Energy and Buildings 42 (2010) 386–392

Fuzzy control model and simulation of supply air system in a test rig oflow-temperature hot-water radiator system

Zhen Lu a,*, Jili Zhang a, Yongpan Chen b, Tianyi Zhao b, Hui Liu c

a School of Civil & Hydraulic Engineering, Dalian University of Technology, Dalian 116024, Chinab School of Municipal & Environmental Engineering, Harbin Institute of Technology, Harbin, Chinac Beijing Siemens Cerberus Electronics Ltd, Beijing, China

A R T I C L E I N F O

Article history:

Received 12 March 2009

Accepted 2 October 2009

Keywords:

Built environment chamber

Parameter identification

Self-extracting rules fuzzy control

Control simulation

A B S T R A C T

This paper proposes a typical multi-variable, large time delay and nonlinear system, self-extracting rules

fuzzy control (SERFC) method to maintain a stable temperature value in a built environment chamber

with supply air system and hot-water system. The parameters of the transfer functions in every control

loop were identified by experimental data in a format of time sequences obtained from the experiment of

dynamical responding performance. Fuzzy control simulations were implemented based on adjustment

of the supply air system and hot-water system by SERFC. The simulation results show that SERFC for

environment chamber has satisfied performance. There is no higher overshoot and stable error. The work

presented in here can be used to deal with those complex thermal processes with difficulties in modeling

of fuzzy control rules and provide a foundation for further application of fuzzy control in HVAC system.

� 2009 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

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1. Introduction

The test rig of low-temperature hot-water radiator system is animportant test set-up to measure radiator performance used inbuilding. To maintain a stable temperature in the environmentchamber (used in the test set-up), taking the test rig as objective tostudy the control algorithm, it can not only obtain accuratemeasurement results, but also can comprehensively ascertain thethermal behaviour of building and HVAC equipments.

Application of fuzzy control in HVAC system has beeninvestigated extensively [1–3], for examples: cascade fuzzy control[4], adaptive optimal control with fuzzy self-tuning forgettingfactor method [5], adaptive neuro-fuzzy [6], self-tuning PID-typefuzzy adaptive control [7]. PID control is considered to be acommon control algorithm for linear systems with short or nodelay time in the thermal process. However, for nonlinear systemswith large delay time, it has encountered many difficulties. Tosolve these problems, fuzzy control, especially self-organizingfuzzy control, appears to be an effective utility [8–12].

Fig. 1 shows a test rig of low-temperature hot-water radiatorsystem, which consists of a built environment chamber, supply airsystem, hot-water system, refrigeration system and monitoringand control system [13]. Fig. 2 is the built environment chamberused to test the performance of thermal characteristic of the HVACsystem and device. It is built with a steel envelop, insulation layer

* Corresponding author. Tel.: +86 411 84706713; fax: +86 411 84706713.

E-mail addresses: zludlut@gmail.com, zluhit@126.com (Z. Lu).

0378-7788/$ – see front matter � 2009 Elsevier B.V. All rights reserved.

doi:10.1016/j.enbuild.2009.10.006

outside and rectangular duct inside. Its dimensions are3976 mm � 3976 mm � 2800 mm. The supply air system, shownin Fig. 3, consists of an evaporator and an electric heater thatregulates electric heating load to control supply air temperature(SAT) and maintain a stable chamber temperature. The designsupply air flow rate is 11,000 m3/h. The hot-water system is shownin Fig. 4, in which the supply water temperature of the elevatedwater tank and inlet temperature of radiator are required to bestable. It is seen that the chamber temperature, supply watertemperature of elevated water tank and inlet temperature ofradiator are critical control targets. According to control systemfunction and various control parameters, the test rig controlsystem can be categorized into 2 system types and 5 control loops,as shown in Table 1.

According to the characteristic of control loops discussed inTable 1, this paper firstly presents self-extracting rules fuzzycontrol (SERFC) method, then identifies the transfer function ofeach involved control loop by experiment, finally carries out fuzzycontrol simulation of the chamber temperature control processusing SERFC.

