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Transient modeling of an air-cooled chiller with economized compressor. Part II: Application to control design
Applied Thermal Engineering 29 (2009) 2403–2407
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Transient modeling of an air-cooled chiller with economized compressor. Part II: Application to control design Wei-Jiang Zhang a, Shu-Fu Ding b, Chun-Lu Zhang b,* a b
Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai 200030, China China R&D Center, Carrier Corporation, 3239 Shen Jiang Road, Pudong, Shanghai 201206, China
a r t i c l e
i n f o
Article history: Received 19 November 2007 Accepted 15 December 2008 Available online 24 December 2008 Keywords: Air-cooled chiller Transient modeling Control PID Fuzzy logic
a b s t r a c t Based on the transient modeling developed in the previous paper, the control design of the air-cooled chiller is studied. The main electronic expansion valve (EXV) controls the suction superheat, the compressor controls the leaving water temperature and the sub EXV regulates the injection superheat. Since the system reliability is sensitive to the control of the suction superheat, it is the focus in this paper. Dynamic simulation cases are built to compare two control algorithms, PID and fuzzy logic. The case studies show that the fuzzy controller has higher reliability and performance. Both the two controllers are fully tested and tuned on a chiller test facility and the experiments indicate that the fuzzy controller works better as well. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Air source heat pumps are widely used in temperate zone and cool temperature zone. The EXV is usually adopted as the regulator of refrigerant flow in the refrigeration systems and heat pumps. The control design in the heating mode illustrated in Fig. 1 is investigated in this paper. The slide valve of the screw compressor can be modulated to match the heating capacity needed. Another approach to modulate the heating capacity is to close or open the economizer port of the compressor. In this system, the leaving water temperature is controlled at a fixed value and the entering water temperature actually reflects the required heating capacity. The main EXV controls the suction superheat (SH) and the sub EXV controls the injection superheat. When we tested the prototype to verify and refine the control design, it’s found that the suction superheat control is difficult. The reason is that the original control design couldn’t cover all the operating conditions and dynamic processes. For example, the control can work well under the rating operating conditions but fails when the ambient temperature is pretty low. Another typical tough case is frosting and defrosting control. The frosting process is a cumulative time-varying disturbance. It is very likely to result in the hunting and instability of the suction superheat. When the frost is heavy, the risk of the suction superheat is even higher. Apparently, the low suction pressure is a kind of common
* Corresponding author. Tel.: +86 21 3860 3010; fax: +86 21 3860 3156. E-mail address: [email protected] (C.-L. Zhang). 1359-4311/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.12.007
risks in the heating mode because both low ambient temperature and heavy frost will lower the suction pressure. Therefore, the suction superheat control is taken as the main objective of this investigation. One of the biggest challenges is to cover all the operating conditions and dynamic processes, particularly under the very low ambient temperature or with large, quick or cumulative dynamics. PID algorithm [1] is the classic control logic widely used in refrigeration systems. Fuzzy logic [2] is based on human reasoning and has better adaptability in a wide range of operating conditions. The applications of the fuzzy logic in refrigeration systems and heat pumps have been reported in some publications [3–5]. Model based control design has been well verified in numerous published works [6–8]. Compared with the experiment based method, it’s more efficient and cost effective. In this paper, both two control method are applied to control the suction superheat. The comparison of the two control methods is based on not only modeling but also experiments. 2. Control design As shown in Fig. 2, three modes are available in the main EXV controller. The fuzzy controller, PID controller or the manual mode can be switched depending on the settings. This controller is implemented both in the online control program and the simulation program. The controls mentioned above are programmed and built in the system model developed in Part I of the paper. Two controllers for the main EXV are studied and compared. Firstly, the controllers are
2404
W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
Nomenclature Kc Ku L1 L2
gain of PID ultimate gain of PID in Ziegler-Nicholas tuning interval length of the input error domain of fuzzy logic (°C) interval length of the input error changing rate domain in fuzzy logic (K/s)
tuned based on modeling so that the comparison can be done at the optimized settings. Secondly, two simulation cases are used to compare the quality of two controllers. 2.1. Fuzzy logic controller
L3 P Ti TD U
interval length of the output domain of fuzzy logic period (s) time constant of the integral block of PID (s) time constant of the derivative block of PID (s) output of the fuzzy logic
as the ultimate gain Ku. Note the period of the oscillations Pu. Lastly, the control parameters can be determined as follows.
