either be in ON or OFF state depending on the temperature preference in the room 2.Cool-Fan-Speed The cool fan can either be in ON or OFF state depending on the temperature preference in the room
3 Determine the linguistic values of the given linguistic variables
linguistic values for Current Temperature (error OR input 1) Linguistic values for Current Temperature are Very COOL(VC), COOL(C), NORMAL(N), HOT(H) and VERY-HOT(VH).
The sensor range should be wide enough to take care of climatic and regional fluctuations. The proposed model works perfectly at any temperature within range 8oC44oC
Table 1: Membership Functions For Current-Temperature MEMBERSHIP
RANGE (oC)
FUNCTIONS
Very COOL
8-16
COOL
15-23
NORMAL
22-30
HOT
29-37
VERY-HOT
36-44
linguistic values for Deviation Current Temperature (change in error OR input 2) Linguistic values for Deviation Current Temperature are negative large(NL), negative
small(NS), zero(Z), positive small(PS) and positive large(PL).
Group two
Page 4
Fuzzy Room temperature control As this model can work between temperature range 8-44’C and user can set any desired temperature from 18-26’C, so temperature difference between the current and the user preferred temperature can never go beyond -26’C (18’C – 44’C) and 18’C (26’C - 8’C). Thus (-26’C) & (+18’C) are the lower and upper limits of the input variable “ deviation from set-temperature”). Table 2: Membership Functions for “Deviation from current temperature” MEMBERSHIP
RANGE(oC)
FUNCTIONS
NL
-26 to -12
NS
-13 to 0
O
-2 to 2
PS
1 to 10
PL
9 to 18
linguistic values for Heat-Fan-Speed(out put 1)
The heta-fan-speed is categorized into 1. stop 2.heat-slow(hs) 3. heat-medium(hm) 4. heat-fast 5. very fast. If the current temperature of the room is below the desired temperature then this fan automatically gets on varies speed according to temperature difference.
Table 3:-Membership Functions For “heat-fan-speed”
Group two
Page 5
Fuzzy Room temperature control MEMBERS
RANGE %
HIP FUNCTION S STOP
0-5
HEAT-
0-30
SLOW HEAT-
25-50
MEDIUM
FAST
45-80
very-FAST
75-100
linguistic values for cool-Fan-Speed(out put 2)
The cool-fan-speed is categorized into 1. STOP 2.COOL-SLOW 3. COOL-MEDIUM 4. COOLFAST. If the current temperature of the room is above the desired temperature then this fan automatically gets on varies speed according to temperature difference. MEMBERSHIP
RANGE %
FUNCTIONS STOP
0-5
COOL-SLOW
0-30
COOL-MEDIUM
25-50
COOL-FAST
45-80
COOL-V.FAST
75-100
Form rule based on the input and output variables to control speed of heat fan and cool fan.
Group two
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Fuzzy Room temperature control
4 Rule generate Rules that relate input and output variables for fuzzy controllers:
1. If (input1 is VC) and (input2 is NL) then (output1 is STOP) and (output2 is STOP) 2. If (input1 is VC) and (input2 is NS) then (output1 is HS) and (output2 is STOP) 3. If (input1 is VC) and (input2 is ZERO) then (output1 is HM) and (output2 is STOP) 4. If (input1 is VC) and (input2 is PS) then (output1 is HF) and (output2 is STOP) 5. If (input1 is VC) and (input2 is PL) then (output1 is HVF) and (output2 is STOP) 6. If (input1 is C) and (input2 is NL) then (output1 is STOP) and (output2 is CS) 7. If (input1 is C) and (input2 is NS) then (output1 is STOP) and (output2 is STOP) 8. If (input1 is C) and (input2 is ZERO) then (output1 is HS) and (output2 is STOP) 9. If (input1 is C) and (input2 is PS) then (output1 is HM) and (output2 is STOP) 10. If (input1 is C) and (input2 is PL) then (output1 is HF) and (output2 is STOP) 11. If (input1 is N) and (input2 is NL) then (output1 is STOP) and (output2 is CF) 12. If (input1 is N) and (input2 is NS) then (output1 is STOP) and (output2 is CM) 13. If (input1 is N) and (input2 is ZERO) then (output1 is STOP) and (output2 is STOP) 14. If (input1 is N) and (input2 is PS) then (output1 is HM) and (output2 is STOP) 15. If (input1 is N) and (input2 is PL) then (output1 is HF) and (output2 is STOP)