2. Self-extracting rules fuzzy control method (SERFC)

2.1. Basic structure of SERFC controller

Fig. 5 shows the SERFC controller structure. ANN represents theneutral network model of the controlled process. The trianglemembership function profile of each variable is shown in Fig. 6.

Fig. 2. Built environment chamber.

Fig. 4. Schematic diagram of water system.

Fig. 3. Schematic diagram of air system.

Fig. 1. Test rig of low-temperature hot-water radiator system.

Z. Lu et al. / Energy and Buildings 42 (2010) 386–392 387

The fuzzy control rule adopts Mamdani type fuzzy control rule,as shown in Eq. (1) and Table 2:

ifx1 isAi1; x2 isAi

2; . . . ; xn isAin theny1 isBi (1)

where, i = 1, 2, . . ., m, m is total number of control rules.Table 2 shows the initial fuzzy control rule, where Ai and Bi are

input fuzzy set, Cij is output fuzzy set, where i,j = 1, 2, . . ., n; NB(Negative Big), NM (Negative Medium), NS (Negative Small), ZE(Zero), PS (Positive Small), PM (Positive Medium), and PB (PositiveBig) are different fuzzy grades.

2.2. Implementation method

Assume the delay time of controlled objective is dT, whichmeans the response at kT from the control effects at (k � d)T.Therefore, the fuzzy control rule at (k � d)T can be adjusted by

Table 1Control loops of test rig of low-temperature hot-water radiator system.

Control loop number Control loop and its delay time characteristic

LP-1 Regulates electric heating load to maintain SAT with short

LP-2 Regulates electric heating load to maintain chamber tempe

LP-3 Regulates electric heating load to maintain supply water te

LP-4 Regulates electric heating load to maintain inlet temperatu

LP-5 Regulates electric heating load to maintain chamber tempe

performance evaluation and calibration rule table (shown inTable 3) according to the responds at kT. With the reference of thenew fuzzy control rule table updated by the calibration rules, thecontrol process is carried out more accurately.

Step 1: Identification of functioning fuzzy control rule. Usingthe method of functioning-fuzzy-subset inference [14], thefunctioning fuzzy control rule can be obtained based one*((k � d)T) and ec*((k � d)T).

Step 2: Identification of calibrated value for consequent offunctioning fuzzy control rule at (k � d)T. As Fig. 5 shown, thealgorithm deliver e*((k � d)T) and ec*((k � d)T) to self-organizing

System type

delay time Supply air system

rature with larger delay time than LP-1

mperature of elevated water tank with short delay time Hot-water system

re of radiator with larger delay time than LP-3

rature with larger delay time than LP-4

Fig. 5. Structure of the SERFC.

Fig. 6. Triangle membership function.

Z. Lu et al. / Energy and Buildings 42 (2010) 386–392388

module. Then the calibrated value of consequent of functioningfuzzy control rule, DCij ((k � d)T), is obtained using functioning-fuzzy-subset inference.

Step3: Calibration of consequent of functioning fuzzy controlrule at (k � d)T. Integrated with Table 2 and Cij((k � d)T), algorithmdeals with the consequent (k � d)T according the Eq. (2), where Cij

((k + 1)T) is defined as the functioning control rule at (k + 1)T:

C i jððkþ 1ÞTÞ ¼ C i jððk� dÞTÞ þDC i jððk� dÞTÞ (2)

Table 2Initial fuzzy control rule.

Ai Bj

NB NM NS ZE PS PM PB

NB PB PB PM PM PS PS ZE

NM PB PM PM PS PS ZE NS

NS PM PM PS PS ZE NS NS

ZE PM PS PS ZE NS NS NM

PS PS PS ZE NS NS NM NM

PM PS ZE NS NS NM NM NB

PB ZE NS NS NM NM NB NB

Note: Values in table are fuzzy value of Cij.

