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INTERNATIONAL JOURNALINFORMATION AND SYSTEMS SCIENCVolume 1, Number 1, Pages 1-2

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INTERNATIONAL JOURNAL OF INFORMATION AND SYSTEMS SCIENCES Volume 3, Number 1, Pages 88-115

©2007 Institute for Scientific Computing and Information

FUZZY MODELING AND IDENTIFICATION OF VAPOR COMPRESSION ELEMENTS OF AIF CONDITIONING SYSTEM FOR INTEGRATED

FUZZY MODEL

JAGDEV SINGH. NIRMAL SINGH AND J. K. SHARMA

Abstract Conventional control techniques are not able to accomplish the stable cooling in vapor compression air conditioning system. This paper describes the fuzzy models of refrigerating compressor, expansion valve, evaporator and condenser as basic elements of vapor compression air conditioning system. Compressor speed, delivery pressure, refrigerant flow rate, valve opening area, pressure difference across the orifice of expansion valve, evaporator temperature, condenser temperature, evaporator superheat and condenser superheat have been taken as different variables for vapor compression elements. Fuzzy model of all the elements has been compared with their respective mathematical models for their validation. Integrated fuzzy model was also developed for vapor compression air conditioning system. Performance was evaluated by comparing, integrated fuzzy model, individual fuzzy model and mathematical model for the vapor compression systems. Fuzzy models were developed using adaptive neuro-fuzzy inference system (ANFIS). R-134a has been used as refrigerant in the vapor compression cycle. Key Words, Vapor compression elements, Individual fuzzy model, Integrated fuzzy model, R-134a, ANFIS, Sugeno fuzzy inference system

1. Introduction Vapor compression cycle is widely used for industrial and residential applications, such as refrigeration and air conditioning systems. Modelling, control and diagnostics of vapour compression cycle has been active research subjects for years for improving its performance. Though vapour compression cycles has already been investigated with different modelling techniques, but fuzzy techniques as indicated by Jim Hindmon (1998) are very new for vapour compression cycle in refrigeration and air conditioning controls. Modeling and control techniques based on fuzzy sets attempt to combine numerical and symbolic processing into one framework. On the one hand, fuzzy systems are knowledge-based systems consisting of linguistic if-then rules that can be constructed using the knowledge of experts in the given field of interest. On the other hand, fuzzy systems are also universal approximators that can realize nonlinear mappings. This duality allows qualitative knowledge to be combined with quantitative data in a complementary way. Compared to other nonlinear approximation techniques, fuzzy systems provide a more transparent representation of the nonlinear system under study, and can also be given a linguistic interpretation in the form of rules. In this way, process data can be translated in a model and analyzed in a manner very similar to what people

Received by the editors July 11, 2006 88

FUZZY MODELING AND IDENTIFICATION 89

are acquainted with. The rules extracted from data can be validated by experts, and combined with their prior knowledge to obtain a complete system model describing the reality over the entire domain of interest.

Very little work has been done in the area of vapor compression air conditioning system using fuzzy techniques. However, Altrock (1996, 1997) worked for the design of fuzzy controller for replacing conventional thermostat by fuzzy logic thermostat. This design which find applications in automobile engineering, has lead to an energy saving and comfort level was enhanced. Mraz (2001) presented one of the alternatives for a fast transition from classical thermostatic control to digital control of the refrigerating compressor on the basis of a fuzzy controller. Liu et al (2004) worked for the improvement of the refrigerant flow control method by using an electronic expansion valve (EEV) and employing the fuzzy self-tuning proportional integral–derivative (PID) control method. Experimental results show that the new control method can feed adequate refrigerant flow into the evaporator in various operations. The evaporator discharge air temperature has dropped to low value as compared with that of the conventional PID control system. Wu et al (2004) also worked on the control of EEV with fuzzy techniques using dynamic model of multi-evaporator air conditioners. Yang & Huang (1998) raised the concept of dual fuzzy controller, first to control the stroke and other to control phase of a linear compressor. Thermal performance of refrigeration compressor has also been predicted by fuzzy techniques. The simple fuzzy model and the compound fuzzy model, which comprises the theoretical model, are studied and compared. Case study by D.Guoliang et al (2000) shows that fuzzy method can produce better effect than the classical thermodynamic method. Aprea et al (2004) studied fuzzy compressor of vapor compression refrigeration plant in the environment of cold store, and observed that significant energy saving on an average has been obtained using the compressor speed control algorithm based on the fuzzy logic. Wu et al (2004), studied that grip of the fuzzy control on the compressor is far better. A self-tuning fuzzy control algorithm with a modifying factor was incorporated in the controller for compressor speed and electronic expansion valves regulation. A controllability test was conducted with a thermodynamic model developed with a special modeling methodology, showed that the control strategy and algorithm are feasible and can achieve desirable control results.