K c ¼ K u =1:7
ð1Þ
T i ¼ Pu =2 T D ¼ Pu =8
ð2Þ ð3Þ
The membership functions of the input variables and output variables are same. The fuzzy sets and the membership function are defined in Fig. 3. The triangular membership function is selected and the range of variables is divided into five grades. Table 1 shows the fuzzy rules and the five fuzzy subsets used to characterize the input and output linguistic variables which are marked with the following labels: big negative (BN), SN (small negative), zero (ZE), small positive (SP), and big positive (BP). And U is the output step change of EXV. The controller’s input error is defined as the superheat minus its set point. Finally, the center-of-gravity method is adopted as the defuzzification method.
Fuzzy Controller Switch PID Controller
EXV
Manual
2.2. Controller tuning 1
Error
The Ziegler–Nicholas method [1] is used to tune the PID parameters. First, set the controller to P mode only. Secondly, set the gain of the controller Kc to a small value. Give a step-function signal to the ambient temperature and observe the response of the suction superheat. Here the height of the signal is 0.5 °C. If Kc is low, the response should be sluggish. Keep increasing Kc until a response is obtained that produces continuous oscillations. This is known
Reciever
SH
Mux du/dt Derivative Fig. 2. Schematic of the main EXV controller.
Shell-and-tube condenser Leaving water
Sub EXV Economizer(BPHX)
SubEXV Controller
MainEXV Controller
Superheat
Set point
+ _
Entering water Water pump
LWT Screw compressor
Compressor Controller
Main EXV Finned-tube Coil Accumulator
Component Control loop Superheat Fig. 1. Schematic of system configurations and control loops in the heating mode.
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W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
Degree of memebership
1.2 BN
1
SN
Z E
SP
-1
0 Variable
1
BP
0.8 0.6 0.4 0.2 0
-4
-3
-2
2
3
4
Fig. 3. Membership function of fuzzy logic. Table 1 Rules of fuzzy logic. U
Rate of change of error
Error
BN SN ZE SP BP
BN
SN
ZE
SP
BP
BN BN BN SN ZE
BN SN SN ZE SP
BN SN ZE SP BP
SN ZE SP SP BP
ZE SP BP BP BP
Table 2 Membership function tuning of fuzzy logic.
1 2 3 4 5
L1 (°C)
L2 (°C/s)
L3 (%)
0.25 0.80 0.80 0.80 0.60
0.1 0.30 0.15 0.15 0.15
1.5 1.5 1.5 2.0 1.5
The details of PID tuning are shown in Fig. 4. Since Ku = 0.35000 and Pu = 241.8 s, the PID controller settings are yielded as Kc = 0.20588, Ti = 120.9 s and TD = 30.2 s. To tune of the fuzzy controller, the interval length is selected as the adjusting factor rather than the fuzzy rule table. Here the interval length is named as L1, L2 and L3, respectively. L1 represents the interval length of input superheat error. L2 stands for the interval length of input error’s changing rate. L3 is the interval length of output. For instance, the error domain of the suction superheat can be expressed as [2L1, L1, 0, L1, 2L1]. Since there is no efficient way to do fuzzy controller tuning, a kind of trail-and-error procedure is accepted to optimize the three parameters. Similar as the tuning of the PID controller settings, the same step-function signal of ambient temperature is used as the disturbance signal. Then multiple sets of the parameters defined in Table 2 are given to the fuzzy controller and the response curves are recorded as shown in Fig. 5. In this figure, the simulated cases are sorted with the numbering from A to E which corresponds with 1 to 5 in Table 2. More cases in addition to those in Table 2 have been studied. The third set is the best and chosen as optimized one. 2.3. Case study Two cases are built to compare the PID controller and the fuzzy controller. The entering water temperature is used as the disturbance signal and it is a sine type curve shown in Fig. 6. The variation of the entering water temperature means the load change and it is a typical disturbance to chillers. The control parameters are obtained in Section 2.2. The compressor controller and the sub EXV controller are used to control the leaving water temperature and the injection superheat, respectively. PID algorithm is selected for the compressor controller and the sub EXV controller. The settings of them in all simulation cases are same. In summary,
15.4 44 42
EWT ( )
Superheat (K)
15.2 15
14.8
P u = 241.8s
40 38
K u = 0.35
14.6
0
100
200
300 Time (s)
400
500
600
Fig. 4. Superheat fluctuation in Ziegler–Nichols closed-loop tuning method.
