ON-LINE MONITORING AND FAULT DETECTION

Transcription

1 ON-LINE MONITORING AND FAULT DETECTION OF CONTROL SYSTEM PERFORMANCE John E. Sm Johnson Controls, Inc. Milwauk, WI USA John M. Hous National Institut of Standards and Tchnology Gaithrsburg, MD USA Richard H. Monro Johnson Controls, Inc. Milwauk, WI USA ABSTRACT This papr prsnts a nw mthod for monitoring th prformanc of control loops. Th mthod dtrmins prformanc indics using rcursiv rlationships. Th rcursiv formulation givs th mthod two dsirabl charactristics, namly, it is computationally fficint, and th mmory rquirmnts ar small bcaus only prvious valus of th prformanc indics ar stord. Consquntly, th mthod can b implmntd in low-cost digital controllrs, thrby rducing traffic on th communication ntwork. Building oprators can us th prformanc indics to quickly assss th prformanc of a larg numbr of controllrs. Prformanc indics may b usd to quantify information about th amount of travl of an actuator, th diffrnc btwn th dsird procss output and th actual output, saturation of a controllr, tc. This papr prsnts laboratory and fild tst rsults dmonstrating th utility of th prformanc indics for prformanc monitoring and fault dtction in variabl-air-volum air-handling units with prssur-indpndnt variablair-volum boxs. INTRODUCTION Modrn control systms for hating, vntilating, and air-conditioning (HVAC) quipmnt contain a ntwork of digital controllrs connctd on a communication trunk or bus. Th digital controllrs ar usd to control a wid varity of quipmnt such as boilrs, chillrs, air-handling units (AHU's), and variabl-air-volum (VAV) boxs. Thr may b hundrds of digital controllrs on a ntwork for an HVAC control systm. Control systms for larg buildings frquntly contain an oprator workstation for monitoring systm prformanc. In othr control systms, th oprator may monitor th systm rmotly by using modms to communicat with th digital controllrs. Systms for small buildings, such as schools, may not b quippd with an oprator workstation. In ths systms, an oprator may connct a portabl computr or othr commissioning dvic to th ntwork to obtain information on systm prformanc. Thr ar svral diffrnt mthods for conncting th digital controllrs to th communication trunk. Hartman (1993) dscribs four diffrnt typs of communication ntworks that ar usd in th HVAC industry. Figur 1 dpicts an architctur that uss pr- 1

2 to-pr communications. In a pr-to-pr architctur, digital controllrs, oprator workstations, and modms all communicat on th sam ntwork. Digital controllrs and communication ntworks giv building oprators a vast capability to monitor th opration of HVAC systms. Howvr, thr ar limitations to this capability. As with most computr systms, th limitations ar mmory rquirmnts, computational spd, and ntwork communication spd. Whil th workstation may hav abundant mmory and computational spd, ntwork communication spd maks it difficult to sampl all digital controllrs at th sam rat at which thy ar controlling (in many cass this can b vry scond). This problm is xacrbatd in largr systms. Hnc, whnvr possibl, computations that ar prformd on-lin (i.., at th sam rat that th digital controllr sampls and controls a particular dvic) ar shiftd to th microprocssors within th digital controllrs and information from th microprocssors is downloadd to th workstation much lss frquntly (vry 15 minuts, hour, day, tc.). Today's microprocssors hav limitd computational rsourcs howvr, so it is not possibl to xcut complx, tim consuming algorithms or stor historical data at this lvl. Th objctivs of this papr ar to dscrib a control prformanc monitoring mthod that can allviat th limitations associatd with on-lin monitoring of control systm prformanc by comprssing th data at th digital controllr lvl, and to dmonstrat th utility of th mthod for dtcting faults in variabl-air-volum (VAV) AHU's and boxs. Dscriptions of a typical VAV AHU and a typical prssur-indpndnt VAV box and th control stratgis utilizd in ths systms ar prsntd first. Nxt, th control prformanc monitoring mthod is dscribd. Laboratory and fild tst rsults dmonstrating th us of th mthod for monitoring and dtcting faults in VAV boxs and AHU's ar thn prsntd. Finally, conclusions of this study ar prsntd. SYSTEM DESCRIPTION Figur 2 is a schmatic diagram of a typical singl duct VAV AHU. Th primary function of an AHU is to provid conditiond air to various rooms. Th AHU consists of variabl spd supply and rturn fans, thr damprs for controlling airflow to and from th AHU to th Oprator Workstation Modm Communication Trunk DC DC DC DC DC DC Digital Controllrs Connct to Actuators and Snsors Figur 1 Communication architctur with pr-to-pr communications. 2