Environment friendly refrigerant R134a has been taken for present study. G. Boccardi

et al (2000) pointed out that it has more marked dependency for saturation temperature-pressure as compared to other refrigerants. An uncertainty in the pressure values bring to bigger discrepancy between the real and calculated values of the saturation temperature of this refrigerant. Therefore even small deviation from the constant pressure within the channel causes uncertainty in the saturation temperature for R134a. For the better control and improved performance with this refrigerant in vapor compression air conditioning systems fuzzy techniques are right choice.

In this paper all the individual fuzzy models of four elements of vapor compression

system for air conditioning are developed and results are validated with standard mathematical models. Four elements taken are refrigerating compressor, expansion valve, and evaporator along with refrigerating condenser. Then an integrated fuzzy model for vapor compression air conditioning system is developed and compared with individual

90 J. SINGH. N. SINGH AND J. SHARMA

fuzzy models and mathematical models to simulate its performance.

2 Vapor compression cycle Vapor compression cycle is mainly comprised of evaporator, condenser, expansion

valve and compressor. Compressor, compresses low-pressure vapor refrigerant into high pressure such that high-pressure refrigerant can condense in a condenser to reject the heat to the second fluid (Fig.1) The entire system is filled with a refrigerant R-134a and only its thermodynamic features are changing.

Fig.1 Vapor compression system and its representation on p-h chart

The rate of refrigerant flow has effect on both the performance and the life of

refrigeration system. Over feeding of refrigerant and insufficient refrigerant in the system, will result in poor performance. So it is very important to the study the coordination among various parameters of vapor compression system for optimum performance.

3 Modeling of vapor compression system based on ANFIS

The modeling of the different elements of vapor compression system has been done using adaptive neuro fuzzy inference system (ANFIS). This technique provides procedure to learn information about a data set, in order to compute the membership function parameters that best allow the associated fuzzy inference system to track the given input/output data. Element wise vapor compression air conditioning systems is fuzzy modeled as given below.

3.1 Refrigerating compressor model

In this model, compressor speed and delivery pressure are taken as input parameters and mass flow rate is considered as output parameter. Developed fuzzy model receives the input signal and generates the output signal to control the mass flow rate from the compressor. The performance of the model is evaluated by comparing the predicted results with the standard mathematical model. 3.1.1 Fuzzy model of compressor

The fuzzy modeling of refrigerating compressor has been done using Adaptive Neuro Fuzzy Inference System (ANFIS) by considering the input parameters; compressor speed


(CS) and delivery pressure (DP) and output as mass flow rate (MFR). These parameters appear to be more promising to regulate mass flow rate in vapor compression system. Fig.2 shows fuzzy model of refrigerating compressor system. Fig, 3, Fig.4 shows various membership functions of CS and DP for the model. Fig.5 indicates the output membership function of MFR of the model. Here the model makes use of nine rules. Set of linguistic rules for fuzzy model are given below:-

(i) If CS is in1mf1 and DP is in2mf1 then MFR is in out1mf1.(ii)If CS is in1mf1 and DP is in2mf2 then MFR is in out1mf2(iii) If CS is in1mf1 and DP is in2mf3 then MFR is in out1mf3.(iv) If CS is in1mf2 and DP is in2mf1 then MFR is in out1mf4(v) If CS is in1mf2 and DP is in2mf2 then MFR is in out1mf5.(vi) If CS is in1mf2 and DP is in2mf3 then MFR is in out1mf6(vii) If CS is in1mf3 and DP is in2mf1 then MFR is in out1mf7(viii) If CS is in1mf3 and DP is in2mf2 then MFR is in out1mf8.(ix) If CS is in1mf3 and DP is in2mf3 then MFR is in out1mf9.

Fig. 2 Fuzzy model of compressor

Fig. 3 Input membership functions (CS)

Fig. 4 Input membership functions (DP)

Fig. 5 Output membership functions (MFR)


Fig. 6 Rule viewers of compressor fuzzy model

Fig. 6 indicates rule viewers that shows value of the various inputs to the model and computed outputs. The mass flow rate (output) can be predicted by varying the input parameters compressor speed CS and delivery pressure DP to the developed fuzzy model. For a particular instance, set of input values given to the model are 532 rpm for compressor speed and 9.03 bar for delivery pressure. The output generated by the model; mass flow rate MFR is 0.047 kg/sec. Similarly by giving the different input values to the model within the universe of discourse UOD 100– 1500 rpm for CS and 6 – 16 bar for DP, output MFR can be generated from this fuzzy model. Outputs generated are as depicted as in Fig 7.This figure is depicting the trend of mass flow rate with change in compressor speed at constant delivery pressure. For different DP different curves are shown. 3.1.2 Mathematical model of compressor

Generally, the mass flow rate is dependent on compression ratio, compressor speed and density of the refrigerants. The compressor speed was taken into consideration in the model. The equation for the mass flow rate in compressor is taken from the paper of Shiming et al (2000) as below:

Mass flow rate = d* V * N* E . . . (1)

Where, d = density of refrigerant at compressor entry, V = swept volume, N =

compressor speed and E = volumetric efficiency and it depends on suction and discharge pressures. The influence of the compressor speed on the variations in volumetric efficiency was neglected.