Group two
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Fuzzy Room temperature control 16. If (input1 is H) and (input2 is NL) then (output1 is STOP) and (output2 is CVF) 17. If (input1 is H) and (input2 is NS) then (output1 is STOP) and (output2 is CF) 18. If (input1 is H) and (input2 is ZERO) then (output1 is STOP) and (output2 is CM) 19. If (input1 is H) and (input2 is PS) then (output1 is STOP) and (output2 is STOP) 20. If (input1 is H) and (input2 is PL) then (output1 is HS) and (output2 is STOP) 21. If (input1 is VH) and (input2 is NL) then (output1 is STOP) and (output2 is CVF) 22. If (input1 is VH) and (input2 is NS) then (output1 is STOP) and (output2 is CF) 23. If (input1 is VH) and (input2 is ZERO) then (output1 is STOP) and (output2 is CM) 24. If (input1 is VH) and (input2 is PS) then (output1 is STOP) and (output2 is CS) 25. If (input1 is VH) and (input2 is PL) then (output1 is STOP) and (output2 is STOP) NB Input 1=current temperature Input 2= Deviation From Set Temperature Output 1= Heat-Fan-speed Output 2= cool-Fan-speed
Group two
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Fuzzy Room temperature control
5 Member ship function
Membership function of Current Temperature (error)
Where VC=very cool temperature C= cool temperature N= normal temperature H=hot temperature VH=very hot temperature
Group two
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Fuzzy Room temperature control
Membership function for Deviation Current Temperature (change in error)
Where NL=the Deviation Current Temperature is very hot or negative large NS=the Deviation Current Temperature hot or negative small Zero=the Deviation Current Temperature is normal or zero PS= the Deviation Current Temperature is cool or positive small Group two
Page 10
Fuzzy Room temperature control PL= the Deviation Current Temperature is very cool or positive large
Membership function for Heat-Fan-Speed
Where Group two
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Fuzzy Room temperature control Stop=the speed of heat-fan is stop HS= the speed of heat-fan is slow HM= the speed of heat-fan is medium HF= the speed of heat-fan is fast HVF fast= the speed of heat-fan is very
Membership function for cool-Fan-Speed
Where
Stop=the speed of cool-fan is stop CS= the speed of cool-fan is slow CM= the speed of cool-fan is medium Group two
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Fuzzy Room temperature control CF= the speed of cool-fan is fast CVF= the speed of cool-fan is very fast
6 Fuzzy quantification of knowledge Give a specific crisp values (numerical values) for the inputs and determine the recommended output value .use the following operations: Membership function: symmetrical triangle AND operation: product Implication: minimum Aggregation: sum Defuzzification method: center average To find the crisp value first determines one appropriate rule from 25 rules. A crisp set of input data are gathered and converted to a fuzzy set using fuzzy linguistic variables. The rule selected for inference process is:
7 Determining Which Rules Are On: Determining the applicability of each rule is called “matching.”
We say that a rule is “on
at time t” if its premise membership function μ𝒑𝒓𝒆𝒎𝒊𝒔(e(t), 𝑑𝑒(𝑡)𝑑𝑡) > 0. Hence, the inference mechanism seeks to determine which rules are on to find out which rules are relevant to the current situation. compute the rules that are on. Suppose that: e(t) = 15.75 and de(t)dt= 12.375
Figure shows the membership functions for the inputs and indicates with thick black vertical lines the values above for e(t) and de(t)dt.
Group two
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Fuzzy Room temperature control
Notice that μvcool(e(t)) = 0.0625 and μcool(e(t)) = 0.1875 but that the other membership functions for the e(t) input are all “off” (i.e., their values are zero). For the 𝑑(𝑡)𝑑𝑡 input we see that μ𝒑𝒐𝒔large (𝑑𝑒(𝑡)𝑑𝑡) = 0.75 and that all the other membership functions are off.
