fuzzy control of cold storage refrigeration system with dynamic coupling...

Research ArticleFuzzy Control of Cold Storage Refrigeration System withDynamic Coupling Compensation

Xiliang Ma 12 and Ruiqing Mao1

1Xuzhou Institute of Technology Xuzhou Jiangsu 221111 China2School of Mechanical and Electrical Engineering China University of Mining and Technology Xuzhou Jiangsu 221116 China

Correspondence should be addressed to Xiliang Ma xlma818sinacom

Received 16 October 2017 Revised 7 January 2018 Accepted 12 February 2018 Published 13 March 2018

Academic Editor Enrique Onieva

Copyright copy 2018 XiliangMa and RuiqingMaoThis is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in anymedium provided the originalwork is properly cited

Cold storage refrigeration systems possess the characteristics of multiple input and output and strong coupling which bringschallenges to the optimize control To reduce the adverse effects of the coupling and improve the overall control performanceof cold storage refrigeration systems a control strategy with dynamic coupling compensation was studied First dynamic model ofa cold storage refrigeration system was established based on the requirements of the control system At the same time the couplingbetween the componentswas studied Second to reduce the adverse effects of the coupling a fuzzy controllerwith dynamic couplingcompensation was designed As for the fuzzy controller a self-tuning fuzzy controller was served as the primary controller and anadaptive neural network was adopted to compensate the dynamic coupling Finally the proposed control strategy was employedto the cold storage refrigeration system and simulations were carried out in the condition of start-up variable load and variabledegree of superheat respectivelyThe simulation results verify the effectiveness of the fuzzy control method with dynamic couplingcompensation

1 Introduction

Automatic control of cold storage refrigeration system is animportant means to save energy and improve the quality ofrefrigeration [1 2] The automatic control can guarantee thestability of the storehouse temperature avoid the unnecessarylow temperature and keep the temperature pressure liquidlevel and other state parameters which ensure the safetyand efficiency of the system in the required range Howevercold storage refrigeration systems possess the characteristicsof multi-input and multi-output and strong coupling whichbrings challenges to the dynamicmodeling and the controllerdesign [3 4]

In the traditional control process of cold storage refriger-ation system the compressor condenser evaporator expan-sion valve and other main components are controlled sep-arately [5] Although those methods realize the automaticcontrol of cold storage refrigeration system it is difficult toachieve higher precision adjustment requirements because ofignoring the coupling On the other hand it is difficult toapply to the system with large change of loads and working

conditions [6] With the improvement of the refrigerationeffect requirements of cold storage researchers have beingconsidered the refrigeration system as a whole and studiedthe combined control methods for the main components(compressor condenser evaporator and expansion valve)[7] Theoretically the combined control methods have bettercontrol effect However the nonlinear characteristics of thecold storage refrigeration system lead to the difficulty ofdynamic modeling the time-varying characteristics lead tothe difficulty of control parameter online adjusting and thecoupling characteristics increase the complexity of the con-troller design [3] Due to the difficulty of dynamic modelingresearchers employed control methods that do not need theaccurate model of the system to get a better solution [8 9]such as fuzzy control and neural network control Basedon the coupling characteristics of cold storage refrigerationsystems scholars proposed decoupling controllers but it ishard to achieve the desired control effect due to the strongcoupling

Studies on control strategy with dynamic couplingcompensation of cold storage refrigeration system were

HindawiJournal of Control Science and EngineeringVolume 2018 Article ID 6836129 7 pageshttpsdoiorg10115520186836129

2 Journal of Control Science and Engineering

Table 1 The input and output variables and the state variables of the dynamic model

Symbol Name

Input variables 119891119884 (Hz) Frequency of the compressor119860119864 Opening of the electronic expansion valve

Output variables 119879119903119894 (∘C) Temperature of the storage room119879119911119900 (∘C) Outlet superheat of the evaporator

State variables

ℎ119871 Outlet enthalpy of the condenserℎ119911 (Jkg) Outlet ratio of enthalpy of the evaporator119879119903119894 (∘C) Temperature of the storage room119879119871 (∘C) Temperature of the tube wall of the condenser119879119911 (∘C) Temperature of the tube wall of the evaporator

conducted First the dynamic model of cold storage refrig-eration systemwas established and the coupling was studiedSecond a fuzzy controller with dynamic coupling compen-sation was designed The control strategy consists of a fuzzycontroller which served as the primary controller and anadaptive neural network which was adopted to compensatethe dynamic coupling Finally the control strategy wasapplied to the control of a cold storage refrigeration system

