fuzzy rough set

8/12/2019 Fuzzy Rough Set

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A Fuzzy Logic and Rough Sets Controllerfor HVAC SystemsMasanori Arima, Elmer H. Hara, Jack D. Katzberg,Faculty of EngineeringUniversity of ReginaRegina, Saskatchewan, S4S OA2

Abstract - This paper will describe an W A C(Heating, Ventilating and Air Conditioning) systemcontroller which em ploys a control algorithm using theseeither fuzzy logic reasoning or rough set theory. Thecontroller deduces the appropriate control outputs fromsensor readings. The system is capable of controllingtemperature and humidity. To maintain temperature atthe referen ce point, the con troller adjusts the flow of hotwater in a heating coil for heating operation or the flowof chilled air through the air duct for cooling operation.To control humidity, the controller turns on and off ahumidifier.

I. INTRODUC TIONThe HVAC system is needed to provide the occupants

with a comfortable and productive working environmentwhich satisfies their physiological needs.Temperature and relative humidity are essential factorsin meeting physiological requirements. When tem perature isabove or below the comfort range, the environment disruptsperson's metabolic processes and disturbs his activities.Therefore, an HV AC system is essential to a building inorder to keep occupants comfortable. Howev er, many HVA Csystems do not maintain a uniform temperature throughoutthe structure because those systems employ anunsophisticated control algorithms. In a modern intelligentbuilding a sophisticate control system should provideexcellent environmental control. The aim of this work is toprovide an HVAC control system compatible with theambiance the designer of intelligent buildings wish to create.

11. CON TRO LLE RChilled air of 16 C to 20 C is supplied through an air

I

SystemControl

IFig. 1.HVA C control system.

duct to moderate room temperature for all seasons. The flowof chilled air is adjusted with a damper for cooling. Hotwater of approximate 70 C is supplied into a heating coilinstalled in the air duct in winter. The flow of hot water i nthe heating coil is adjusted to heat the chilled air up forheating.The block diagram of the HVAC system is a simpleclosed loop in Fig. 1 . The controller achieves fuzzy logicreasoning according to the if-then rules which are the modelof the system under control.

Figure 2shows the block diagr am of the controller. Thecontroller consists of four blocks; the input interface, theoutput interface, the host microcontroller, and the fuzzyinference processor.The input interface block receives signals from the sensorunits. The host microcontroller, Motorola M68HC 711, is an8 bit microcontroller running with 8 MHz clock [l]. Itconverts an input analogue signal to a digital signal,commands all the control processes and computes systemconditions.The fuzzy inference processor, OMR ON FP-3000, is an 8bit microprocessor specially designed to perform fuzzyapproximate reasoning [2]. The output interface blockconverts digital signals to analogue signals and transmits

them to the damper driver and the hot water valve driver.To control the room temperature, the controller reads theroom temperature T and the reference point Ti every 1minute of a sampling period. Then, the host microcontrollerM68HC711 calculates temperature error Te and rate oftemperature change Tc. The Te and Tc are inputs ofinference performed by the fuzzy inference processor FP-3000. The temperature error Te and the rate of thetemperature change T c are calculated as follows:

Te = T - Ti [ C] andTc = (T2 -Tl)/At [OC/min]where Te = temperature error [ C],

T = room temperature [ C],Ti = temperature reference point [ C],Tc = rate of the temperature change [ C/min],TI = present room temperature [ C],T 2 = past room temperature [ C] andAt = sampling period of 1 minute.

IEEE CAT. NO. 95CH3581-6/0-7803-2741-1/95/$3.001995 IEEE


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Fuzzy Logic Controller

Fig. 2. Block diagram of the controller.The FP-3000 then ded uces an inference outpu t IC whichis the rate of a control output chan ge. Th e M68HC711

changes a control output referred to the IC.To control humidity, the controller calculates humidityerror He and rate of humidity change Hc in same fashion asthe Te and Tc are calculated. Then , the controller turns thehumidifier on or off according to an inference output whichis a decision to turn the humidifier on or off.

111.CONTROL ALGORITHMF u u y approximate reasoning

Fuzzy set theory was first proposed by L. A . Zadeh in1965 [4] and is an extension of the classical set theory. Asthe name implies, it deals with fuzziness of the real worldand simulates a human's subjective thinking byincorporating the inherent imprecision of the human thoughtprocess. Fuzzy approximate reasoning, which is also calledfuzzy logic inference or fuzzy logic reasoning, is based onthe generalized modus ponens of fuzzy logic [ 5 ] . It is theinference process used in subjective human thinking todeduce new information from vague information.The fuzzy inference processor Fp-3000 performs fuzzyapproximate reasoning according to the if-then rules anduses two inputs to ded uce an output. This means the if-thenrule has two antecedent statements and one consequentstatement represented by fuzzy sets.The fuzzy approximate reasoning refers to thegeneralized modus ponens which of two antecedenlstatements (inputs) and one consequent statement (output) iswritten as:

if x , is A , and x , is A then y is B,x , is A , and x 2 is AZ ,

y is B'wherex I and x2 = input variables,Y = output variable

DamperHot Water ValveHumidifier

,, and A?, = antecedent fuzzy sets,B = consequent fuzzy set,A, ' , and A i = fuzzy sets of inputs andB'For temperature control xl s the Te, and xz is the Tc. Theoutput y is the IC.