This implies that rules that have the premise terms: “error is very cool” “error is cool” Group two
Page 14
Fuzzy Room temperature control “change-in-error is poslarge” are on (all other rules have μ𝒑𝒓𝒆𝒎𝒊𝒔𝒆 (e(t), 𝑑𝑒(𝑡)𝑑𝑡) = 0.
the rules that are on are the following:
Rule 1 If (input1 is VCool) and (input2 is PL) then (output1 is HVF)(output2 is STOP) Rule2
If (input1 is Cool) and (input2 is PL) then (output1 is HF)(output2 is STOP)
Membership function for premise terms
Fig Membership function for Current Temperature is very cool.
Group two
Page 15
Fuzzy Room temperature control Membership function for Deviation Current Temperature is cool or positive large
Current Temperature e(t) is very cool member ship function E(t)=[8 12 16] Select e(t)=15.75 on the Deviation Current Temperature Ce(t )is very cool or positive large member ship function Ce(e)=[9 13.5 18]
Select Ce(t)=12.375
μ vc e(t)=0.0625 this value is the membership function at e(t)=15.75 on and the other membership functions for e(t) input are all zero(off). μ pl Ce(t)=0.75this value is the membership function at Ce(t)=12.375 on and the other membership functions for Ce(t) input are all zero(off). For “and” operator we use product rule for premise μ1premise=product of(μvce(t),μPL Ce(t)) product (0.0625, 0.75) =0.046875
Rule 2. If (input1 is C) and (input2 is PL) then (output1 is HF)(output2 is STOP)
Group two
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Fuzzy Room temperature control
Fig Membership function for Current Temperature is cool.
Fig Membership function for Deviation Current Temperature is very cool or positive large
Determine which rule is on from the given membership function of the above premise terms Current Temperature e(t) is cool member ship function E(t)=[15 19 23] Select e(t)=15.75 the Deviation Current Temperature Ce(t )is very cool or positive large member ship function Ce(e)=[9 13.5 18]
Group two
Page 17
Fuzzy Room temperature control Select Ce(t)=12.375
μ c e(t)=0.1875 this value is the membership function at e(t)=15.75on and the other membership functions for e(t) input are all zero(off). μ pl Ce(t)=0.75 this value is the membership function at Ce(t)=12.375 on and the other membership functions for Ce(t) input are all zero(off).
For “and” operator we use product rule for premise μ2premise=product of(μce(t),μPL Ce(t)) Product (0.1875 0.75) =0.140625
Implication Membership function for consequence terms
speed of heat-fan is very fast
Group two
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Fuzzy Room temperature control
speed of cool-fan is stop
we can divide rule 1 in to two i.e . If (input1 is VC) and (input2 is PL) then (output1 is HVF) If (input1 is VC) and (input2 is PL) then (output2 is STOP) For “implication” we use minimum operator The membership function for this consequent is μ1 μ1(heat-fan speed ) =minimum {μ1premise ,μv.fast(heat fan speed)} =minimum {0.046875,1} =0.046875
Figure speed of heat-fan output( consequent )membership function for rule (1) μ1(cool-fan speed ) =minimum {μ1premise,μstop(cool fan speed)} =minimum {0.046875,1} Group two
Page 19
Fuzzy Room temperature control =0.046875
Figure speed of cool-fan output( consequent )membership function for rule (1)
Membership function for consequence terms rule 2
speed of heat-fan is fast
speed of cool-fan is stop
Group two
Page 20
Fuzzy Room temperature control we can divide rule 2 in to two i.e Rule 2. If (input1 is C) and (input2 is PL) then (output1 is HF) If (input1 is C) and (input2 is PL) then (output2 is STOP)
For “implication” we use minimum operator The membership function for this consequent is μ2 μ2(heat-fan speed ) =minimum {μ2premise,μfast(heat fan speed)} =minimum {0.140625, 1} =0.140625
Figure speed of heat-fan output( consequent )membership function for rule (2)
μ2(cool-fan speed ) =minimum {μ2premise,μstop(cool fan speed)} =minimum {0.140625, 1} =0.140625
Figure speed of heat-fan output( consequent )membership function for rule (2) Group two
Page 21
Fuzzy Room temperature control
8 Aggregation Fuzzy Logic provides a number of functions for aggregating two or more fuzzy sets or fuzzy relations. When using the aggregation operations, the fuzzy sets or fuzzy relations being combined must be defined on the same universal space. It does not make sense to combine items defined on different universal spaces. In this project we use sum for aggregation for the implied fuzzy sets.