36
0
100
200
300 Time (s)
400
500
600
Fig. 6. Entering water temperature (EWT) used as disturbance signal.
Fig. 5. Superheat in fuzzy controller settings tuning.
W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
the settings and the initial states of the system model are listed in Table 3. As shown in Figs. 7 and 8, the fluctuation of SH and SST with the fuzzy logic is much smaller than those with the PID controller. Moreover, the PID controller cannot keep saturated suction temperature (SST) stable, which is caused by slow action and poor adaptability of the PID controller. The actions of the main EXV can be seen in Fig. 9. The regulation of the fuzzy controller is faster than the PID controller. It is very important to keep SST and superheat stable, particularly when the outdoor ambient temperature is low. Too low SST (or suction pressure) should be prevented for the compressor protection. When the outdoor ambient temperature is low, the suction pressure will be close to the limit which triggers the alarm and protection. If the main EXV moves frequently and acutely, the suction pressure will fluctuate strongly and the system could be out of control. The leaving water temperature (LWT) is shown in Fig. 10. It can be seen that LWT under the control of the fuzzy logic is a little bit
Table 3 The settings and initial steady states. Settings
Initial states
Work fluid Ambient DB/WB temperature (°C) Air mass flow rate (kg/s) Water mass flow rate (kg/s)
R134a 2/1
Compressor load Main EXV
100% 35.87%
35.4 14.2
72.71% 12.4
Refrigerant charge (kg)
134
Suction superheat set point (°C) Leaving water temperature set point (°C)
15 45
Sub EXV Saturated suction temperature (°C) Saturated discharge temperature (°C) Suction superheat (°C) Subcooling (°C)
48.5 15 4.3
45 Fuzzy
Opening (%)
2406
35
25 PID
15 0
100
200
300 Time (s)
400
500
600
Fig. 9. Opening of the main EXV.
higher than that under the control of the PID controller, which means larger heating capacity is got in the first case. Saturated discharge temperature and subcooling are measured and shown in Figs. 11 and 12, respectively. Figs. 13 and 14 show the smooth switch between the economized mode and the noneconomized mode. When the compressor load is lower than 75%, the economizer port will be closed and the system will turn to the non-economized mode. 3. Control validation Online tuning is performed to the PID controller and the fuzzy logic controller, respectively. The model-based tuning results got in Section 2.2 are selected as the initial values of the controller parameters. By a trail-and-error procedure, the optimal parameter set has been got. The online optimized settings are not far from the tuning results got from modeling. Based on the well tuned controllers, some transient curves are recorded shown in Figs. 15 and 16. The operating conditions are the same as those defined in Table 3. In the frosting process, the
20 Fuzzy
48
12 8
PID
)
Fuzzy
46
LWT (
Superheat (K)
16
44
4
42
0
40
PID
0
100
200
300 Time (s)
400
500
0
600
100
200
300 Time (s)
400
500
600
Fig. 10. Predicted leaving water temperature (LWT).
Fig. 7. Predicted suction superheat.
50
-10 Fuzzy
Fuzzy
48 SDT ( )
SST ( )
-12 -14
46
PID
-16 PID
-18 0
100
200
300 Time (s)
400
500
Fig. 8. Predicted saturated suction temperature (SST).
600
44
0
100
200
300 Time (s)
400
500
Fig. 11. Predicted saturated discharge temperature (SDT).
600
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W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
6 Set point =16K
Superheat (K)
Subcooling (K)
Fuzzy
18
Fuzzy
5 4 3 2
15 12 PID
9
PID
1 6
0 0
100
200
300 Time (s)
400
500
600
0
200
400
600 Time (s)
800
1000
1200
Fig. 15. Measured suction superheat under frosting condition. Fig. 12. Predicted subcooling at condenser outlet.