E =0.850565 – 0.024084 (P2/P1) . . . (2)

Where, P2 = delivery pressure, P1 = suction pressure. The evaporator model does not give the superheated refrigerant vapor density d’ at

compressor entry, but the following empirical equation is assumed:


d = d’ – C (Toe - Tie) . . . (3)

Where, d’ = density of liquid refrigerant at evaporator entry, Tie = temperature at

evaporator entry, Toe = temperature at evaporator exit, C is a coefficient relating to the evaporating pressure as:

C = - 0.0246 + 0.0259 P1 . . . (4)

Degree of superheat on evaporator side and specific volume at entry of evaporator is

assumed to be fixed at 5o C and 0.04699 m3/kg in the model for refrigerant R-134a respectively. Swept volume of the compressor is also fixed at 0.0004m3. Suction pressure is kept at one bar through out the investigations. The refrigerant mass flow rate at compressor outlet is assumed to be equal to that at its inlet. The equations from 1-4 have been analyzed through a MATLAB programme. Results achieved from this mathematical model are shown in Fig.8.

Fig.7 Compressor speed versus mass flow rate at different delivery pressure from fuzzy model

Fig.8 Compressor speed versus mass flow rate at different delivery pressures from mathematical model

3.2 Expansion valve model 3.2.1 Fuzzy model of expansion valve

For the expansion valve-opening trend depending upon differential pressure across it (delP) and refrigerant mass flow rate MFR a fuzzy model using ANFIS has been developed here. Differential pressures (delP) are in the range of 3 – 7 bar and mass flow rate is up to 0.15 kg /sec. Here mass flow rate MFR and pressure difference across the orifice delP are taken as input parameters and valve opening area as output. Similar type of fuzzy model as given in previous section (Fig.2-5) has also been developed for expansion valve. But various membership functions for mass flow rate and delP which are triangular in shape are partitioned depending upon the linguistic levels within the given ranges of expansion valve. Then a set of rules has been designed for proper control


of valve opening area as given below: (i) If Mass Flow Rate is in 1mf1 and delP is 2mf1 then Valve Opening Area is out1mf1.

(ii) If Mass Flow Rate is in 1mf1 and delP is 2mf2 then Valve Opening Area is out1mf2 (iii) If Mass Flow Rate is in 1mf1 and delP is 2mf3 then Valve Opening Area is out1mf3.(iv) If Mass Flow Rate is in 1mf2 and delP is 2mf1 then Valve Opening Area is out1mf4.(v) If Mass Flow Rate is in 1mf2 and delP is 2mf2 then Valve Opening Area is out1mf5.(vi) If Mass Flow Rate is in 1mf2 and delP is 2mf3 then Valve Opening Area is out1mf6.(vii) If Mass Flow Rate is in 1mf3 and delP is 2mf1 then Valve Opening Area is out1mf7.(viii) If Mass Flow Rate is in 1mf3 and delP is 2mf2 then Valve Opening Area is out1mf8.(ix) If Mass Flow Rate is in 1mf3 and delP is 2mf3 then Valve Opening Area is out1mf9

These rules were implemented in MATLAB environment using sugeno type of fuzzy

inference Fig.9 indicates rule viewers which shows that Valve Opening Area (output) can be predicted by varying the input parameters from developed fuzzy model. This Fig shows a particular case that when input values given to the model are 0.08 kg/sec for mass flow rate and 5 bar for delP then output generated by the model is 0.382 cm2.

Fig.9 Rule viewer of expansion valve fuzzy model

Similarly by giving other input values to the model within the UOD 0.1 to 0.15 kg/sec for mass flow rate and 3 bar to 7 bar for delP, output MFR can be generated from fuzzy model of expansion valve. Outputs generated from this model are as depicted in Fig 10.

3.2.2 Mathematical model of expansion valve system

Liquid refrigerant flowing through an expansion valve can be modeled as given by X He et al (1995) as the following orifice equation:

m = CvAv[dvdelP]1/ 2

Where m = Mass Flow Rate of refrigerant through the expansion valve, Cv = Orifice coefficient Av =Valve opening area, dv = the density of the refrigerant, delP = Pressure


across the orifice After working on this relation a programme was developed in MATLAB. Variations of

mass flow rate, valve opening area and delP from the model was obtained as shown in Fig.11.