10 Deffuzification It the processes of converting output of inference mechanism into crisp value (numerical value) .It operate based on implied fuzzy set to provide the most certain controller output. There are two possible rules: 1 center of gravity (COG) 2 center average. For our calculation let us use center average as follow
Group two
Page 22
Fuzzy Room temperature control From the two rules b1= 87.5
b2=62.5
Ucrisp =
µpremise (1) =0.046875
µpremise (2) =0.140625 for the heater output.
(87.5*0.046875+62.5*0.140625)/(0.046875+0.140625) =67 for heater. b1=2.5 and b2=2.5 for the output of cooler. Ucrisp= (2.5*0.046875+2.5*0.140625)/(0.046875+0.140625) =2.5 for cooler
Group two
Page 23
Abstract: This project paper describes the design of a room temperature controller using fuzzy logic. The proposed model consists of fuzzy logic controllers to control temperature. The controller accepts two input values- the current temperature as detected by temperature sensor and its deviation from user set-temperature, and controls the speed of heat-fan and cool-fan accordingly. This research work will increase the capability of fuzzy logic control systems in process automation with potential benefits. MATLAB-simulation is used to achieve the designed goal.
1 Introduction This proposed design work of room temperature controller can be used in a processing plant to maintain comfortable atmosphere in the room the basic model of the proposed structure consists of room temperature controller with fuzzy logic control system. The room atmosphere controller has a heating fan, a cooling fan to heat or cool the room according to user demand; temperature sensors used to monitor the environment of room are mounted in the room and are connected with the fuzzifiers of the fuzzy logic control system. The fuzzy controller is composed of the following four elements: 1. A rule-base (a set of If-Then rules), which contains a fuzzy logic quantification of the expert’s linguistic description of how to achieve good control 2.An inference mechanism (also called an “inference engine” or “fuzzy inference” module), which emulates the expert’s decision making in interpreting and applying knowledge about how best to control the plant. Group two
Page 1
Fuzzy Room temperature control 3.A fuzzification interface, which converts controller inputs into information that the inference mechanism can easily use to activate and apply rules.
4.A defuzzification interface, which converts the conclusions of the inference mechanism into actual inputs for the process
Figure 1: Fuzzy controller
Group two
Page 2
Fuzzy Room temperature control
e(t) FLC
Heater fan
Y(t)
Plant
Cooler fan Ce(t)
Figure 2: Block diagram of temperature control by fuzzy
2 Determining linguistic variables for the system. Input Variables:1 Current Temperature (error) It is the current temperature of the room as recorded by the temperature sensor mounted in the room 2. Deviation From Set Temperature(change in error) It gives the difference between the user preferred temperature and current temperature of the room as recorded by the temperature sensor in the room Output Variables 1.Heat-Fan-Speed
Group two
Page 3
Fuzzy Room temperature control The heat fan can either be in ON or OFF state depending on the temperature preference in the room 2.Cool-Fan-Speed The cool fan can either be in ON or OFF state depending on the temperature preference in the room
3 Determine the linguistic values of the given linguistic variables
linguistic values for Current Temperature (error OR input 1) Linguistic values for Current Temperature are Very COOL(VC), COOL(C), NORMAL(N), HOT(H) and VERY-HOT(VH).
The sensor range should be wide enough to take care of climatic and regional fluctuations. The proposed model works perfectly at any temperature within range 8oC44oC
Table 1: Membership Functions For Current-Temperature MEMBERSHIP
RANGE (oC)
FUNCTIONS
Very COOL
8-16
COOL
15-23
NORMAL
22-30
HOT
29-37
VERY-HOT
36-44
linguistic values for Deviation Current Temperature (change in error OR input 2) Linguistic values for Deviation Current Temperature are negative large(NL), negative
small(NS), zero(Z), positive small(PS) and positive large(PL).