3 Exhaust Air Exhaust Air Dampr Rturn Air Plnum Q r Flow Station T&H Tmpratur & Humidity Snsor Rturn Fan Outdoor Air Mixd Air Plnum Outdoor Air Dampr Rcirculation Air Dampr Q s H C C C Hating Coil Cooling Coil Supply Fan T&H Flow Station AIR HANDLING CONTROLLER Figur 2 VAV AHU with a singl duct. outdoor nvironmnt, hating and cooling coils for conditioning th air, various snsors and actuators, and a controllr that rcivs snsor masurmnts and computs and transmits nw control signals. In th discussion that follows, normal oprating stratgis ar dscribd for a VAV AHU that uss volum matching control of th rturn fan. VAV AHU's ar typically controlld to maintain a constant stpoint tmpratur at som location in th supply duct downstram of th supply fan. This is achivd by controlling th outdoor air, rcirculation air, and xhaust air dampr positions, and by controlling th flow of hot watr and cold watr through th hating and cooling coils, rspctivly. Th supply fan of a VAV AHU is controlld to maintain th static prssur in th supply duct at a constant stpoint valu. Constant tmpratur supply air is distributd to various zons (not shown), which may hav diffrnt loads and stpoint tmpraturs. To account for th variability of th conditions in th zons, VAV boxs (not shown) that rgulat th amount of air that ntrs a zon ar placd at th nd of th supply air ductwork lading to ach zon. As a zon load dcrass, th corrsponding VAV box rstricts th flow of air to th zon, thrby incrasing th static prssur in th supply duct and causing th supply fan spd to dcras in ordr to maintain th static prssur stpoint condition. If th zon load incrass, th VAV box and supply fan rspond in th opposit mannr. Thr ar svral ways to control th rturn fan of a VAV AHU to maintain zon prssurization. With a volum matching control stratgy, th rturn fan is controlld to maintain a constant diffrntial btwn th supply and rturn airflow rats so that th zons hav a small positiv prssurization, thus rducing infiltration. Airflow stations ar usd to masur th airflow rats in th supply and rturn air ducts. Th control systm for a prssur-indpndnt VAV box is dpictd in Figur 3. Th prssur-indpndnt VAV box has a dampr for adjusting th flow rat of supply air into th room and a flow station for masuring th flow rat of air into th room. Th thrmostat is usd to masur th room tmpratur, and som thrmostats allow th building occupant to adjust th stpoint. Control systms for prssur-indpndnt VAV boxs commonly us a 3

4 cascad control stratgy to maintain th zon tmpratur at th stpoint valu. Th cascad control stratgy is shown in Figur 4. Th tmpratur controllr dtrmins th stpoint for th flow controllr. Th scondary control loop for flow is nstd insid th tmpratur control loop. Control Signal Dampr Motor VAV Controllr Stpoint & Room Tmpratur ROOM Flow Station Thrmostat Figur 3 Control systm for prssur-indpndnt VAV box. Room Tmpratur Stpoint Scondary Control Loop Prssur Disturbancs Load Disturbancs + - Tmpratur Controllr + - Flow Controllr Motor and Dampr Flow Rspons Thrmal Rspons of Room Flow Snsor Tmpratur Snsor Figur 4 Block diagram for cascad control of room tmpratur implmntd in prssurindpndnt VAV box controllrs. CONTROL PERFORMANCE MONITOR Th control prformanc monitoring algorithm is usd to comput indics that quantify control systm prformanc. Exampls of prformanc indics ar th duty cycl of a motor and th numbr of starts, stops, and rvrsals of an actuator. Both of ths indics ar usful for idntifying unstabl control that can lad to xcssiv componnt war. Figur 5 is a block diagram of a digital control systm that has a control prformanc monitor. Th fdback controllr adjusts th actuator to bring th snsd valu for th procss output toward th stpoint. Simultanously, th control prformanc monitor collcts data (i.., rror 4