The mathematical expression of the modus ponens byMandani's imp licati on rule is written as [ 6 ] :

= fuzzy set of inference conclusion.

~ 5Y )= v W A l n , x ; XI A p A , n A 2 , XI 1A ~ l sY)

Since an inference conclusion B' is represented by afuzzy set, and the controller requires a crisp value to controla driver, the inference conclusion B' is converted to the crispvalue by defuzzifiing the B' . The defuzzification methodused in the 3 -3000 is the center of gravity method which isexpressed as:

J Y x PB ( Y N YY = JPB (yIdy

Membership functionsThe if-the rules are written with fuzzy sets which arecharacterized by membership functions. The FP-3000 isdesigned to have only a single set of antecedent membershipfunctions and consequent membership functions [2].Therefore, the membership functions shown in Fig. 3 andFig. 4 are used for temperature control and humidity control.

INM NS ZR PS PM PL1 - NL

-&4 20 -12 06 0 +06 12 +20 +254 CMDC'mnlI or o/dm~n]Fig. 3. Antecedent membership functions.


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Figure 3 shows the antecedent membership functions.They represent temperature error, rate of temperaturechange, or humidity error and rate of humidity change.The fuzzy sets NM through PM of temperature error aremapped to cover 2 C in order to maintain the temperatureclose to the reference point because a wider range offluctuation makes the occupants feel uncomfortable 131.UCX NL NM NS ZR PS PM PL

-15 -10 -5 0 +5 +10 +15 [ IFig.4.Consequent memb ership functions.Figure 4 shows the consequent membership functionswhich represent the rate of the control output change inpercentage. They are bar-shaped membership functions(singleton shapes) which do not have width. Themembership functions in the con sequent are mapped every 5% and cover 15 % of change in the output voltage to thedriver. The membership function ZR gives no change in theoutput voltage.The 15 range is selected so that the damper cancompletely change its angle corresponding to the outputvoltage before the subsequent change in the output voltage ismade.Inference rule

Table 1shows the fuzzy rules for cooling, and Table 2isthe look up table of Table 1 . Table 3 shows the fuzzy rulesfor heating, and Table 4s the look up table of Table 3. Thetemperature error Te is at row. The rate of temperaturechange Tc is at column. The inference output IC appears atcross section of the Te and Tc. In Table 2and 4, IC is therate of output voltage change i n percentage.Table 1. Fuzzy rules for cooling.

Table 2 . Look up table of Table 1

Table 3. Fuzzy rules for heating.I Te I

Table 4. Look up table of Table 3.

Fuzzy rules for the humidity control is shown in Table 5 .Table 6is the look up table of Table 5 . For humidity control,the inference output is either turn on the humidifier or turn itoff. Therefore, at a cross section of He and Hc, PL meansON, and NL means OFFTable 5. Fuzzy rules for humidifying.

~

PM

He

Table 6 . Look up table of Table 5 .


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NL NM NS ZR PS PM PL~ ~ \ , \ # ~ , \ , ~. . . , .

IEEE WESCANEX 95 PROCEEDINGS

Reasoning using rough setsThe rough sets theory was introduced by Pawlak in 1982

[7]. It is a mathematical theory for reasoning about vagueknowledge and is a data reduction system, as is the fuzzy settheory. However, rough sets theory uses crisp sets as thedata representation, in contrast to fuzzy sets. The inferencealgorithm using rough sets is the modus ponens in theclassical logic written as:if x , E A and x 2 E A then y E B,x E A , and x2 E A , ,

Y EB',whereB' = BB' = V

if A , E A , and Az z andif A , Q A or A? Q Az.

The reasoning using rough sets is also performed by theFp-3000 because the rough sets theory uses crisp sets whichare considered as rectangular shapes of fuzzy sets.Therefore, inference using rough sets can be done byredefining shapes of fuzzy sets from triangular to rectangularas shown in Fig. 5 It shows the rough sets of the conditionattributes (antecedent). To compare performances of thefuzzy reasoning and the reasoning based on rough setstheory, rough sets are mapped in the same fashion as thefuzzy sets. In Fig. 5 gaps between the sets are to show noneof elements belongs to two sets. Each of all the elementsbelongs to only one of the sets. Rough se ts of the decisionattributes (consequent) are identical to the consequentmembership functions of the fuzzy sets shown i n Fig. 4w

Fig. 5 Antecedent membership functions of rough sets.The decision tables of rough sets theory is identical to thetables of the fuzzy inference rules as shown in Table 1, 3 and5

1i Rmm 1ig. 6 Floor plan of the experimental site.