Group two
Page 4
Fuzzy Room temperature control As this model can work between temperature range 8-44’C and user can set any desired temperature from 18-26’C, so temperature difference between the current and the user preferred temperature can never go beyond -26’C (18’C – 44’C) and 18’C (26’C - 8’C). Thus (-26’C) & (+18’C) are the lower and upper limits of the input variable “ deviation from set-temperature”). Table 2: Membership Functions for “Deviation from current temperature” MEMBERSHIP
RANGE(oC)
FUNCTIONS
NL
-26 to -12
NS
-13 to 0
O
-2 to 2
PS
1 to 10
PL
9 to 18
linguistic values for Heat-Fan-Speed(out put 1)
The heta-fan-speed is categorized into 1. stop 2.heat-slow(hs) 3. heat-medium(hm) 4. heat-fast 5. very fast. If the current temperature of the room is below the desired temperature then this fan automatically gets on varies speed according to temperature difference.
Table 3:-Membership Functions For “heat-fan-speed”
Group two
Page 5
Fuzzy Room temperature control MEMBERS
RANGE %
HIP FUNCTION S STOP
0-5
HEAT-
0-30
SLOW HEAT-
25-50
MEDIUM
FAST
45-80
very-FAST
75-100
linguistic values for cool-Fan-Speed(out put 2)
The cool-fan-speed is categorized into 1. STOP 2.COOL-SLOW 3. COOL-MEDIUM 4. COOLFAST. If the current temperature of the room is above the desired temperature then this fan automatically gets on varies speed according to temperature difference. MEMBERSHIP
RANGE %
FUNCTIONS STOP
0-5
COOL-SLOW
0-30
COOL-MEDIUM
25-50
COOL-FAST
45-80
COOL-V.FAST
75-100
Form rule based on the input and output variables to control speed of heat fan and cool fan.
Group two
Page 6
Fuzzy Room temperature control
4 Rule generate Rules that relate input and output variables for fuzzy controllers:
1. If (input1 is VC) and (input2 is NL) then (output1 is STOP) and (output2 is STOP) 2. If (input1 is VC) and (input2 is NS) then (output1 is HS) and (output2 is STOP) 3. If (input1 is VC) and (input2 is ZERO) then (output1 is HM) and (output2 is STOP) 4. If (input1 is VC) and (input2 is PS) then (output1 is HF) and (output2 is STOP) 5. If (input1 is VC) and (input2 is PL) then (output1 is HVF) and (output2 is STOP) 6. If (input1 is C) and (input2 is NL) then (output1 is STOP) and (output2 is CS) 7. If (input1 is C) and (input2 is NS) then (output1 is STOP) and (output2 is STOP) 8. If (input1 is C) and (input2 is ZERO) then (output1 is HS) and (output2 is STOP) 9. If (input1 is C) and (input2 is PS) then (output1 is HM) and (output2 is STOP) 10. If (input1 is C) and (input2 is PL) then (output1 is HF) and (output2 is STOP) 11. If (input1 is N) and (input2 is NL) then (output1 is STOP) and (output2 is CF) 12. If (input1 is N) and (input2 is NS) then (output1 is STOP) and (output2 is CM) 13. If (input1 is N) and (input2 is ZERO) then (output1 is STOP) and (output2 is STOP) 14. If (input1 is N) and (input2 is PS) then (output1 is HM) and (output2 is STOP) 15. If (input1 is N) and (input2 is PL) then (output1 is HF) and (output2 is STOP)
Group two
Page 7
Fuzzy Room temperature control 16. If (input1 is H) and (input2 is NL) then (output1 is STOP) and (output2 is CVF) 17. If (input1 is H) and (input2 is NS) then (output1 is STOP) and (output2 is CF) 18. If (input1 is H) and (input2 is ZERO) then (output1 is STOP) and (output2 is CM) 19. If (input1 is H) and (input2 is PS) then (output1 is STOP) and (output2 is STOP) 20. If (input1 is H) and (input2 is PL) then (output1 is HS) and (output2 is STOP) 21. If (input1 is VH) and (input2 is NL) then (output1 is STOP) and (output2 is CVF) 22. If (input1 is VH) and (input2 is NS) then (output1 is STOP) and (output2 is CF) 23. If (input1 is VH) and (input2 is ZERO) then (output1 is STOP) and (output2 is CM) 24. If (input1 is VH) and (input2 is PS) then (output1 is STOP) and (output2 is CS) 25. If (input1 is VH) and (input2 is PL) then (output1 is STOP) and (output2 is STOP) NB Input 1=current temperature Input 2= Deviation From Set Temperature Output 1= Heat-Fan-speed Output 2= cool-Fan-speed