2 Dynamic Coupling of Cold StorageRefrigeration System

The working process of refrigeration systems is a nonlinearand strong coupling dynamic process with fusion heat trans-fer and mass transfer flow The dynamic model is the basis ofthe simulation and the control system design In this paperwith the consideration of the requirements of refrigerationcontrol system a nonlinear dynamic model is establishedModels of the main components such as frequency conver-sion compressor electronic expansion valve condenser andevaporator are established under the premise of idealizedassumptions [10] Assume that the fan speed of the condenserand the evaporator are constant and the control processcan be realized by controlling the frequency of the invertercompressor and the opening of the electronic expansionvalve In addition the temperature of the cold storage roomis one of the most important controlled parameters and thecontrol of the evaporator outlet superheat is an importantway to improve the stability and efficiency of the refrigerationsystem

In the overall dynamic model the input and outputvariables and the state variables are listed in Table 1

Based on the energy equation of refrigerant in thecondenser [11] the heat transfer energy equation of thecondenser tube wall [12] the energy equation of refrigerantin the evaporator [11] the heat energy equation of theevaporator tube wall [11] and the dynamic model of thestorage room [10] the dynamic model of the cold storagerefrigeration system can be established Ordering that x =[ℎ119871 119879119871 ℎ119911 119879119911 119879119903119894]119879 and u = [119891119910 119860119864]119879 the dynamicmodel ofthe form of state space equation can be expressed as follows

x = f (x) + g (x) uy = h (x) (1)

where

f (x)

=

[[[[[[[[[[[[[[[[

120572119871119894119860119871119894119898119871 (119879119871 minus 119879119911)120572119871119900119860119871119900119862119871119871119871 (119879119903119900 minus 119879119871) minus120572119871119894119860119871119894119862119871119871119871 (119879119871 minus 119879119911)120572119911119894119860119911119894119898119911 (119879119911119861 minus 119879119911119871)120572119911119900119860119911119900119862119911119871119911 (119879119903119894 minus 119879119911119861) minus120572119911119894119860119911119894119862119911119871119911 (119879119911119861 minus 119879119911119871)120572119903119860119903119862119903 + 120588119896119862119896119881119903 (119879119903119900 minus 119879119903119894) minus120572119911119860119911119894119862119903 + 120588119896119862119896119881119903 (119879119903119894 minus 119879119911119871) + 119876119903

]]]]]]]]]]]]]]]]

g (x) = [1198921 (x) 0 0 0 00 0 1198922 (x) 0 0]

1198921 (x) = 119891120582119881119910 (1 minus 119904) (ℎz + 119881119888119891119873th minus ℎ119871)119901119881119888119898119871 1198922 (x) = 119891119898V (ℎ119871 minus ℎ119911)119898119911 h (x) = [ 119879119903119894119879119910 minus 119879119911119871]

119891120582 = 098 minus 0085 [( 119901119894119901119900)1119896 minus 1]

119891119873th = 119901119900 1198961198641 minus 119896 [1 minus ( 119901119894119901119900)(119896119864minus1)119896119864]

119891119898V = 119862119864radic2120588119864 (119901119894 minus 119901119900)

(2)

The included variables are listed in Table 2In the refrigeration system inverter compressors elec-

tronic expansion valve evaporator and condenser and othercomponents are not independent the coupling can bedescribed as in Figure 1 The two components of con-denser and evaporator are connected with the indoor andexternal environment The outdoor ambient temperature119879119903119900 influences the performance of the condenser while thetemperature of the storage room 119879119903119894 and the refrigerationsystem are mutually restricted The coupling between theexpansion valve and the environment is indirectly connectedthrough the condenser and the evaporator

Journal of Control Science and Engineering 3

Table 2 Variables and parameters in (2)