3. Indentification of transfer function

3.1. Transfer function

Ignoring the thermal storage of the 2 mm thick steel envelopand assuming the distribution of temperature field in chamber andduct is uniform, without consideration of the affecting factor ofhot-water system, based on the energy conservation law andLaplace transform theory, the transfer function of chambertemperature and average supply air temperature could be writtenas Eqs. (3) and (4):

uaverðsÞQEaðsÞ

¼ mrCpasþ KaFa

mrCpamacpas2 þ KaFaðmrCpa þmacpaÞs(3)

uRoomðsÞQEaðsÞ

¼ KaFa

mrCpamaCpas2 þ KaFaðmrCpa þmaCpaÞs(4)

where uRoom, uaver and QEa are Laplace transform value of chambertemperature, average temperature of supply air and electric heaterpower, respectively; QEa is power of electric heater in supply airsystem, kW; mr is chamber air mass, kg; ma is supply air mass

Table 3Calibration rule table of self-organizing module.

ec e

NB NM NS ZE PS PM PB

NB �6 �6 �4 �4 �2 �2 0

NM �6 �4 �4 �2 �2 0 2

NS �4 �4 �2 �2 0 2 2

ZE �4 �2 �2 0 2 2 4

PS �2 �2 0 2 2 4 4

PM �2 0 2 2 4 4 6

PB 0 2 2 4 4 6 6

Note: Values in table are u0 .

Z. Lu et al. / Energy and Buildings 42 (2010) 386–392 389

supplied by wall duct, kg; Cpa is air specific heat at constantpressure, kJ/(kg 8C); TRoom is chamber temperature, 8C; Taver is theaverage temperature of supply air temperature and return airtemperature, 8C; Ka is heat transfer coefficient of envelop, W/(m2 8C); Fa is heat transfer area of envelop, m2.

It is seen from Eqs. (3) and (4) that LP-1 and LP-2 both aresecond-order system. In LP-1, the input variable and outputvariable are electric heater power and average temperature ofsupply air, respectively. In LP-2, the input variable and outputvariable are electric heater power and chamber temperature,respectively. The unknown parameters in Eqs. (3) and (4) will beidentified by test data.

3.2. Transfer function identification of LP-1

The difference form of Eq. (3) can be written as

TaverðkTÞ ¼ a1TaverðkT � TÞ þ a2TaverðkT � 2TÞ þ b1QEaðkT

� TÞ þ b2QEaðkT � 2TÞ (5)

where a1, a2, b1, and b2 are equation coefficients need to beidentified.

According to the identification demands, the experiment adoptsa sampling period of 10 s, in each sampling period, the continuousrunning time of electric heater is 2 s with 20% power while the hot-water system is not working. Based on the experiment resultsshown in Figs. 7 and 8, the identified z transfer function is obtained

Fig. 7. Identification results of z transfer function of average supply air temperature

to electrical heating load.

Fig. 8. Identification results of z transfer function of chamber temperature to

electrical heating load.

as

uaverðzÞQEaðzÞ

¼ 0:02629z

z2 � 0:6382z� 0:36(6)

Fig. 7 compares the output of Eq. (6) with the test results, alsoprovides identified results of the 3-order model of Eq. (6), it is seenfrom the comparison results that the 2-order model could satisfythe identification accuracy.

3.3. Transfer function identification of LP-2

From the test we can see that the delay time of the chambertemperature to electric heating load is 260 s. Because the electricheating signal is a step type function and remains constant in theexperiment, the z transfer function can first be identified as Eq. (7)without consideration of delay characteristics:

uRoomðzÞQEaðzÞ

¼ 0:174z

z2 � 0:766z� 0:2252(7)

Considering the delay time and sample period, the z transferfunction can be presented as

uRoomðzÞQEaðzÞ

¼ 0:174z�25

z2 � 0:766z� 0:2252(8)

Fig. 8 shows the comparison results of Eq. (8) output and theexperiment results, the maximum absolute value identificationerror is 0.265 8C.

3.4. Transfer function identification of LP-3

The experiment adopts the sampling period of 8 s. In eachsampling period, the electric heater heats water with 100% powerwhile the supply air system is not working. With the aid of theidentification method of LP-1 z transfer function, LP-3 z transferfunction is obtained as

uWaterðzÞQEwðzÞ

¼ 0:02821z

z2 � 0:5904z� 0:4059(9)

where uWater and Q̄Ew is z transform value of supply watertemperature and electric heater power, respectively. Fig. 9compares output of Eq. (9) with the experiment results.