5 signal to Communication Trunk Digital Control Systm Prformanc Indics Control Prformanc Monitor Stpoint + - Controllr Actuator Procss A/D Figur 5 Singl loop fdback control systm with control prformanc monitor. th controllr, chang in th control signal, and procss output) and computs indics that quantify th controllr prformanc. Th control prformanc monitor dtrmins stimats of th indics using xponntially wightd moving avrags (EWMA's). Th quation for computing an EWMA is givn by (Huntr, 1986) X t j λ λ Xt jt (1) j=0 = (1 - ) - whr X t = EWMA of prformanc indx X at tim t λ = xponntial smoothing constant X t-jt = valu of prformanc indx X at discrt tim t - jt T = sampl tim for analog-to-digital convrtr Pandit and Wu (1983) rfr to th trm λ (1 - λ) j as an xponntial smoothing wight. Equation 1 is calld an xponntially wightd moving avrag bcaus th xponntial smoothing wights dcras xponntially or gomtrically as j incrass (Box and Jnkins, 1976). Figur 6 shows th rlationship btwn th xponntial smoothing wights and j for λ qual to and 0.5. As λ incrass, th wights dcras at a fastr rat. Consquntly, mor past data will affct th EWMA whn λ is small. Montgomry (1991) dscribs th us of EWMA control charts and claims that valus of λ btwn 5 and 5 work wll in practic. Pandit and Wu (1983) rcommnd that th valu of λ should b btwn 0 and 0.3. To implmnt Equation 1 in computr cod, it would b ncssary that all past data b stord in computr mmory. Howvr, Equation 1 can b rformulatd as ( ) X = X + λ X - X (2) t t-t t t-t Equation 2 is a rcursiv form of Equation 1. An important advantag of Equation 2 is that only th prvious valu of th smoothd stimat of th prformanc indx must b stord. 5

6 By comparison, if a typical moving avrag (Sborg t al., 1989) is to b computd, all past valus of th variabl bing avragd must b stord in mmory. If moving avrags ar 0.5 λ (1 λ) j λ = λ = j Figur 6 Exponntial smoothing wights for smoothing constants of and 0.5. dsird for numrous variabls, thr may b insufficint mmory to stor th ncssary data. Equation 2 should only b usd during tim priods that th controllr is oprating. Also, a building controls nginr may want to us Equation 2 only during occupid tim priods. Som controllrs hav built in diagnostics for confirming that a snsor is connctd to th controllr. If a controllr dtcts that a snsor is not connctd, thn th controllr can issu a command that a snsor failur has occurrd. Th EWMA should not b updatd during tim priods that th controllr has dtctd a snsor failur. Whn monitoring th prformanc of a fdback control systm with an EWMA, th smoothing constant, λ, nds to b chosn carfully. If th smoothing constant is too larg (.g., if λ = 1, th EWMA is qual to th currnt point masurmnt), th EWMA will tak on larg valus following a load disturbanc or stpoint chang. This may caus th prformanc monitor to indicat a fault whn no fault is prsnt. If th smoothing constant is too small, it will tak a long tim for th prformanc monitor to dtct a fault. Th following guidlins can b usd to slct a smoothing constant basd on th rspons charactristics for a fdback control systm:: whr T = sampling tim of th analog-to-digital convrtr t s = sttling tim of th controllr T T < λ < (3) 20 t 5 t s Whn λ = T/5t s, th summation of th xponntial smoothing wights btwn tims t and t - 5t s is approximatly 32. This mans that approximatly 63.2% of th EWMA is basd on th data btwn tims t and t - 5t s. Whn λ = T/20t s, approximatly 63.2% of th EWMA is basd on th data btwn tims t and t - 20t s. Figur 7 shows a typical closd-loop rspons to a stp chang in stpoint and th sttling tim. Th sttling tim is th tim rquird for th procss output to sttl to and s 6

