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AN APPROACH ON FUZZY CONTROL FOR A CONDITIONING AIR 

Bucuci Stefania

Constanta Maritime University

Abstract

This paper outlines the study of a fuzzy logic controlled air-conditioner. Ambient

conditions that influence the perception of temperature serve as inputs parameters to the

thermostat and the output is automated and put into effect in temperature adjustment.

One of the most outstanding reasons for the use of fuzzy logic air-conditioners is

energy save and human comfort. Fuzzy logic is especially promising as it provides a

comfortable environment together with energy save.

1. IntroductionThe concept of fuzzy logic was conceived by Lotfi Zadeh, a professor at the

University of California at Berkley, and presented not as a control methodology, but as a way

of processing data by allowing partial set membership rather than crisp set membership or 

non-membership.

He claimed that many sets in the world that surrounds us are defined by a non-distinct

 boundary. Indeed, the set of high mountains, or, the set of low level measurements are

examples of such sets. Zadeh, the father of fuzzy logic, decided to extend two-valued logic,defined by the binary pair {0,1} to the whole continuous interval [0,1] thereby introducing a

gradual transition from falsehood to truth. Primary references can be found conveniently in a

 book with 18 selected papers by himself. (1)

With the widespread use of fuzzy-logic based control systems, air-conditioning has

also been included into the scope of its implementation. Air-conditioning studies are usually

carried out for greenhouses. These studies can be abundantly found in the literature. See

references (2), (3), and (4) for examples. In addition to these, fuzzy air-conditioning control

can as well be implemented in living environment, especially in houses and offices. These

systems are called as HVAC (Heating, Ventilation, and Air conditioning) systems. (5)

Keeping consumers of home cooling appliances like air conditioners at comfortable

temperatures over long periods of time has been difficult to achieve.Fuzzy logic is able to achieve control using elements of everyday human language.

Factors that bring about the need for temperature adjustment are incorporated into the

electronic thermostat model so that adjustment is automated with the objective of reducing

energy loss in home air conditioners and adding great functionality to their control systems

 based on human perception and reasoning. (6)

Fuzzy controllers are very simple conceptually. They consist of an input stage, a

 processing stage, and an output stage. The input stage maps sensor or other inputs, to the

appropriate membership functions and truth values. The processing stage invokes each

appropriate rule and generates a result for each, then combines the results of the rules.

Finally, the output stage converts the combined result back into a specific control output

value.

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The most common shape of membership functions is triangular, although trapezoidal

and bell curves are also used, but the shape is generally less important than the number of 

curves and their placement. From three to seven curves are generally appropriate to cover the

required range of an input value, or the "universe of discourse" in fuzzy jargon. There are

several different ways to define the result of a rule. The results of all the rules that have fired

are "defuzzified" to a crisp value by one of several methods.

2. Problem formulationThe problem I propose is the study of a fuzzy logic controlled air-conditioner.

Ambient conditions that influence the perception of temperature serve as inputs parameters to

the thermostat and the output is automated and put into effect in temperature adjustment.

Input parameters are:

ΔT temperature difference between ambient temperature and controlled

temperature

VΔt speed of ambient temperature variation.

As output parameter, I choose:

C electrical installation command coefficientAutomatic decision of the controller is based on a set of 9 rules and the relationship

 between the inputs and outputs.

3. Problem solution3.1. Notations used 

Input parameters: ΔT = Tamb – Tctrl

(1.1)

t

TV

t

∆

∆=

∆

(1.2)

where: ΔT is the temperature difference between ambient temperature and

controlled temperature;

Tamb is the ambient temperature;

Tctrl is the controlled temperature;

VΔt is the speed of ambient temperature variation;

Δt is the temperature variation period.

The "universe of discourse" associated with parameter ΔT is defined in three language

expressions as: {negative, neutral, positive} and the "universe of discourse" associated with

 parameter VΔt is also defined in three language expressions as: {high, medium, null}.

Output parameters: C which is the electrical installation command coefficient.

The "universe of discourse" associated with parameter C is defined in five languageexpressions as:{ rapid heating, normal heating, stationary situation, normal cooling, fast

cooling}.

3.2. Membership functions

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Figure 1.1. Membership functions of parameter ΔT

Figure 1.2. Membership functions of 

 parameter VΔt

Figure 1.3. Membership functions for points

C

3.3. The set of fuzzy rulesThe set of fuzzy rules for this example contains 9 rules designed as shown below:

Rule 1 If  the temperature difference between ambient temperature and controlled

temperature is negative and the speed of ambient temperature variation is null then the

electrical installation command coefficient must ensure rapid heating;

Rule 2 If  the temperature difference between ambient temperature and controlled

temperature is negative and the speed of ambient temperature variation is medium then

the electrical installation command coefficient must ensure heating;

Rule 3 If  the temperature difference between ambient temperature and controlled

temperature is negative and the speed of ambient temperature variation is high then the

electrical installation command coefficient must ensure stationary situation;The other 6 rules are composed after the same pattern as the first 3 rules.