IV.TEST AND RESULTTest System and Environment

Figure6 shows the floor plan of the experimental site.The volume of the room is approximately 63 m3. One side ofthe room faces a hallway. Each of other three sides adjoinsanother room. A single door connects the room to theadjoining room There are no windows.Tw o air ducts of 7 inch diameter supply air to two outletslocated on the false-ceiling, indicated as I'D. The driver forthe air duct damper s installed above the false-ceiling. Theair return is through the return air slots that form a criss-cross pattern on the false-ceiling.The heatin g coil and the driver for the heating coil valveare installed above the false-ceiling. The heating coil,damper, hot water valve driver and damper driver aremanufactured by E. H. Price in Toronto [SI.A humidifier H, manufactured by Nortec [9], is installedon the wall with the outlet located at a height ofapproximately 1.8 m (6 ft) from the floor The capacity ofthe humidifier is 330 m3 (12,000 ft3). The moisture isdiffused throughout the room by a fan in the humidifier.The controller is located on a desk. The height from thefloor is approximately 1 m. The temperature sensor unit andthe humidity sensor unit, indicated as S, are located at center

of the room on the desk indicated.The Physical Plant of the university activates theventilation system of the building from 8:00 a.m. to 11:OOp.m. The temperature of the air in the duct supplied by thephysical plant is approximately 16 C to 20 C throughoutthe year when the air arrives at the experimental site Room 2above the false-ceiling.


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ARIMA, M. et al. A FUZZY LOGIC AND ROUGH SET CONTROLLER FOR HV AC SYSTEMS 137

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Temperature [ C] Humidity [ ]40 I 1 20HumidityI w = - = U = . U m g m = U = = - 15

3g. 7. Steady state response with fuzzy logic control.Temperature [ C] Humidity40 , 20

t8:OO 1 1 :oo 14:OO 17 :OO 20:oo 23:OO

TimeFig. 8 Steady state response with a rough set con troller.

Test ProcedureThe controller was tested for steady state and stepresponse in heating operation. Both fuzzy logic reasoningand the rough set method were implemented and compared

under similar conditions.Steady State Test: In the steady state test for roomtemperature and relative humidity control, the roomtemperature and humidity were measured every half an hourstarting from 8:00 in the morning till 11:OO in the evening.Air flow was set at a constant 6.7 m3/min(240 f?/min) while the flow of hot water was manipulated.The temperature reference point was set at 24.5 C. The

humidity reference point was set at 17.0 because thecapacity of the humidifier was too small to keep the humiditymore than 20 . The humidity was approximately 10without humidification.Step Response Test: In the step response of the

temperature control, the air flow was set at 6.7 m3/min (240ft3/min). Th e controller adjusted the flow of the hot water tocontrol the room temperature. At first, the temperaturereference point was set at 24.5 C. After the roomtemperature was stabilized, the reference point was reset at25 0 O C to provide a step input of 0.5 C. The roomtemperature was measured every 5 minutes. The controllerwas also tested w ith step inputs of 1 O C nd 1.5 C.


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0 10 20 30 40 50 6 70 80 90 100 110 120Time [min]

Fig. 9. Step responses for fuzzy logic reasoning and rough set controllers.Test Results 131

Test results are as shown i n Fig. 7, 8 and 9. Figure 7shows the result of steady state test for the fuzzy logicreasoning. An average temperature deviation is [4approximately 0.1 C, and a temperature deviation range,the difference between the highest and lowest tempe rature, is [5]approximately 0.7 C. An average humidity deviation isapproximately 0.2 , and a humidity deviation range isapproximately 0.9 .Figure 8 shows the result of steady state test for the roughsets method. An average temperature deviation isapproximately 0.2 C, and a temperature deviation range of1.0 C. An average humidity deviation is approximately 0.5%, and a humidity deviation range is approximately 2.9 .

Figure 9 shows the result of step response test of thefuzzy logic reasoning and the rough set method. The Rou ghsets method responded to the step input faster than fuzzylogic reasoning.

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191V. CONCLUSIONThe fuzzy logic reasoning shows better performance in

both temperature and humidity control than the rough setmethod. In particular, for humidity control, the method offuzzy logic reasoning shows better performance than therough set method. In conclusion, the HVAC system canprovide a well-controlled environment in a r c with thefuzzy logic or rough se t controller.

1977 Fundamental Handbook, New York: AmericanSociety of Heating, Refrigerating and Air-Conditioning Engineering Inc. (ASHRAE), 1980.Zadeh, A. Lotfi , Fuzzy Sets, Information control,Vol. 8, pp. 338-353, 1965.Zimmerman, H. J . Fuzzy set Theory and ItsADpkations, 2nd edition, Boston, Kluwer AcademicPublishers, 1990.Sugeno Michio, Fuzzy Control (in Japanese), Tokyo,Nikkan Kogyo Shinbun-Sha, 1988.Pawlak, Zdzislaw, Rough Sets Theoretical Aspects ofReasoning about Data, Boston, Kluwer AcademicPublishers, 1991.SEV Installation & Service Manual for ElectronicSi nd e Duct Variable Volume Control Assemblies,Winnipeg, E. H. Price Limited.CONDAIR RES Steam H umidifier Installation,Operation and Maintenance Ma nual, New York,Nortec Industries Inc.

REFERENCES[ I[2]

M68HC 711 Reference Manual, Motorola Inc., 1990.FP-3000 Digital Fuzzy Processor User's Manual,OMR ON C orporation, 199 1.

fuzzy rough set

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