-5
Fuzzy
1
Fuzzy
SST ( )
Economizer on/off
-9
PID
-13 PID
-17 -21
0 0
100
200
300 Time (s)
400
500
600
-25
0
200
400
600 Time (s)
800
1000
1200
Fig. 13. Economized/non-economized mode switch. Fig. 16. Measured saturated suction temperature under frosting condition.
110
and fuzzy logic of the main EXV. The predicted results show that the fuzzy logic controller has better quality than the PID controller. Under the fuzzy logic controller, response curves of SH and SST are more stable, while the risk of too low suction pressure is also reduced. The optimized parameters obtained based on modeling are used as initial settings of the online fine tuning. With the best settings of online tuning, the fuzzy logic controller and the PID controller are fully tested. The experiment results also show that the fuzzy logic controller is the better one.
Compressor load (%)
Fuzzy
100 90 80
75%
70 60
PID
0
100
200
300 400 Time (s)
500
600
Fig. 14. Compressor load change with economized/non-economized mode switch.
growth of the frost keeps reducing the heat transfer on air side, which drives SST drop. The comparison illustrates the fuzzy logic controller is better than the PID controller in this case, not only SH is more stable but also SST drops less. The fuzzy logic controller improves the stability and performance of the system. 4. Conclusion The control design of an air-cooled chiller in heat mode is investigated based on transient modeling and experiments. Firstly, controller tuning is executed based on modeling. Using the optimized controls, simulation cases are built to compare PID
References [1] M. J. Willis. Proportional-Integral-Derivative control 1999 [Online]. Available from: http://lorien.ncl.ac.uk/ming/pid/PID.pdf. [2] L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353. [3] J.Y.M. Cheung, A.S. Kamal, Fuzzy logic control of refrigerant flow, UKACC International Conference on Control, (1996) 125–130. [4] C. Aprea, R. Mastrullo, C. Renno, Fuzzy control of the compressor speed in a refrigeration plant, International Journal of Refrigeration 27 (2004) 639–648. [5] X.X. Zhou, J. Xia, X.Q. Jin, Z.F. Zhou, Study on fuzzy control of electronic valve in the air-conditioner with inverter, in: 20th International Congress of Refrigeration, Sydney, paper, 588 (1999). [6] J.V.C. Vargas, J.A.R. Parise, Simulation in transient regime of a heat pump with close-loop and on-off control, International Journal of Refrigeration 18 (4) (1995) 235–243. [7] X.D. He, S. Liu, H. Asada, H. Itoh, Multivariable control of vapor compression systems, HVAC&R Research 4 (3) (1998) 205–230. [8] R. Shah, A.G. Alleyne, C.W. Bullard, B.P. Rasmussen, P.S. Hrnjak, Dynamic modeling and control multi-evaporator subcritical vapor compression systems, ACRC TR-216, 2003.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Transient modeling of an air-cooled chiller with economized compressor. Part II: Application to control design Wei-Jiang Zhang a, Shu-Fu Ding b, Chun-Lu Zhang b,* a b
Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai 200030, China China R&D Center, Carrier Corporation, 3239 Shen Jiang Road, Pudong, Shanghai 201206, China
a r t i c l e
i n f o
Article history: Received 19 November 2007 Accepted 15 December 2008 Available online 24 December 2008 Keywords: Air-cooled chiller Transient modeling Control PID Fuzzy logic
a b s t r a c t Based on the transient modeling developed in the previous paper, the control design of the air-cooled chiller is studied. The main electronic expansion valve (EXV) controls the suction superheat, the compressor controls the leaving water temperature and the sub EXV regulates the injection superheat. Since the system reliability is sensitive to the control of the suction superheat, it is the focus in this paper. Dynamic simulation cases are built to compare two control algorithms, PID and fuzzy logic. The case studies show that the fuzzy controller has higher reliability and performance. Both the two controllers are fully tested and tuned on a chiller test facility and the experiments indicate that the fuzzy controller works better as well. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Air source heat pumps are widely used in temperate zone and cool temperature zone. The EXV is usually adopted as the regulator of refrigerant flow in the refrigeration systems and heat pumps. The control design in the heating mode illustrated in Fig. 1 is investigated in this paper. The slide valve of the screw compressor can be modulated to match the heating capacity needed. Another approach to modulate the heating capacity is to close or open the economizer port of the compressor. In this system, the leaving water temperature is controlled at a fixed value and the entering water temperature actually reflects the required heating capacity. The main EXV controls the suction superheat (SH) and the sub EXV controls the injection superheat. When we tested the prototype to verify and refine the control design, it’s found that the suction superheat control is difficult. The reason is that the original control design couldn’t cover all the operating conditions and dynamic processes. For example, the control can work well under the rating operating conditions but fails when the ambient temperature is pretty low. Another typical tough case is frosting and defrosting control. The frosting process is a cumulative time-varying disturbance. It is very likely to result in the hunting and instability of the suction superheat. When the frost is heavy, the risk of the suction superheat is even higher. Apparently, the low suction pressure is a kind of common
* Corresponding author. Tel.: +86 21 3860 3010; fax: +86 21 3860 3156. E-mail address: [email protected] (C.-L. Zhang). 1359-4311/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2008.12.007
risks in the heating mode because both low ambient temperature and heavy frost will lower the suction pressure. Therefore, the suction superheat control is taken as the main objective of this investigation. One of the biggest challenges is to cover all the operating conditions and dynamic processes, particularly under the very low ambient temperature or with large, quick or cumulative dynamics. PID algorithm [1] is the classic control logic widely used in refrigeration systems. Fuzzy logic [2] is based on human reasoning and has better adaptability in a wide range of operating conditions. The applications of the fuzzy logic in refrigeration systems and heat pumps have been reported in some publications [3–5]. Model based control design has been well verified in numerous published works [6–8]. Compared with the experiment based method, it’s more efficient and cost effective. In this paper, both two control method are applied to control the suction superheat. The comparison of the two control methods is based on not only modeling but also experiments. 2. Control design As shown in Fig. 2, three modes are available in the main EXV controller. The fuzzy controller, PID controller or the manual mode can be switched depending on the settings. This controller is implemented both in the online control program and the simulation program. The controls mentioned above are programmed and built in the system model developed in Part I of the paper. Two controllers for the main EXV are studied and compared. Firstly, the controllers are
2404
W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
Nomenclature Kc Ku L1 L2
gain of PID ultimate gain of PID in Ziegler-Nicholas tuning interval length of the input error domain of fuzzy logic (°C) interval length of the input error changing rate domain in fuzzy logic (K/s)
tuned based on modeling so that the comparison can be done at the optimized settings. Secondly, two simulation cases are used to compare the quality of two controllers. 2.1. Fuzzy logic controller
L3 P Ti TD U
interval length of the output domain of fuzzy logic period (s) time constant of the integral block of PID (s) time constant of the derivative block of PID (s) output of the fuzzy logic
as the ultimate gain Ku. Note the period of the oscillations Pu. Lastly, the control parameters can be determined as follows.
K c ¼ K u =1:7
ð1Þ
T i ¼ Pu =2 T D ¼ Pu =8
ð2Þ ð3Þ
The membership functions of the input variables and output variables are same. The fuzzy sets and the membership function are defined in Fig. 3. The triangular membership function is selected and the range of variables is divided into five grades. Table 1 shows the fuzzy rules and the five fuzzy subsets used to characterize the input and output linguistic variables which are marked with the following labels: big negative (BN), SN (small negative), zero (ZE), small positive (SP), and big positive (BP). And U is the output step change of EXV. The controller’s input error is defined as the superheat minus its set point. Finally, the center-of-gravity method is adopted as the defuzzification method.
Fuzzy Controller Switch PID Controller
EXV
Manual
2.2. Controller tuning 1
Error
The Ziegler–Nicholas method [1] is used to tune the PID parameters. First, set the controller to P mode only. Secondly, set the gain of the controller Kc to a small value. Give a step-function signal to the ambient temperature and observe the response of the suction superheat. Here the height of the signal is 0.5 °C. If Kc is low, the response should be sluggish. Keep increasing Kc until a response is obtained that produces continuous oscillations. This is known
Reciever
SH
Mux du/dt Derivative Fig. 2. Schematic of the main EXV controller.