4. Case studyTo ilustrate the above procedure we will study the following example:

Assuming the ambient temperature is 300C and the controlled temperature is 230C

find how the fuzzy controller works.

4.1. Estimation of the level of membership of parameter ΔT 

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Figure 1.4. Calculation of the membership

level of parameter ΔT

The details gets:

Figure 1.5. Calculus of By

• Straight line equation passing trough points (x1=5 ; y1=0) and (x2=2 ; y2=1):

12

1

12

1

yy

yy

xx

xx

−

−=−

− 

(1.3)

Replacing, we obtain:01

0y

52

5x

−

−=

−

−

(1.4) or 3

5x

3

1y +−=

(1.5)

• Straight line equation passing trough point (x1=4; y1=0) which is parallel to the axis of 

ordinates: 4x =(1.6)

• Calculation of By:

=

+−=

4x 3

5x

3

1y

(1.7), we obtain: By = y = 0.33

(1.8)

• Similarly, for Ay we obtain: Ay=0.67

(1.9)

Conclusion: Membreship coefficients of parameter ΔT are:

T1 = 0.00 (negative variation membership level)

T2 = 0.33 (neutral variation membership level)

T3 = 0.67 (positive variation membership level)

4.2. Estimation of the level of membership of parameter V  Δt 

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Figure 1.6. Calculation of the membership

level of parameter VΔt

The details gets:

Figure 1.7. Calculus of Ay for VΔt

• Straight line equation passing trough points (x1=6 ; y1=0) and (x2=9 ; y2=1):

12

1

12

1

yy

yy

xx

xx

−

−=

−

−(1.10)

Replacing, we obtain:01

0y

69

6x

−

−=

−

−

(1.11) or  2x3

1y −=  

(1.12)

• Straight line equation passing trough point (x1=0.52; y1=0) which is parallel to the

axis of ordinates: 7x =  

(1.13)

• Calculation of Ay:

=

−=

7x

2x3

1y

(1.14), we obtain: Ay = 0.33

(1.15)

• Similarly, for By we obtain: By = 0.67

(1.16)

Conclusion: Membreship coefficients of parameter VΔt are:

T1 = 0.00 (null variation membership level)

T2 = 0.33 (medium variation membership level)

T3 = 0.67 (high variation membership level)

4.3. The " center -average" method for defuzzification

C1 ) Rapid heating Rule 1

(If 0.00 and 0.00) = 0.00

−=

=

0 .x

0 . 0μ

1

1C

C2) Heating Rule 2

(If 0.00 and 0.33) = 0.00

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−=

=

0 .x

0 .μ

2

2C

C3) Stationary situation Rule 3 OR Rule 4 OR Rule 5

(If 0.00 and 0.67) OR (If 0.33 and 0.00) OR (If 0.33 and 0.33) =

= 0.00 OR  0.00 OR  0.33 = 0.33

=

=

0 . 0x

0 .μ

3

3C

C4) Cooling Rule 6 OR Rule 8 OR Rule 9

(If 0.33 and 0.67) OR  (If 0.67 and 0.33) OR (If 0.67 and 0.67) == 0.33 OR 0.33 OR 0.67 = 0.67

=

=

0 . 3x

0 .μ

4

4C

C5) Rapid cooling Rule 7

(If 0.67 and 0.00) = 0.00

=

=

0 . 6x

0 .μ

5

5C

Figure 8. Center - average

54321

5544332211

Cμμμμμ

μxμxμxμxμxx

++++

×+×+×+×+×=

0.220.000.670.330.000.00

0.000.670.330.6700.330.000.330.000.67x

C=

++++

×+×+×+×+×=

5. References

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(1.) R.R. Yager et al. (John Wiley, New York, 1987), "Fuzzy Sets and Applications:

Selected Papers by L.A. Zadeh".

(2.) Occhipinti, L, Nunnari, G, “Synthesis of a greenhouse climate controller using AI-

 based techniques” Electrotechnical Conference, 1996. MELECON '96, 8th Mediterranean

Volume 1, 13-16, vol. 1, pp230 – 233, 1996.

(3.) Caponetto, R, Fortuna, L, Nunnari, G, Occhipinti, L, “A fuzzy approach togreenhouse climate control” American Control Conference, Proceedings of the 1998,

vol.3, pp.1866- 1870, 1998.

(4.) Pan Lanfang, Wang Wanliang, Wu Qidi, “Application of adaptive fuzzy logic system

to model for greenhouse climate” Intelligent Control and Automation, Proceedings of the

3rd World Congress on vol. 3, pp.1687-1691, 2000.

(5.) Kuntze, H.-B, Bernard, Th, “A new fuzzy-based supervisory control concept for the

demand-responsive optimization of HVAC control systems” Decision and Control,

Proceedings of the 37th IEEE Conference on, vol. 4, pp. 4258-4263, 1998.

(6.) Mu’Azu, Muhammed Bashir, Bozimo Tare, “Design and simulation of an intelligent

fuzzy logic controlled electronic thermostat (a research proposal)”.