3.5. Transfer function identification of LP-4

The experiment adopts a sampling period of 4 s. In eachsampling period, the heating signal of electric heater is adopted as

Fig. 9. Identification results of z transfer function of supply water temperature to

electrical heating load.

Fig. 10. Experimental result of electrical heating load and inlet water temperature

of radiator. Fig. 12. Identification results of z transfer function of chamber temperature to

electrical heating load.

Z. Lu et al. / Energy and Buildings 42 (2010) 386–392390

square wave signal as shown in Fig. 10 while the supply air systemis not working. In Fig. 10, the delay time of inlet water temperatureto the electric heater and closed electric heater, Ton and Toff, isabout 150 s and 224 s, respectively. According to 6 times testresults, the delay time is adopted as 224 s.

The identification experiment adopts a sampling period of 8 swhile the electric heating is under rated power and the supply airsystem is closed. Ignoring the delay characteristic, the z transferfunction is obtained as

uRInðzÞQEwðzÞ

¼ 0:01144z

z2 � 1:412zþ 0:4135(10)

where uRIn refers to z transform value of inlet water temperature ofradiator.

Considering the 224 s delay time to LP-4, the z transfer functioncan be rewritten as

uRInðzÞQEwðzÞ

¼ 0:01144z�27

z2 � 1:412zþ 0:4135(11)

Fig. 11 shows the comparison results of Eq. (11) outputwith experiment results. Fig. 12 are identification results ofz transfer function of chamber temperature to electrical heatingload.

Fig. 11. Identification results of z transfer function of inlet water temperature to

electrical heating load.

3.6. Transfer function identification of LP-5

Ignoring the 420 s delay time of chamber temperature toelectric heater, the LP-5 z transfer function can be identified as

uRoomðzÞQEwðzÞ

¼ 0:0009814z

z2 � 0:8326z� 0:1984(12)

Considering the delay characteristic, the z transfer function can berewritten as

uRoomðzÞQEwðzÞ

¼ 0:0009814z�4

z2 � 0:8326z� 0:1984(13)

4. SERFC simulation

4.1. Case 1: regulating supply air system

The diagram of SERFC control system based on adjustment ofsupply air system is shown in Fig. 13. The cooling capacity of systemand heating capacity of radiator are considered to be the disturbanceof chamber temperature control. The controller determines theelectric heater power based on the error and variation rate of errorbetween chamber temperature and its set point.

In simulation stage, the initial control rules and the calibrationcontrol rules are adopted as zero rules and Table 3, respectively.The control period is 10 s. The practical domain of regulatingvariable, error and variation of error in basic fuzzy controller aredefined as [0, +6] kW, [�0.6, 0.6] 8C and [�0.2, 0.2] 8C, respectively.The practical domain of regulating variable, error and variation oferror in self-organizing module are defined as [�0.1, +0.1] kW,[�0.6, 0.6] 8C and [�0.2, 0.2] 8C, respectively. The simulationcondition is under 3 kW cooling load and 2.6 kW heating load. The

Table 4Calibrated rule table by the SERFC of chamber temperature by regulating supply air

temperature.

ec e

NB NM NS ZE PS PM PB

NB 0 0 0 0 0 0 0

NM 0 0 0 0 0 0 0

NS 0 0 �0.95 �1.42 �0.47 0 0

ZE 0 0 0.88 0.73 �0.15 0 0

PS 0 0 6.0 6.0 0.33 0 0

PM 0 0 6.0 6.0 0 0 0

PB 0 0 6.0 6.0 4.37 0 0

Note: Values in table are u. The bold values are the controller output value after

calibration by SERFC.

Fig. 13. Schematic diagram of rule self-organizing fuzzy control system of chamber temperature by regulating supply air temperature.

Fig. 14. Simulation result of the SERFC for chamber temperature by regulating

supply air temperature.