Symbol Name120572119871119894 Inner heat transfer coefficient of the condenser tube119898119871 (kg) Weight of refrigerant in the condensing tube120572119871119900 Air side heat transfer coefficient of the condenser tube119862119871 (J (kg∘C)) Heat capacity of unit length of the condensing tube wall119879119903119900 (∘C) Temperature of the outdoor ambient120572119911119894 Inner heat transfer coefficient of the evaporator tube119898119911 (kg) Weight of the refrigerant in the evaporator tube119879119911119871 (mm2) Evaporation temperature of the refrigerant119860119911119900 (mm2) Heat transfer area of air side the evaporator tube119871119911 (mm) Length of the evaporator pipe119860119903 (mm2) Heat transfer area of the wall in the storage room120588119896 (kgmm3) Density of the air119881119903 (mm3) Area of the storage room119876119903 Heat load of the objects in the storage room119881119888 Ratio of gaseous refrigerant in suction of the compressor119901 Magnetic pole logarithm of the motor119901o (Pa) Outlet pressure of the electronic expansion valve119862119864 Flow coefficient of the electronic expansion valve119860119871119894 (mm2) Heat transfer area of the inner condenser tube119879119911 (∘C) Condensation temperature of the refrigerant119860119871119900 (mm2) Heat transfer area of the air side condenser tube119871119871 (mm) Length of the condensing pipe119879119871 (∘C) Temperature of the condensation tube wall119860119911119894 (mm2) Heat transfer area of the evaporator tube119879119911119861 (mm2) Temperature of the evaporator tube wall120572119911119900 Air side heat transfer coefficient of the evaporator tube119862119911 (J(kg∘C)) Heat capacity of unit length of the evaporator tube wall120572119903 Comprehensive heat transfer coefficient of the wall in the storage room119862119903 (J(kg∘C)) Heat capacity of the objects in the storage room119862119896 Constant pressure specific heat of the air120572119911 Comprehensive heat transfer coefficient of the evaporator119881119910 Swept volume of the compressor119904 (rs) Speed difference of the motor119901119894 (Pa) Inlet pressure of the electronic expansion valve119896119864 Multidegree index120588119864 (kgmm3) Density of inlet refrigerant of the electronic expansion valve

3 Fuzzy Control with DynamicCoupling Compensation

Due to the complexity of the transfer process of quality andthe energy it is difficult to establish a precise mathematicalmodel of refrigeration system Furthermore cold storagerefrigeration system is a typical MIMO strong couplingtime-varying and nonlinear complex system it is difficultto achieve the desired control effect through a SISO controlmethod Fuzzy control and neural network control are notdependent on the precise mathematical model of a controlobject which are effective methods to deal with the uncer-tainty nonlinearity and strong coupling in a control system[13] In this paper a multivariable fuzzy neural networkcontroller with dynamic coupling compensation is proposed

The controller which takes the advantages of fuzzy controland neural network control is designed from the wholerefrigeration systemThe schematic diagram of the controlleris shown in Figure 2

As can be seen from Figure 2 the proposed controlleris composed of a self-tuning fuzzy controller and an adap-tive neural network coupling compensation controller Inthe controller the self-tuning fuzzy control determines thedynamic characteristics of the system while the adaptiveneural network control estimates the coupling of the multi-variable

The output deviation 119890 is transformed to the formal con-trol variables 119891119884 and 119860119864 by the self-tuning fuzzy controllerThe formal control variables are the inputs of the adap-tive neural network coupling compensation controller The


Tro

Tro

Tri

po poℎz

ℎa

mc

pi

pi

m

ℎL

ℎL

Compressor

Evaporator

Condenser

Expansionvalve

Figure 1 The coupling

Desiredload

e Variation ofcold load

Model ofrefrigerationsystem

Mass flow ofrefrigerant

Minimumcondensationpressure

Self-tuning fuzzy control

Frequencyadjustment ofcompressor

Openingadjustment ofexpansion valve

Temperaturemeasurement of theoutdoor and indoor

fY

AE

Adaptive neuralnetwork couplingcompensation controller

Estimation ofdynamic coupling

Cold storagerefrigerationsystem

Output

Figure 2 Fuzzy neural network controller with dynamic coupling compensation

coupling effects are compensated as measurable disturbanceThrough the dynamic coupling characteristic estimation andthe neural network weights correction the control objectbecomes a system with less coupling degree and the outputof the adaptive neural network coupling compensation con-troller is the input of the controlled object