Fig.10 delP versus valve opening area from fuzzy model

Fig.11 delP versus valve opening area from mathematical model

3.3 Evaporator model 3.3.1 Fuzzy Model of Evaporator Superheat

Mass flow rate MFR and evaporator temperature have been taken as input parameters and superheat as output. Fuzzy model has been developed to predict the mass flow rate and evaporator temperatures within user defined limits in order to regulate the superheat of the system for minimum energy consumption. As done in section 3.1.1 partitioning of membership functions for input variables has been done depending upon the linguistic levels. These levels have been designed within universe of discourse 0.04-0.14 kg/sec for mass flow rate and -15 0C to 150C for evaporator temperature. Triangular membership functions have been selected for different linguistic levels. In this model nine linguistic rules are employed .Set of linguistic rules for this fuzzy model are given below:

(i)If Evaporator Temperature is in 1mf1 and Mass Flow Rate is in 2mf1 then Superheat is out1mf1

(ii)If Evaporator Temperature is in 1mf1 and Mass Flow Rate is in 2mf2 then Superheat is out1mf2

(iii)If Evaporator Temperature is in 1mf1 and Mass Flow Rate is in 2mf3 then Superheat is out1mf3

(iv)If Evaporator Temperature is in 1mf2 and Mass Flow Rate is in 2mf1 then Superheat is out1mf4

(v)If Evaporator Temperature is in 1mf2 and Mass Flow Rate is in 2mf2 then Superheat is out1mf5

(vi)If Evaporator Temperature is in 1mf2 and Mass Flow Rate is in 2mf3 then Superheat is out1mf6

(vii)If Evaporator Temperature is in 1mf3 and Mass Flow Rate is in 2mf1 then Superheat is out1mf7


(viii)If Evaporator Temperature is in 1mf3 and Mass Flow Rate is in 2mf2 then Superheat is out1mf8

(ix)If Evaporator Temperature is in 1mf3 and Mass Flow Rate is in 2mf3 then Superheat is out1mf9

These rules were implemented in MATLAB environment using Sugeno type of fuzzy inference

Fig.12 Rule viewer of evaporator superheat fuzzy model

Fig, 12 indicates rule viewers that show different values of mass flow rate and evaporator temperature as inputs to the developed fuzzy model. This model computes outputs of superheat at evaporator exit. Rule viewer is showing the output for one set of inputs i.e. for evaporator temperature 00C and Mass Flow Rate 0.09 kg/sec superheat generated by the fuzzy model is 2.130C. Predicted outputs of superheat for different inputs to the fuzzy model in its respective UOD have been reflected in Fig.13.

3.3.2 Mathematical Model of Evaporator Superheat

Here the output variable to be monitored is superheat SH, while mass flow rate and evaporator temperature Te were used as the control inputs to the system. The superheat as given by X He et al (1998) is expressed as follows:

Where, SH = Superheat, Tae= Ambient air temperature, Tre= Refrigerant temperature

in evaporator, Die= Inner diameter of evaporator tube, Le=Length of heat exchanger tube in evaporator, le=length of two phase section in evaporator, Cp=Constant pressure specific heat, mcom=Mass flow rate


Fig.13 Evaporator temperature versus evaporator superheat from fuzzy model

Fig.14 Evaporator temperature versus evaporator superheat from mathematical model

Where αioe is the equivalent heat transfer coefficient between the refrigerant and the

ambient air at the superheated section. Above mathematical model has been investigated through MATLAB programme. Fig.14 shows a graphical representation of parameters, evaporator temperature; mass flow rate and evaporator superheat.

3.4 Condenser Model 3.4.1 Fuzzy Model of Condenser Superheat

Fuzzy model of two input variables; mass flow rate, and condensing temperature, one output variable; condenser superheat have been developed within the selected universe of discourse for condenser model. Input variable of Mass Flow Rate varies in the range 0.04 -0.14 kg/sec and other variable condenser temperature range is 150C- 450C.Membership function selected for these variables are triangular in shape. After designing the linguistic levels for input variables within the selected range a rule base has been developed for the appropriate control of input parameters in order a achieve minimum condenser superheat. Formulated set of rules of the model are outlined below:

(i) If Mass Flow Rate is in 1mf1 and Condenser Temperature is 2mf1 then Condenser Superheat is out1mf1 (ii) If Mass Flow Rate is in 1mf1 and Condenser Temperature is 2mf2 then Condenser Superheat is out1mf2 (iii) If Mass Flow Rate is in 1mf1 and Condenser Temperature is 2mf3 then Condenser Superheat is out1mf3 (iv) If Mass Flow Rate is in 1mf2 and Condenser Temperature is 2mf1 then Condenser Superheat is out1mf4 (v)If Mass Flow Rate is in 1mf2 and Condenser Temperature is 2mf2 then Condenser Superheat is out1mf5(vi)If Mass Flow Rate is in 1mf2 and Condenser Temperature is 2mf3 then Condenser Superheat is out1mf6 (vii)If Mass Flow Rate is in 1mf3 and Condenser Temperature is 2mf1 then Condenser Superheat is out1mf7 (viii)If Mass Flow Rate is in 1mf3 and Condenser Temperature is 2mf2 then Condenser Superheat is out1mf8 (ix)If Mass Flow Rate is in 1mf3 and Condenser Temperature is 2mf3 then Condenser Superheat is out1mf9


Fig.15 Rule viewer of condenser model

Fig.15 indicates rule viewer that shows that model predicts the condenser superheat

(output) by varying the inputs of mass flow rate and condenser temperature. Rule viewer is showing the computed output for one data set of inputs i.e. for mass flow rate 0.09 kg/sec and condenser temperature 300C superheat generated by the fuzzy model is 11.30C. Likewise this fuzzy model has generated other values of output variable for different set of data points in the specified range.Fig.16 is indicating the results predicted from the fuzzy model of vapor compression condenser.