Group two
Page 8
Fuzzy Room temperature control
5 Member ship function
Membership function of Current Temperature (error)
Where VC=very cool temperature C= cool temperature N= normal temperature H=hot temperature VH=very hot temperature
Group two
Page 9
Fuzzy Room temperature control
Membership function for Deviation Current Temperature (change in error)
Where NL=the Deviation Current Temperature is very hot or negative large NS=the Deviation Current Temperature hot or negative small Zero=the Deviation Current Temperature is normal or zero PS= the Deviation Current Temperature is cool or positive small Group two
Page 10
Fuzzy Room temperature control PL= the Deviation Current Temperature is very cool or positive large
Membership function for Heat-Fan-Speed
Where Group two
Page 11
Fuzzy Room temperature control Stop=the speed of heat-fan is stop HS= the speed of heat-fan is slow HM= the speed of heat-fan is medium HF= the speed of heat-fan is fast HVF fast= the speed of heat-fan is very
Membership function for cool-Fan-Speed
Where
Stop=the speed of cool-fan is stop CS= the speed of cool-fan is slow CM= the speed of cool-fan is medium Group two
Page 12
Fuzzy Room temperature control CF= the speed of cool-fan is fast CVF= the speed of cool-fan is very fast
6 Fuzzy quantification of knowledge Give a specific crisp values (numerical values) for the inputs and determine the recommended output value .use the following operations: Membership function: symmetrical triangle AND operation: product Implication: minimum Aggregation: sum Defuzzification method: center average To find the crisp value first determines one appropriate rule from 25 rules. A crisp set of input data are gathered and converted to a fuzzy set using fuzzy linguistic variables. The rule selected for inference process is:
7 Determining Which Rules Are On: Determining the applicability of each rule is called “matching.”
We say that a rule is “on
at time t” if its premise membership function μ𝒑𝒓𝒆𝒎𝒊𝒔(e(t), 𝑑𝑒(𝑡)𝑑𝑡) > 0. Hence, the inference mechanism seeks to determine which rules are on to find out which rules are relevant to the current situation. compute the rules that are on. Suppose that: e(t) = 15.75 and de(t)dt= 12.375
Figure shows the membership functions for the inputs and indicates with thick black vertical lines the values above for e(t) and de(t)dt.
Group two
Page 13
Fuzzy Room temperature control
Notice that μvcool(e(t)) = 0.0625 and μcool(e(t)) = 0.1875 but that the other membership functions for the e(t) input are all “off” (i.e., their values are zero). For the 𝑑(𝑡)𝑑𝑡 input we see that μ𝒑𝒐𝒔large (𝑑𝑒(𝑡)𝑑𝑡) = 0.75 and that all the other membership functions are off.
This implies that rules that have the premise terms: “error is very cool” “error is cool” Group two
Page 14
Fuzzy Room temperature control “change-in-error is poslarge” are on (all other rules have μ𝒑𝒓𝒆𝒎𝒊𝒔𝒆 (e(t), 𝑑𝑒(𝑡)𝑑𝑡) = 0.
the rules that are on are the following:
Rule 1 If (input1 is VCool) and (input2 is PL) then (output1 is HVF)(output2 is STOP) Rule2
If (input1 is Cool) and (input2 is PL) then (output1 is HF)(output2 is STOP)
Membership function for premise terms
Fig Membership function for Current Temperature is very cool.