31 Self-Tuning Fuzzy Control The intelligent weight func-tion fuzzy algorithm is adopted to realize the self-tuning ofthe control rules By using this method it is not necessaryto determine the membership function and fuzzy controlrules of the fuzzy variables and the interaction between othervariables is not considered in the designed fuzzy controller Ina single loop of the self-tuning fuzzy controller the selectionof the fuzzy membership function is omitted and the fuzzyquantity of the sampled discrete values 119890(119896) and Δ119890(119896) ismultiplied by the quantization factors shown as follows [14]

119864 = 119870119864119890 (119896) 119864119862 = 119870119862Δ119890 (119896) (3)

where 119870119864 and 119870119862 are the quantitative gains of the error andthe error variation respectively

To ensure that the outputs of the weight function aremeaningful when 119864 and 119864119862 are zero at the same time the

weighted factors of the error and the error variation aredetermined as follows

119870119864 = 119864|119864| + 10038161003816100381610038161198641198621003816100381610038161003816 + 120575 119870119862 = 119864119862|119864| + 10038161003816100381610038161198641198621003816100381610038161003816 + 120575

(4)

where 120575 is a small positive numberThe rule of fuzzy control of intelligent weight function is

Δ119880 = 119870119864119864 + 119870119862119864119862 (5)

The output of the self-tuning fuzzy controller can beexpressed as follows

1199060119894 (119896) = 119870119880Δ119880 + 119870119868sumΔ119880 (6)

where119870119880 is the proportional gain and119870119868 is the integral gain32 Adaptive Neural Network Coupling Compensation Con-trol Based on the output of the self-tuning fuzzy controller(there are two output variables) ordering that the weightedcoefficients of the neural networks are 120596119894119895 (119894 = 1 2 119895 = 1 2)and the output of the coupling compensation controller is


CompensatedWithout being compensated

minus15

minus10

minus5

0

5

10

15

20

25Te

mpe

ratu

re(∘

C)

500 1000 1500 2000 25000Time (s)

(a) The temperature of the storage room


3

4

5

6

7

8

Tem

pera

ture

(∘C)

500 1000 1500 20000Time (s)

(b) The degree of superheat

Figure 3 Response curves after the system start-up

u119902 = [1199061199021 1199061199022] and the following relationship can be estab-lished [14]

119906119902119895 (119896) = 2sum119894=1

120596119894119895 (119896) 1199060119894 (119895 = 1 2) (7)

The neural network and the controlled object areregarded as a whole and the minimum value of the quadraticsum of the difference between the expected output and theactual one is used as the evaluation function of the systemshown as follows

119864 (119896) = 122sum119894=1

[119903119894 (119896) minus 119910119894 (119896)]2 (119894 = 1 2) (8)

where 119903119894(119896) is the desired value and 119910119894(119896) is the actual valueIn (8) the value of 119864(119896) can be minimized by online

adjustment and self-learning of120596119894119895(119896) In the paper the onlineadjustment method of 119864(119896) is referred to as the method in[15] The self-learning of 120596119894119895(119896) is completed by adopting theGradient descentmethod and the iteration value at time 119896+1can be expressed as follows

120596119894119895 (119896 + 1) = 120596119894119895 (119896) minus 120578 120597119864 (119896)120597120596119894119895 (119896) (9)

where 120578 is the learning rateTherefore

120597119864 (119896)120597120596119894119895 (119896) = minus2sum119894=1

[119903119894 (119896) minus 119910119894 (119896)] sdot 120597119910119894 (119896)120597119906119902119895 (119896) sdot 1199060119894 (10)

where 120597119910119894(119896)120597119906119902119895(119896) is the rate of the affection of the jthinput 119906119902119895(119896) on the controlled object in relation to the output120597119910119894(119896)120597119906119902119895(119896) can represent the dynamic coupling of the

jth input to the ith output and it can be calculated by thefollowing equation

120597119910119894 (119896)120597119906119902119895 (119896) asymp sign[ 119910119894 (119896 + 1) minus 119910119894 (119896)119906119902119894 (119896) minus 119906119902119894 (119896 minus 1)] (11)