3.4.2 Mathematical Formulation of Condenser Superheat

The following relation is taken from the paper of X He et al (1998) which express evaporator superheat as:

(1) Where αioe is the equivalent heat transfer coefficient between the refrigerant and the

ambient air at the superheated section. Tae temperature of ambient air is taken as an average value of 30 0 C.

Bhatti M.S (1999) has given the relationship between the temperature at the compressor outlet Td (temperature at the condenser inlet) and the temperature at the compressor inlet Ts (temperature at the evaporator outlet) as below:

(2)

Where Pd and Ps are discharge and suction pressures and is the isentropic

efficiency of the compression. For reciprocating compressor used in air conditioning,


isentropic efficiency is in the range 0.5 –0.7. is adiabatic index and its value 1.118 for refrigerant R134a as given in manual of HIDECOR Publications (2000) which is being used in the present problem. Going through the equations (1) to (2) condenser superheat can be expressed in the form of relation given by

(3)

For refrigerant R134a the relation has been taken from the paper of Abou-Ziyan H.Z et

al (1996) as given Log (Pd) =A0 + A1Tc + A2Tc2 +A3Tc3 Where A0 = -35.94481, A1 = 0.265213, A2= -0.6782399 E-3, A3 = 0.6323821 E-6.

A0, A1, A2, A3, are constants taken for refrigerant R134a. Equation (3) is proposed mathematical model for condenser superheat. This mathematical model is investigated using MATLAB environment. Effect of condenser temperatures and mass flow rate on condenser superheat from this model is shown in Fig 17

Fig.16 Mass flow rate versus condenser superheat from fuzzy model

Fig.17 Mass flow rate versus condenser superheat from mathematical model

4 Integrated fuzzy model of vapour compression air conditioning system 4.1 Integrating the vapor compression air conditioning variables

Evaporator model and condenser model has shown very interdependently similar behavior. As refrigerant (R134a) with superheat SHe at the exit of evaporator has been treated as the entry conditions for compressor. It has been observed that after compression in the refrigerating compressor, superheat at the exit of compressor or at entry of condenser has shown such a results that for integrating fuzzy model, evaporator superheat SHe and evaporator temperature Te can be taken as integrating variables for condenser model and evaporator model. In compressor model compressor speed CS and delivery pressure DP were taken as controlling parameters for mass flow rate MFR. But in expansion valve fuzzy model output of compressor model i.e. MFR is taken as its


input. Other input parameter of this valve model is delP. As delivery pressure DP is used in the compressor fuzzy model by keeping the suction pressure constant, so out of delivery pressure DP (from compressor fuzzy model) and delP (from expansion valve fuzzy model) only delP has been taken as integrating variables. Compressor speed CS is an input parameter of compressor model and mass flow rate MFR is its output parameter which is in turn input variable for expansion valve model. These parameters CS and MFR are also added as integrating variables. Valve opening area has been substituted by mass flow rate in integrated fuzzy model. Possible integration of all fuzzy controllers of vapor compression elements is shown in Fig.18 Thus compressor speed, delP, mass flow rate, evaporator superheat and evaporator temperature can be concluded as variables for integrated fuzzy model.

Fig.18 Integration of all fuzzy controllers of vapor compression elements along with possible variables.

4.2 Integrated Fuzzy Model of vapor compression air conditioning system 4.2.1. Input and output variables and their linguistic labels

Variables for integrated fuzzy model have already been identified as compressor speed CS, pressure difference across the orifice is delP, mass flow rate MFR, and evaporator superheat SHe which are taken as input parameters and evaporator temperature Te is selected as output parameter of the integrated fuzzy model. Universe of discourses for input parameters are 200 rpm to 1400 rpm, 3 bar to 9 bar, 0.02 kg/sec to 0.14 kg/sec and 0.2 0C to 8 0C respectively. The membership functions have been selected such that linguistic variables show suitable coverage on the universe of discourse.


Fig.19 Membership function plots for input variable compressor speed (RPM)

Fig.20 Membership function plots for input variable delP (bar)

Fig.21 Membership function plots for input

variable mass flow rate kg/sec

Fig.22 Membership function plots for input variable evaporator superheat (0C)


Fig.23 Membership function plots for output variable evaporator temperature (0C)

Fig.24 Integrated fuzzy model of vapor compression air conditioning system

A moderate overlap is described to allow for reasoning with uncertainty and the need

for completeness of the control rules. Membership functions for different variables along with their linguistic levels are shown in Fig.19, Fig.20, Fig.21, Fig.22, and Fig.23. Integrated fuzzy model of vapor compression air conditioning system is given in Fig. 24.