Table 5Calibrated rule table by the SERFC of chamber temperature by regulating supply

water temperature.

ec e

NB NM NS ZE PS PM PB

NB 0 0 0 0 0 0 0

NM 0 0 0 0 0 0 0

NS 0 0 �4.2 �6.0 �3.68 0 0

ZE 0 0 1.46 �0.75 �2.20 0 0

PS 0 0 6.0 6.0 1.47 0 0

PM 0 0 6.0 6.0 0 0 0

PB 0 0 6.0 6.0 1.99 0 0

Note: Values in table are u. The bold values are the controller output value after

calibration by SERFC.

Z. Lu et al. / Energy and Buildings 42 (2010) 386–392 391

aim of the control simulation is to increase the chambertemperature by 1 8C and then to keep it stable.

Fig. 14 is the simulation results and Table 4 is the adjustedcontrol rules. It is seen from Fig. 14 that the chamber temperatureslowly increases with satisfied overshoot. It can be concluded fromTable 3 that only the control rules in the central table isfunctioning.

4.2. Case 2: regulating hot-water system

LP-5, the control loop with largest delay time among LP-3 to LP-5, is selected to be simulated loop to control chamber temperature.

Fig. 15. Schematic diagram of the SERFC of chamber tem

The construction of its control system is shown in Fig. 15. Theinitial control rules and the adjusting control rules are adopted aszero rules and Table 3, respectively. The control period is 80 s. Thepractical domain of regulating variable, error and variation of errorin basic fuzzy controller are defined as within [0, +6] kW, [�0.6,0.6] 8C and [�0.2, 0.2] 8C, respectively. The practical domain ofregulating variable, error and variation of error in self-organizingmodule are defined as [�0.1, +0.1] kW, [�0.6, 0.6] 8C and [�0.2,0.2] 8C, respectively. The simulation condition is under 3 kWcooling load and 2.5 kW heating load. The aim of the controlsimulation is to increase the chamber temperature by 1 8C andthen to keep it stable. Fig. 15 presents the simulation results andTable 5 shows the adjusted control rules.

From Fig. 16 we can see that SERFC obtained satisfied controlperformance with small overshoot. The results show that the

perature by regulating supply water temperature.

Fig. 16. Simulation result of the SERFC of chamber temperature by regulating supply

water temperature.

Z. Lu et al. / Energy and Buildings 42 (2010) 386–392392

simulated method is suitable for the process control of large timedelay control loop like LP-5.

5. Conclusions

The low-temperature hot-water radiator test rig that consists ofbuilt environment chamber, supply air system, hot-water systemand refrigeration system, is a typical thermal system withnonlinearity, multi-variables and large delay time. SERFC methodand control loops LP-1–LP-5 extracted from the test rig are present.z transfer function of each loop by experiment is identified. Thecontrol process of supply air system and hot-water system usingSERFC method are simulated. The following conclusions can bedrawn:

(1) For z transfer function of each chamber temperature based onsupply air system and hot-water system, 2-order type inertialsystem model could accurately describe the dynamic thermalcharacteristic of each control loops through the comparisonstudy with 3-order model output and test results.

(2) LP-1 and LP-3 are both basic 2-order inertial systems and thetime-delayed characteristics can be ignored during theinvestigation and control process. The other control loopsincluding LP-2, LP-4 and LP-5, are typical 2-order inertial

systems with time delay. Their delay time is 7 min, particularlyfor LP-5.

(3) Simulation results of LP-2 and LP-5 shows that the SERFCmethod has satisfied control accuracy with a small overshoot.Furthermore, SERFC is proved to be an effective way to dealwith those complex thermal processes with difficulties inmodeling of fuzzy control rules. The algorithm of adjusting andself-extracting of fuzzy control rules is also capable ofobtaining proper fuzzy control rules and satisfied controlperformance.

Acknowledgements

This project is supported by National Natural Science Founda-tion of China (50578049) and Key Projects in the National Science& Technology Pillar Program in the Eleventh Five-year Plan Period(2006BAJ01A09, 2008BAJ12B05).

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