4 Numerical Simulation

To verify the effectiveness of the proposed control methodfor cold storage refrigeration system numerical simulationswere carried out A small cold storage refrigeration systemwhich consists of R22 refrigerant single-stage steam pistontype compression refrigerator electronic expansion valveair-cooled evaporator and air-cooled condenser is takenas an example In the study 119896119864 = 118 the sizes of thecold storage room are 119871 times 119882 times 119867 4500mm times 3600mmtimes 2700mm During the process of simulation the initialtemperature of the storage room and the outdoor is 25∘Cand 30∘C respectively and the desired temperature of thestorage room and the degree of superheat are minus10∘C and 5∘Crespectively After the system start-up the response curvesof the temperature of the storage room and the degree ofsuperheat are obtained as shown in Figure 3

As can be observed from Figure 3 although the temper-ature of the storage room and the degree of superheat canreach the predetermined steady-state values with or withoutthe dynamic coupling compensated there are no overshootand fluctuation if the dynamic coupling is compensated Inanother case the temperature of the storage room is droppedfromminus10∘C tominus15∘Cwhile the degree of superheat is still 5∘Cand the response curves are shown in Figure 4

As can be observed from Figure 4 the curve of thetemperature of the storage room is smoothwithout overshootafter the coupling compensated Because of the rapid increaseof the cooling load the speed of the variable frequency



100 200 300 400 5000Time (s)

minus16

minus15

minus14

minus13

minus12

minus11

minus10Te

mpe

ratu

re(∘

C)



48

5

52

54

56

58

6

Tem

pera

ture

(∘C)

50 100 150 2000Time (s)


Figure 4 Response curves when the load changed


minus10

minus99

minus98

minus97

minus96

minus95

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)



1

15

2

25

3

35

4

45

5

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)


Figure 5 Response curves when the degree of superheat changed

compressor causes the expansion valve to be open too late toadjust which leads to a certain fluctuation of the superheatThe comparison of the two results in Figure 4(b) shows thatthe proposed controller has a better tracking performance Inanother case the degree of superheat is dropped from 5∘C to2∘C while the temperature of the storage room is still minus10∘Cand the response curves are shown in Figure 5

As can be observed from Figure 5 when the degreeof superheat changed the change of the expansion valvecauses the fluctuation of the temperature of the storage roomand the changing process is smoother if the coupling iscompensated Overshoot appears in the adjustment process

of the degree of superheat but the fluctuation is small andthe control effect is satisfied

5 Conclusions

In the paper studies on control strategy with dynamiccoupling compensation of cold storage refrigeration systemwere conducted First the dynamic model of cold storagerefrigeration system was established and the coupling wasstudied Second a fuzzy controller with dynamic couplingcompensation was designed the self-tuning fuzzy controllerwas the primary controller and the adaptive neural network


was used to compensate the dynamic coupling Finally thedesigned control strategy was applied to the control of a coldstorage refrigeration system and simulationswere carried outin the condition of start-up variable load and variable degreeof superheat respectively

As can be observed from the results of the simulationin the condition of start-up there are no overshoot andfluctuation if the dynamic coupling is compensated In thecondition of the variable load and the variable degree ofsuperheat the curve of the temperature of the storage roomis smooth without overshoot after the coupling compensatedand the comparison of the results shows that the proposedcontroller has a better tracking performance The simulationresults indicate that the fuzzy controller with dynamic cou-pling compensation has good control performance and canbe used in the control process of cold storage refrigerationsystem

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] N D Mukhopadhyay and E S Chowdhury ldquoPerformanceanalysis of solar assisted cascade refrigeration system of coldstorage systemrdquo International Journal of Advanced Research inElectrical Electronics amp Instrumentation Engineering vol 2 no4 pp 1248ndash1254 2013

[2] A Polzot P DrsquoAgaro P Gullo and G Cortella ldquoModellingcommercial refrigeration systems coupled with water storageto improve energy efficiency and perform heat recoveryrdquoInternational Journal of Refrigeration vol 69 pp 313ndash323 2016

[3] Y P Pan Research on Multivariable Adaptive Fuzzy Controlfor Cold Storage Refrigeration Syste Guangdong University ofTechnology Guangzhou China 2007

[4] J Tian R Zhu and Q Feng ldquoStudy on multi-variable fuzzyneural control for air cooled refrigeration systemrdquo Journal ofXirsquoan Jiaotong University vol 40 no 5 pp 514ndash517 2006

[5] T Q Chu and M J Lv ldquoResearch on parameter-adaptive fuzzycontroller for cold storage refrigeration system based on PLCrdquoRefrigeration andAir Conditioning vol 8 no 4 pp 67ndash70 2008