4.2.2. Fuzzy control rules

For the integrated fuzzy model, variables generate ten numbers of conditional statements as if-then rules of the model. Formulated set of rules of the model are outlined below:

(i)If compressor Speed is in1mf1 and delP is in2mf1 and Mass Flow Rate is in3mf1 and Evaporator Superheat is in4mf1 then Evaporator Temperature is out1mf1. (ii)If compressor Speed is in1mf2 and delP is in2mf2 and Mass Flow Rate is in3mf2 and Evaporator Superheat is in4mf2 then Evaporator Temperature is out1mf2.(iii)If compressor Speed is in1mf3 and delP is in2mf3 and Mass Flow Rate is in3mf3 and Evaporator Superheat is in4mf3 then Evaporator Temperature is out1mf3.(iv)If compressor Speed is in1mf4 and delP is in2mf4 and Mass Flow Rate is in3mf4 and Evaporator Superheat is in4mf4 then Evaporator Temperature is out1mf4.(v)If compressor Speed is in1mf5 and delP is in2mf5 and Mass Flow Rate is in3mf5 and Evaporator Superheat is in4mf5 then Evaporator Temperature is out1mf5.(vi)If compressor Speed is in1mf6 and delP is in2mf6 and Mass Flow Rate is in3mf6 and Evaporator Superheat is in4mf6 then Evaporator Temperature is out1mf6.(vii)If compressor Speed is in1mf7 and delP is in2mf7 and Mass Flow Rate is in3mf7 and Evaporator Superheat is in4mf7 then Evaporator Temperature is out1mf7.(viii)If compressor Speed is in1mf8 and delP is in2mf8 and Mass Flow Rate is in3mf8 and Evaporator Superheat is in4mf8 then Evaporator Temperature is out1mf8. (ix)If compressor Speed is in1mf9 and delP is in2mf9 and Mass Flow Rate is in3mf9 and Evaporator Superheat is in4mf9 then Evaporator Temperature is out1mf9. (x) If compressor Speed is in1mf10 and delP is in2mf10 and Mass Flow Rate is in3mf10 and Evaporator Superheat is in4mf10 then Evaporator Temperature is out1mf10.

Fig.25 indicates rule viewer that shows the values of the various input to the model and computed outputs. Rule viewer is showing the computed output for one data set of inputs i.e. for compressor speed 800 RPM, delP 6 bar, Mass Flow Rate 0.08 kg/sec and evaporator superheat 4.22 0C,


Fig.25 Rule viewer of integrated fuzzy model

Fig.26a Evaporator temperature versus evaporator superheat at compressor speed 1400 RPM and delP 7 bar

Fig.26b Evaporator temperature versus evaporator superheat at compressor speed 1400 RPM and delP 6 bar


Fig.26c Evaporator temperature versus evaporator superheat at compressor speed 1200 RPM and delP 8 bar

Fig.26d Evaporator temperature versus evaporator superheat at compressor speed 1000 RPM and delP 7 bar

Fig.26e Evaporator temperature versus evaporator superheat at compressor speed 800 RPM and delP 6 bar

Fig.26f Evaporator temperature versus evaporator superheat at compressor

speed 600 RPM and delP 5 bar


Fig.26g Evaporator temperature versus evaporator superheat at compressor speed 400 RPM and delP 4 bar

Evaporator temperature generated by integrated fuzzy model is –9.68 0C. Likewise this

fuzzy model has generated other values of output variable for different set of data points in the specified range for all input variables.Fig.26a to Fig.26g are indicating the results predicted by the integrated fuzzy model of vapor compression air conditioning system.

5 Results and discussions 5.1 Validation of expansion valve Fuzzy model

Pressure differences across the expansion valve orifice delP versus valve opening area at different mass flow rate from fuzzy model and mathematical model are indicated by Fig.10 & Fig.11.Results predicted from fuzzy model and mathematical model are investigated. It has been analyzed that as delP changes from 3 bar to 7 bar, behavior of valve opening with mass flow shows maximum error as 2.14 percent and minimum is 0.19 percent. In this model total 75 data points were involved and over all average error for the model are determined as 1.444 percent. Thus simulated fuzzy model gave an overall 98.5 percent accuracy. Comparison at delP 3 bar & 7 bar is also shown in Fig 27.

At delP=3bar

At delP=7bar

Fig. 27 Comparison of mathematical and fuzzy predicted valve opening area


5.2 Validation of compressor Fuzzy model Compressor speed versus mass flow rate at different delivery pressure from fuzzy

model and mathematical model are as given in Fig.7 & Fig.8. Results obtained from both these model have been analyzed for validating the compressor fuzzy model. Comparison is studied for the behavior of mass flow rate with compressor speed at different delivery pressure of 6 bar, 8 bar, 10 bar, 14 bar and 16 bar.