Shell-and-tube condenser Leaving water
Sub EXV Economizer(BPHX)
SubEXV Controller
MainEXV Controller
Superheat
Set point
+ _
Entering water Water pump
LWT Screw compressor
Compressor Controller
Main EXV Finned-tube Coil Accumulator
Component Control loop Superheat Fig. 1. Schematic of system configurations and control loops in the heating mode.
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W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
Degree of memebership
1.2 BN
1
SN
Z E
SP
-1
0 Variable
1
BP
0.8 0.6 0.4 0.2 0
-4
-3
-2
2
3
4
Fig. 3. Membership function of fuzzy logic. Table 1 Rules of fuzzy logic. U
Rate of change of error
Error
BN SN ZE SP BP
BN
SN
ZE
SP
BP
BN BN BN SN ZE
BN SN SN ZE SP
BN SN ZE SP BP
SN ZE SP SP BP
ZE SP BP BP BP
Table 2 Membership function tuning of fuzzy logic.
1 2 3 4 5
L1 (°C)
L2 (°C/s)
L3 (%)
0.25 0.80 0.80 0.80 0.60
0.1 0.30 0.15 0.15 0.15
1.5 1.5 1.5 2.0 1.5
The details of PID tuning are shown in Fig. 4. Since Ku = 0.35000 and Pu = 241.8 s, the PID controller settings are yielded as Kc = 0.20588, Ti = 120.9 s and TD = 30.2 s. To tune of the fuzzy controller, the interval length is selected as the adjusting factor rather than the fuzzy rule table. Here the interval length is named as L1, L2 and L3, respectively. L1 represents the interval length of input superheat error. L2 stands for the interval length of input error’s changing rate. L3 is the interval length of output. For instance, the error domain of the suction superheat can be expressed as [2L1, L1, 0, L1, 2L1]. Since there is no efficient way to do fuzzy controller tuning, a kind of trail-and-error procedure is accepted to optimize the three parameters. Similar as the tuning of the PID controller settings, the same step-function signal of ambient temperature is used as the disturbance signal. Then multiple sets of the parameters defined in Table 2 are given to the fuzzy controller and the response curves are recorded as shown in Fig. 5. In this figure, the simulated cases are sorted with the numbering from A to E which corresponds with 1 to 5 in Table 2. More cases in addition to those in Table 2 have been studied. The third set is the best and chosen as optimized one. 2.3. Case study Two cases are built to compare the PID controller and the fuzzy controller. The entering water temperature is used as the disturbance signal and it is a sine type curve shown in Fig. 6. The variation of the entering water temperature means the load change and it is a typical disturbance to chillers. The control parameters are obtained in Section 2.2. The compressor controller and the sub EXV controller are used to control the leaving water temperature and the injection superheat, respectively. PID algorithm is selected for the compressor controller and the sub EXV controller. The settings of them in all simulation cases are same. In summary,
15.4 44 42
EWT ( )
Superheat (K)
15.2 15
14.8
P u = 241.8s
40 38
K u = 0.35
14.6
0
100
200
300 Time (s)
400
500
600
Fig. 4. Superheat fluctuation in Ziegler–Nichols closed-loop tuning method.
36
0
100
200
300 Time (s)
400
500
600
Fig. 6. Entering water temperature (EWT) used as disturbance signal.
Fig. 5. Superheat in fuzzy controller settings tuning.
W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
the settings and the initial states of the system model are listed in Table 3. As shown in Figs. 7 and 8, the fluctuation of SH and SST with the fuzzy logic is much smaller than those with the PID controller. Moreover, the PID controller cannot keep saturated suction temperature (SST) stable, which is caused by slow action and poor adaptability of the PID controller. The actions of the main EXV can be seen in Fig. 9. The regulation of the fuzzy controller is faster than the PID controller. It is very important to keep SST and superheat stable, particularly when the outdoor ambient temperature is low. Too low SST (or suction pressure) should be prevented for the compressor protection. When the outdoor ambient temperature is low, the suction pressure will be close to the limit which triggers the alarm and protection. If the main EXV moves frequently and acutely, the suction pressure will fluctuate strongly and the system could be out of control. The leaving water temperature (LWT) is shown in Fig. 10. It can be seen that LWT under the control of the fuzzy logic is a little bit
Table 3 The settings and initial steady states. Settings
Initial states
Work fluid Ambient DB/WB temperature (°C) Air mass flow rate (kg/s) Water mass flow rate (kg/s)
R134a 2/1
Compressor load Main EXV
100% 35.87%
35.4 14.2
72.71% 12.4
Refrigerant charge (kg)
134
Suction superheat set point (°C) Leaving water temperature set point (°C)
15 45
Sub EXV Saturated suction temperature (°C) Saturated discharge temperature (°C) Suction superheat (°C) Subcooling (°C)
48.5 15 4.3
45 Fuzzy
Opening (%)
2406
35
25 PID
15 0
100
200
300 Time (s)
400
500
600
Fig. 9. Opening of the main EXV.