[6] Q S Shao X W Shi T X Li et al ldquoPerformance and controlscheme of compressor and condenser in VRV air conditioningsystemrdquo Compressor Technology vol 1 pp 1ndash4 2002

[7] X DWuM S Jin D G Fan et al ldquoElectronic expansion valve-compressor synchronous controlrdquo Fluid Machinery vol 33 no5 pp 78ndash80 2005

[8] S Li T Liang X Wang and L Kong ldquoDesign for airconditioning evaporator superheat based on direct adaptivefuzzy controllerrdquo in Proceedings of the 2011 IEEE InternationalConference on Automation and Logistics ICAL 2011 pp 248ndash253 China August 2011

[9] C Gao ldquoStudy on the energy-saving of cold storage based onfuzzy neural-networkrdquo Journal of Anhui Agricultural Sciencesvol 39 no 18 pp 11213-11214 2011

[10] W Chen X Z Cai and X X Zhou ldquoModeling and controlresearch of the triple-evaporator air-conditioner with inverterrdquoJournal of System Simulation vol 16 no 10 pp 2123ndash2127 2004

[11] J Z XieMIMOModel And Decoupling Control of RefrigerationSystem Xirsquoan Jiaotong University Xirsquoan China 2001

[12] J Nyers and G Stoyan ldquoA dynamical model adequate forcontrolling the evaporator of a heat pumprdquo International Journalof Refrigeration vol 17 no 2 pp 101ndash108 1994

[13] M Li J Y Lin and Y G Ma ldquoAdaptive neural non-modeldecouple control for MIMO systemrdquo Computer Simulation vol6 no 3 pp 346ndash350 2003

[14] H Li ldquoDesign of multivariable fuzzy-neural network decou-pling controllerrdquo Kongzhi yu JueceControl and Decision vol 21no 5 pp 593ndash596 2006

[15] Z J Zhou and Z J Han ldquoA Newmultivariable fuzzy self-tuningcontrol systemrdquo Acta Automatica Sinica vol 25 no 2 pp 215ndash219 1999

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Table 1 The input and output variables and the state variables of the dynamic model

Symbol Name

Input variables 119891119884 (Hz) Frequency of the compressor119860119864 Opening of the electronic expansion valve

Output variables 119879119903119894 (∘C) Temperature of the storage room119879119911119900 (∘C) Outlet superheat of the evaporator

State variables

ℎ119871 Outlet enthalpy of the condenserℎ119911 (Jkg) Outlet ratio of enthalpy of the evaporator119879119903119894 (∘C) Temperature of the storage room119879119871 (∘C) Temperature of the tube wall of the condenser119879119911 (∘C) Temperature of the tube wall of the evaporator

conducted First the dynamic model of cold storage refrig-eration systemwas established and the coupling was studiedSecond a fuzzy controller with dynamic coupling compen-sation was designed The control strategy consists of a fuzzycontroller which served as the primary controller and anadaptive neural network which was adopted to compensatethe dynamic coupling Finally the control strategy wasapplied to the control of a cold storage refrigeration system

2 Dynamic Coupling of Cold StorageRefrigeration System

The working process of refrigeration systems is a nonlinearand strong coupling dynamic process with fusion heat trans-fer and mass transfer flow The dynamic model is the basis ofthe simulation and the control system design In this paperwith the consideration of the requirements of refrigerationcontrol system a nonlinear dynamic model is establishedModels of the main components such as frequency conver-sion compressor electronic expansion valve condenser andevaporator are established under the premise of idealizedassumptions [10] Assume that the fan speed of the condenserand the evaporator are constant and the control processcan be realized by controlling the frequency of the invertercompressor and the opening of the electronic expansionvalve In addition the temperature of the cold storage roomis one of the most important controlled parameters and thecontrol of the evaporator outlet superheat is an importantway to improve the stability and efficiency of the refrigerationsystem

In the overall dynamic model the input and outputvariables and the state variables are listed in Table 1