At delivery pressure 6 bar

At delivery pressure 16 bar

Fig. 28 Comparison of compressor speed versus mass flow rate for fuzzy and mathematical model

Almost all the data points from fuzzy model (at 6bar) have the deviations in the range

of 0-3 percent as compared with curve from mathematical model. At 8 bar, 10 bar, 14 bar and 16 bar maximum deviations is even less than 3 percent. Fig.28 shows the comparison at 6 bar and 16 bar. Developed fuzzy model is found to be 98 percent accurate and this supports the use of fuzzy logic in controlling the mass flow rate with compressor speed and delivery pressure, as it is very easy to handle non-linear situations with the use of fuzzy model than mathematical model, as no explicit input-output equations are available and readily applicable to control design. 5.3 Validation of Fuzzy model of evaporator superheat

Evaporator superheat fuzzy model for vapor compression air-conditioning system has been developed and compared with corresponding mathematical model. Fig.13 and Fig.14 show evaporator temperature versus evaporator superheat from two models. Results from fuzzy model and mathematical model are investigated at different mass flow rate of 0.04 kg/sec, 0.06 kg/sec, 0.08 kg/sec, 0.10 kg/sec, 0.12 kg/sec, and 0.14 kg/sec respectively. Evaporator temperatures and mass flow rates of refrigerant are having the reciprocal effect on the evaporator superheat. It is evident from the Fig. 13 & 14 that superheat is smaller in case fuzzy model as compared to mathematical model.


For more clarity comparison at mass flow are of 0.04 kg/sec and 0.14 kg/sec has also been given in Fig29.

At mass flow rate of 0.04 kg/sec


Fig.29 Evaporator superheat versus evaporator temperature from mathematical and fuzzy model.

Lesser superheat value is always desirable in vapor compression refrigeration systems.

Fuzzy model has shown that superheat is improved to the extent of 30C.So new approach of fuzzy is better than the mathematical. It can command more efficient control of superheat in vapor compression air conditioning system.

5.4 Validation of Fuzzy model of condenser superheat

Condenser superheat model of vapor compression air conditioning system has been studied as mathematical model and fuzzy model. Behavior of condenser superheat with variation of refrigerant mass flow rate and condenser temperature is shown in Fig.16 & Fig.17. Results of fuzzy model were compared with mathematical model. It is evident from these figures that condenser superheat is smaller for fuzzy model. Comparisons is also shown at mass flow rate 0.04 kg/sec and 0.14 kg/sec in Fig30.




Fig. 30 Condenser superheat versus nser temperature from mathematical

Condenser superheat has improved to the extent of 130C in case of fuzzy model. L

.5 Validation of integrated Fuzzy model ure on evaporator superheats at different

co

conde

and fuzzy model.

esser superheat value is always desirable in vapor compression air conditioning systems. These lesser superheat values will lead to improve the size of the vapor compression condenser and amount of coolant circulated in the condenser. Energy requirement will also be conserved. So control based on new approach of fuzzy model can establish efficient grip over condenser superheat. 5

Behavior of the evaporator temperatmpressor speeds and pressure difference across orifice for integrated fuzzy model is

shown in Fig 26a to Fig.26g. Results from integrated fuzzy model, individual fuzzy model and mathematical model have been compared. Fig.31 shows the variation of evaporator temperature with evaporator superheat at compressor speed 1400 RPM and delP 7 bar for different mass flow rate. Integrated fuzzy model has shown lesser superheat as compared to mathematical model. Lesser superheat reduces the overall energy consumptions and improves the design of evaporator and condenser. When compared with fuzzy model, integrated fuzzy model has shown improved superheat for fifty percent of the data points.


At refrigerant flow rate 0.04 kg/sec




Fig.31 Evaporator temperature versus evaporator superheat at compressor speed 1400 RPM, delP 7 bar

It is also observed that keeping other parameters unchanged, if the mass flow rate is increased then the maximum range of superheat shows variations from 9 0C to2.7 0C and minimum range from 30C to 0.90C approximately, for mathematical model. For fuzzy model maximum range temperature from 70C to 00C and minimum variations remains within 00C to 1.50C. For integrated fuzzy model maximum range of superheat variations is within 3.62 0C to 1.56 0C and minimum range is within 1.910C to 0.2 0C. As variations are very small with integrated fuzzy model so it is more stable as compared to other two models. When compressor speed is reduced to 1200 RPM and pressure across the orifice of expansion valve is increased to 8 bar then behavior of the three models will be as


shown in Fig.32. Superheat improvement is being shown in favor of integrated fuzzy model as compared to mathematical model. Even it has improved to greater extent with respect to fuzzy model. But for mass flow rate beyond 0.08 kg/sec improved superheat values are loosing the favor for integrated fuzzy model for very few data points. Minimum and maximum range trend is same as described before and integrated model is comparatively stable.