Group two
Page 15
Fuzzy Room temperature control Membership function for Deviation Current Temperature is cool or positive large
Current Temperature e(t) is very cool member ship function E(t)=[8 12 16] Select e(t)=15.75 on the Deviation Current Temperature Ce(t )is very cool or positive large member ship function Ce(e)=[9 13.5 18]
Select Ce(t)=12.375
μ vc e(t)=0.0625 this value is the membership function at e(t)=15.75 on and the other membership functions for e(t) input are all zero(off). μ pl Ce(t)=0.75this value is the membership function at Ce(t)=12.375 on and the other membership functions for Ce(t) input are all zero(off). For “and” operator we use product rule for premise μ1premise=product of(μvce(t),μPL Ce(t)) product (0.0625, 0.75) =0.046875
Rule 2. If (input1 is C) and (input2 is PL) then (output1 is HF)(output2 is STOP)
Group two
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Fuzzy Room temperature control
Fig Membership function for Current Temperature is cool.
Fig Membership function for Deviation Current Temperature is very cool or positive large
Determine which rule is on from the given membership function of the above premise terms Current Temperature e(t) is cool member ship function E(t)=[15 19 23] Select e(t)=15.75 the Deviation Current Temperature Ce(t )is very cool or positive large member ship function Ce(e)=[9 13.5 18]
Group two
Page 17
Fuzzy Room temperature control Select Ce(t)=12.375
μ c e(t)=0.1875 this value is the membership function at e(t)=15.75on and the other membership functions for e(t) input are all zero(off). μ pl Ce(t)=0.75 this value is the membership function at Ce(t)=12.375 on and the other membership functions for Ce(t) input are all zero(off).
For “and” operator we use product rule for premise μ2premise=product of(μce(t),μPL Ce(t)) Product (0.1875 0.75) =0.140625
Implication Membership function for consequence terms
speed of heat-fan is very fast
Group two
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Fuzzy Room temperature control
speed of cool-fan is stop
we can divide rule 1 in to two i.e . If (input1 is VC) and (input2 is PL) then (output1 is HVF) If (input1 is VC) and (input2 is PL) then (output2 is STOP) For “implication” we use minimum operator The membership function for this consequent is μ1 μ1(heat-fan speed ) =minimum {μ1premise ,μv.fast(heat fan speed)} =minimum {0.046875,1} =0.046875
Figure speed of heat-fan output( consequent )membership function for rule (1) μ1(cool-fan speed ) =minimum {μ1premise,μstop(cool fan speed)} =minimum {0.046875,1} Group two
Page 19
Fuzzy Room temperature control =0.046875
Figure speed of cool-fan output( consequent )membership function for rule (1)
Membership function for consequence terms rule 2
speed of heat-fan is fast
speed of cool-fan is stop
Group two
Page 20
Fuzzy Room temperature control we can divide rule 2 in to two i.e Rule 2. If (input1 is C) and (input2 is PL) then (output1 is HF) If (input1 is C) and (input2 is PL) then (output2 is STOP)
For “implication” we use minimum operator The membership function for this consequent is μ2 μ2(heat-fan speed ) =minimum {μ2premise,μfast(heat fan speed)} =minimum {0.140625, 1} =0.140625
Figure speed of heat-fan output( consequent )membership function for rule (2)
μ2(cool-fan speed ) =minimum {μ2premise,μstop(cool fan speed)} =minimum {0.140625, 1} =0.140625
Figure speed of heat-fan output( consequent )membership function for rule (2) Group two
Page 21
Fuzzy Room temperature control
8 Aggregation Fuzzy Logic provides a number of functions for aggregating two or more fuzzy sets or fuzzy relations. When using the aggregation operations, the fuzzy sets or fuzzy relations being combined must be defined on the same universal space. It does not make sense to combine items defined on different universal spaces. In this project we use sum for aggregation for the implied fuzzy sets.
10 Deffuzification It the processes of converting output of inference mechanism into crisp value (numerical value) .It operate based on implied fuzzy set to provide the most certain controller output. There are two possible rules: 1 center of gravity (COG) 2 center average. For our calculation let us use center average as follow
Group two
Page 22
Fuzzy Room temperature control From the two rules b1= 87.5
b2=62.5
Ucrisp =
µpremise (1) =0.046875
µpremise (2) =0.140625 for the heater output.
(87.5*0.046875+62.5*0.140625)/(0.046875+0.140625) =67 for heater. b1=2.5 and b2=2.5 for the output of cooler. Ucrisp= (2.5*0.046875+2.5*0.140625)/(0.046875+0.140625) =2.5 for cooler
Group two
Page 23
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