Based on the energy equation of refrigerant in thecondenser [11] the heat transfer energy equation of thecondenser tube wall [12] the energy equation of refrigerantin the evaporator [11] the heat energy equation of theevaporator tube wall [11] and the dynamic model of thestorage room [10] the dynamic model of the cold storagerefrigeration system can be established Ordering that x =[ℎ119871 119879119871 ℎ119911 119879119911 119879119903119894]119879 and u = [119891119910 119860119864]119879 the dynamicmodel ofthe form of state space equation can be expressed as follows

x = f (x) + g (x) uy = h (x) (1)

where

f (x)

=

[[[[[[[[[[[[[[[[

120572119871119894119860119871119894119898119871 (119879119871 minus 119879119911)120572119871119900119860119871119900119862119871119871119871 (119879119903119900 minus 119879119871) minus120572119871119894119860119871119894119862119871119871119871 (119879119871 minus 119879119911)120572119911119894119860119911119894119898119911 (119879119911119861 minus 119879119911119871)120572119911119900119860119911119900119862119911119871119911 (119879119903119894 minus 119879119911119861) minus120572119911119894119860119911119894119862119911119871119911 (119879119911119861 minus 119879119911119871)120572119903119860119903119862119903 + 120588119896119862119896119881119903 (119879119903119900 minus 119879119903119894) minus120572119911119860119911119894119862119903 + 120588119896119862119896119881119903 (119879119903119894 minus 119879119911119871) + 119876119903

]]]]]]]]]]]]]]]]

g (x) = [1198921 (x) 0 0 0 00 0 1198922 (x) 0 0]

1198921 (x) = 119891120582119881119910 (1 minus 119904) (ℎz + 119881119888119891119873th minus ℎ119871)119901119881119888119898119871 1198922 (x) = 119891119898V (ℎ119871 minus ℎ119911)119898119911 h (x) = [ 119879119903119894119879119910 minus 119879119911119871]

119891120582 = 098 minus 0085 [( 119901119894119901119900)1119896 minus 1]

119891119873th = 119901119900 1198961198641 minus 119896 [1 minus ( 119901119894119901119900)(119896119864minus1)119896119864]

119891119898V = 119862119864radic2120588119864 (119901119894 minus 119901119900)

(2)

The included variables are listed in Table 2In the refrigeration system inverter compressors elec-

tronic expansion valve evaporator and condenser and othercomponents are not independent the coupling can bedescribed as in Figure 1 The two components of con-denser and evaporator are connected with the indoor andexternal environment The outdoor ambient temperature119879119903119900 influences the performance of the condenser while thetemperature of the storage room 119879119903119894 and the refrigerationsystem are mutually restricted The coupling between theexpansion valve and the environment is indirectly connectedthrough the condenser and the evaporator










Tro

Tro

Tri

po poℎz

ℎa

mc

pi

pi

m

ℎL

ℎL

Compressor

Evaporator

Condenser

Expansionvalve


Desiredload









fY

AE




Output




119864 = 119870119864119890 (119896) 119864119862 = 119870119862Δ119890 (119896) (3)




119870119864 = 119864|119864| + 10038161003816100381610038161198641198621003816100381610038161003816 + 120575 119870119862 = 119864119862|119864| + 10038161003816100381610038161198641198621003816100381610038161003816 + 120575

(4)


Δ119880 = 119870119864119864 + 119870119862119864119862 (5)


1199060119894 (119896) = 119870119880Δ119880 + 119870119868sumΔ119880 (6)




minus15

minus10

minus5

0

5

10

15

20

25Te

mpe

ratu

re(∘

C)

500 1000 1500 2000 25000Time (s)



3

4

5

6

7

8

Tem

pera

ture

(∘C)

500 1000 1500 20000Time (s)




119906119902119895 (119896) = 2sum119894=1

120596119894119895 (119896) 1199060119894 (119895 = 1 2) (7)


119864 (119896) = 122sum119894=1

[119903119894 (119896) minus 119910119894 (119896)]2 (119894 = 1 2) (8)



120596119894119895 (119896 + 1) = 120596119894119895 (119896) minus 120578 120597119864 (119896)120597120596119894119895 (119896) (9)


120597119864 (119896)120597120596119894119895 (119896) = minus2sum119894=1

[119903119894 (119896) minus 119910119894 (119896)] sdot 120597119910119894 (119896)120597119906119902119895 (119896) sdot 1199060119894 (10)










100 200 300 400 5000Time (s)

minus16

minus15

minus14

minus13

minus12

minus11

minus10Te

mpe

ratu

re(∘

C)