At refrigerant flow rate=0.04 kg/sec


At refrigerant flow rate=0.08 kg/sec Fig. 32 Evaporator temperature versus evaporator superheat at compressor speed 1200 RPM, delP 8 bar

Fig.33 & Fig.34 depict the model behavior at further reduced level of compressor


speed (1000 RPM and 800 RPM) and delP (7 bar and 6 bar) respectively. Integrated fuzzy model is superior at all the data points as compared to mathematical model and for sixty percent of the data points as compared to fuzzy model. Under the given set of conditions of compressor speed & delP beyond 0.08 kg/sec of mass flows rate, superheat improvement is slightly reduced.




Fig. 33 Evaporator temperature versus evaporator superheat at compressor speed 1000 RPM, delP 7 bar





Fig. 34 Evaporator temperature versus evaporator superheat at compressor speed 800 RPM, delP 6 bar

At further reduced speed and delP, three models are showing similar behavior as

described by Fig.33 & Fig.34. But for higher mass flow rate, performance of integrated fuzzy model is less favorable.

In view of the entire foregoing discussions it can be said that integrated fuzzy model can generate the same results as generated by the four individuals’ fuzzy model of vapor compression air conditioning system. So it can be substituted for all these fuzzy models and also for mathematical models.


6 Conclusions

The main results and contributions of this paper are summarized as follows: 6.1 Compressor model was identified for compressor speed and delivery pressure as

input parameters and refrigerant flow rate as output parameter. Fuzzy model for compressor was developed. The results predicted from this fuzzy model were very close with that of mathematical model for compressor speed and delivery pressure variations. This fuzzy model is found to be 98 percent accurate and support the use of fuzzy logic for making appropriate control for compressor used in vapour compression air conditioning system. It is also evident that problems hard to be treated by mathematical modelling can be solved in this way with more ease.

6.2 To regulate the refrigerant flow control in vapor compression system fuzzy logic is a viable alternative. Fuzzy model for expansion valve was validated by comparing it with standard mathematical model for given conditions. It has been found that fuzzy model prediction for opening area of expansion valve along with mass flow rate and differential pressure across the orifice of expansion valve show good agreement (98.5 percent accurate) with mathematical model. Thus it can be concluded that appropriate control system for refrigerant flow in vapor compression air conditioning system can be designed on the basis of fuzzy techniques.

6.3 Evaporator superheat fuzzy model was developed and compared with mathematical model. Comparison shows that Fuzzy model has better precision and generalization ability. This model is giving lesser superheat value for the same range of evaporator temperature and mass flow rate. Control based on fuzzy modeling will be more efficient as it improves the evaporator superheat in vapour compression refrigeration system. Fuzzy system retains the mass flow rate and evaporator temperatures within user defined limits and regulate the superheat of the system for minimum energy consumption.

6.4 A fuzzy model was developed to predict the thermal performance of vapor compression air conditioning system with reference to condenser superheat. This model is also giving lesser superheat value for the same range of condenser temperature and mass flow rate. Control based on fuzzy model will be more efficient as it improves the condenser superheat and hence the condenser design in vapor compression air conditioning system.

6.5 Integrated fuzzy model for vapor compression elements of air conditioning system has also been presented here and it was concluded that integrated fuzzy model could generate the same results as generated by the four individuals’ fuzzy models of vapor compression air conditioning system. So it can be substituted for all these fuzzy models and for mathematical models too. This fuzzy model is simpler and tractable for control design. This new model is flexible and capable of handling infinite control situations. This model relates the dynamic responses of several critical variables such as evaporating temperature and the refrigerant superheat of evaporator and condenser. REFERENCES

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Jagdev Singh , Mechanical Engineering Department, Beant College of Engineering and Technology, Gurdaspur-143521, E.mail :[email protected] received the B.E. and M.E. degrees in Mechanical Engineering from Punjab University, Chandigarh (India) in 1988 and 1998, respectively and registered for PhD degree in faculty of Mechanical Engineering since 2003 with Punjab Technical University, Jalandhar Punjab (India).His current research interests include fuzzy modeling of Heating Ventilating and Air Conditioning (HVAC) systems . He has published several papers in these areas.

Dr. Nirmal Singh, Department of Mechanical Engineering, Gurdaspur-143 521,E-mail: [email protected], working as Professor in the department of Mechanical and Production Engineering in Beant College of Engineering & Technology, Gurdaspur, Punjab. His area of interest is modeling, identification, validation, and control of Mechanical Engineering systems & sub systems using fuzzy logic as methodology in MATLAB environment. He has more than 12 publications in national/international journals.

M Dr. J.K. Sharma, Swami Parmanand College of Engineering and Technology,, VPO Jaulan Kalan Lalru, Tehsil Derabassi District, Patiala 140 507,E-mail: [email protected]. He has done his Master in Mechanical Engineering from M.S. University Baroda in 1969 and PhD from IIT Delhi India in 1982. He has experience of 41 years in industry, teaching and research. He has published 75 research papers in National & International Journals and Conferences. Areas of interest include mathematical modeling of thermal systems and energy conservations.

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