higher than that under the control of the PID controller, which means larger heating capacity is got in the first case. Saturated discharge temperature and subcooling are measured and shown in Figs. 11 and 12, respectively. Figs. 13 and 14 show the smooth switch between the economized mode and the noneconomized mode. When the compressor load is lower than 75%, the economizer port will be closed and the system will turn to the non-economized mode. 3. Control validation Online tuning is performed to the PID controller and the fuzzy logic controller, respectively. The model-based tuning results got in Section 2.2 are selected as the initial values of the controller parameters. By a trail-and-error procedure, the optimal parameter set has been got. The online optimized settings are not far from the tuning results got from modeling. Based on the well tuned controllers, some transient curves are recorded shown in Figs. 15 and 16. The operating conditions are the same as those defined in Table 3. In the frosting process, the
20 Fuzzy
48
12 8
PID
)
Fuzzy
46
LWT (
Superheat (K)
16
44
4
42
0
40
PID
0
100
200
300 Time (s)
400
500
0
600
100
200
300 Time (s)
400
500
600
Fig. 10. Predicted leaving water temperature (LWT).
Fig. 7. Predicted suction superheat.
50
-10 Fuzzy
Fuzzy
48 SDT ( )
SST ( )
-12 -14
46
PID
-16 PID
-18 0
100
200
300 Time (s)
400
500
Fig. 8. Predicted saturated suction temperature (SST).
600
44
0
100
200
300 Time (s)
400
500
Fig. 11. Predicted saturated discharge temperature (SDT).
600
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W.-J. Zhang et al. / Applied Thermal Engineering 29 (2009) 2403–2407
6 Set point =16K
Superheat (K)
Subcooling (K)
Fuzzy
18
Fuzzy
5 4 3 2
15 12 PID
9
PID
1 6
0 0
100
200
300 Time (s)
400
500
600
0
200
400
600 Time (s)
800
1000
1200
Fig. 15. Measured suction superheat under frosting condition. Fig. 12. Predicted subcooling at condenser outlet.
-5
Fuzzy
1
Fuzzy
SST ( )
Economizer on/off
-9
PID
-13 PID
-17 -21
0 0
100
200
300 Time (s)
400
500
600
-25
0
200
400
600 Time (s)
800
1000
1200
Fig. 13. Economized/non-economized mode switch. Fig. 16. Measured saturated suction temperature under frosting condition.
110
and fuzzy logic of the main EXV. The predicted results show that the fuzzy logic controller has better quality than the PID controller. Under the fuzzy logic controller, response curves of SH and SST are more stable, while the risk of too low suction pressure is also reduced. The optimized parameters obtained based on modeling are used as initial settings of the online fine tuning. With the best settings of online tuning, the fuzzy logic controller and the PID controller are fully tested. The experiment results also show that the fuzzy logic controller is the better one.
Compressor load (%)
Fuzzy
100 90 80
75%
70 60
PID
0
100
200
300 400 Time (s)
500
600
Fig. 14. Compressor load change with economized/non-economized mode switch.
growth of the frost keeps reducing the heat transfer on air side, which drives SST drop. The comparison illustrates the fuzzy logic controller is better than the PID controller in this case, not only SH is more stable but also SST drops less. The fuzzy logic controller improves the stability and performance of the system. 4. Conclusion The control design of an air-cooled chiller in heat mode is investigated based on transient modeling and experiments. Firstly, controller tuning is executed based on modeling. Using the optimized controls, simulation cases are built to compare PID
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