48

5

52

54

56

58

6

Tem

pera

ture

(∘C)

50 100 150 2000Time (s)




minus10

minus99

minus98

minus97

minus96

minus95

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)



1

15

2

25

3

35

4

45

5

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)






5 Conclusions







References


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











Tro

Tro

Tri

po poℎz

ℎa

mc

pi

pi

m

ℎL

ℎL

Compressor

Evaporator

Condenser

Expansionvalve


Desiredload









fY

AE




Output




119864 = 119870119864119890 (119896) 119864119862 = 119870119862Δ119890 (119896) (3)




119870119864 = 119864|119864| + 10038161003816100381610038161198641198621003816100381610038161003816 + 120575 119870119862 = 119864119862|119864| + 10038161003816100381610038161198641198621003816100381610038161003816 + 120575

(4)


Δ119880 = 119870119864119864 + 119870119862119864119862 (5)


1199060119894 (119896) = 119870119880Δ119880 + 119870119868sumΔ119880 (6)




minus15

minus10

minus5

0

5

10

15

20

25Te

mpe

ratu

re(∘

C)

500 1000 1500 2000 25000Time (s)



3

4

5

6

7

8

Tem

pera

ture

(∘C)

500 1000 1500 20000Time (s)




119906119902119895 (119896) = 2sum119894=1

120596119894119895 (119896) 1199060119894 (119895 = 1 2) (7)


119864 (119896) = 122sum119894=1

[119903119894 (119896) minus 119910119894 (119896)]2 (119894 = 1 2) (8)



120596119894119895 (119896 + 1) = 120596119894119895 (119896) minus 120578 120597119864 (119896)120597120596119894119895 (119896) (9)


120597119864 (119896)120597120596119894119895 (119896) = minus2sum119894=1

[119903119894 (119896) minus 119910119894 (119896)] sdot 120597119910119894 (119896)120597119906119902119895 (119896) sdot 1199060119894 (10)










100 200 300 400 5000Time (s)

minus16

minus15

minus14

minus13

minus12

minus11

minus10Te

mpe

ratu

re(∘

C)



48

5

52

54

56

58

6

Tem

pera

ture

(∘C)

50 100 150 2000Time (s)




minus10

minus99

minus98

minus97

minus96

minus95

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)



1

15

2

25

3

35

4

45

5

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)






5 Conclusions







References


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




minus15

minus10

minus5

0

5

10

15

20

25Te

mpe

ratu

re(∘

C)

500 1000 1500 2000 25000Time (s)



3

4

5

6

7

8

Tem

pera

ture

(∘C)

500 1000 1500 20000Time (s)




119906119902119895 (119896) = 2sum119894=1

120596119894119895 (119896) 1199060119894 (119895 = 1 2) (7)


119864 (119896) = 122sum119894=1

[119903119894 (119896) minus 119910119894 (119896)]2 (119894 = 1 2) (8)



120596119894119895 (119896 + 1) = 120596119894119895 (119896) minus 120578 120597119864 (119896)120597120596119894119895 (119896) (9)


120597119864 (119896)120597120596119894119895 (119896) = minus2sum119894=1

[119903119894 (119896) minus 119910119894 (119896)] sdot 120597119910119894 (119896)120597119906119902119895 (119896) sdot 1199060119894 (10)










100 200 300 400 5000Time (s)

minus16

minus15

minus14

minus13

minus12

minus11

minus10Te

mpe

ratu

re(∘

C)



48

5

52

54

56

58

6

Tem

pera

ture

(∘C)

50 100 150 2000Time (s)




minus10

minus99

minus98

minus97

minus96

minus95

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)



1

15

2

25

3

35

4

45

5

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)






5 Conclusions







References


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




100 200 300 400 5000Time (s)

minus16

minus15

minus14

minus13

minus12

minus11

minus10Te

mpe

ratu

re(∘

C)



48

5

52

54

56

58

6

Tem

pera

ture

(∘C)

50 100 150 2000Time (s)




minus10

minus99

minus98

minus97

minus96

minus95

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)



1

15

2

25

3

35

4

45

5

Tem

pera

ture

(∘C)

20 40 60 80 1000Time (s)






5 Conclusions







References


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







References


















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


fuzzy control of cold storage refrigeration system with dynamic coupling...

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