7 rmain within ± δ of th final valu. Common valus for δ ar 1%, 2%, or 5% of th siz of th stpoint chang (Åström and Hägglund, 1995, and Sborg t al., 1989). Prformanc indics computd using EWMA's mak it practical to simultanously Procss Output y final y initial Stpoint Sttling Tim 2δ δ is commonly 1%, 2%, or 5% of (y final - y initial ) Tim Figur 7 Sttling tim spcification for stp chang in stpoint. monitor th rcnt prformanc of hundrds of local digital controllrs bcaus thy ffctivly comprss th prformanc data. Bcaus th EWMA algorithm is numrically fficint and rquirs vry littl mmory, it can b usd in today's digital control systms to comput prformanc indics on-lin. Thr ar svral possibl uss of th prformanc indics: 1) Th prformanc indics can b usd to compar th prformanc of similar controllrs. For instanc, a building oprator can download prformanc indics for a larg numbr of VAV boxs from th digital controllrs to a cntral workstation and quickly compar th prformanc of th controllrs. Bcaus of th similarity of th controllrs and th controlld dvics, controllrs dmonstrating poor prformanc can b radily idntifid. Th oprator can thn collct additional data and/or assign a srvic prson to inspct th controllr and HVAC systm. 2) Th prformanc indics can b usd in a ral-tim fault dtction systm to dtrmin a fault in a control systm or componnt of th HVAC systm. A fault is dtrmind by comparing th prformanc indics with control limits that ar dtrmind ithr by xprt knowldg of th systm or by using mthods from statistical quality control (Montgomry, 1991). 3) A diagnostic systm can b idntify possibl causs of a fault. dvlopd that uss pattrns of prformanc indics to Thr ar a numbr of prformanc indics that could b usd to assss control systm prformanc. Svn prformanc indics ar listd in Tabl 1. Th EWMA of th procss rror is a good prformanc indx for comparison of diffrnt control systms or algorithms. Th procss rror is th diffrnc btwn th dsird procss output y st and th actual procss output y. Th EWMA of th absolut valu of th procss rror is an vn bttr prformanc indx for this purpos bcaus positiv and ngativ rrors associatd with unstabl control do not cancl on anothr. Th EWMA of th procss output y givs information similar to that of th EWMA of th procss rror, although th indx for th procss output may b mor illustrativ in som circumstancs. Controllr stability and th amount that an actuator is drivn can b assssd using th EWMA for th absolut valu of 7

8 th chang in th control signal u. Th EWMA of th control signal u is usful for dtrmining whn a controllr is saturatd. Lik u, th EWMA of th duty cycl of an lctric motor d and th EWMA of th numbr starts, stops, and rvrsals of an actuator S can b rlatd to controllr stability and actuator war. As mntiond prviously, most if not all of th prformanc indics can b usd in a straightforward mannr to dtct faulty oprating Tabl 1 Prformanc indics for monitoring control systm opration. Prformanc Indx Dscription Mathmatical Exprssion = + λ - procss rror, 1 t t-t ( t t-t ) absolut valu of procss rror t = t-t + λ ( t - t-t ) procss output, y y = y + λ ( y - y ) absolut valu of chang in control input, c t t-t t t-t u t = u t-t + λ ( u t - ut-t ) u ontrol input, u u = u + λ ( u - u ) t t-t t t-t duty cycl, d d = d + ( d - d ) t t-t λ t t-t numbr of starts, stops, and rvrsals, S S = S + ( S - S ) t t-t λ t t-t 1 = (y st - y) conditions. EWMA's of th prformanc indics can b computd in th oprator workstation using signals from th digital controllrs. Howvr, thr ar svral advantags to dtrmining th EWMA's in th digital controllrs. Two of ths advantags hav bn alludd to prviously, namly, that communication rats on th ntwork would b improvd bcaus th frquncy at which data nds to b transfrrd on th ntwork is rducd, and that th amount of procssing that nds to b prformd in th oprator workstation would b rducd. A third advantag of computing th prformanc indics in th digital controllrs is that a systm rprsntativ could connct a portabl computr to th ntwork and rad th prformanc indics for various controllrs. This would b important for control systms that did not hav an oprator workstation on th communication trunk. Finally, thr ar tims whn th communication ntwork is not connctd or is malfunctioning. Aftr th ntwork communication is r-stablishd, a building oprator could quickly dtrmin th prformanc of th control systm by pulling down data from th local digital controllrs. Control Prformanc Monitoring of Laboratory VAV Boxs Control systms for VAV boxs hav a numbr of componnts that may fail. For xampl, th dampr could stick, th dampr motor could fail, thr could b a problm with th flow station, or th airflow controllr could b unstabl. To dmonstrat th us of prformanc indics to monitor th opration of VAV boxs, two faults ar introducd in a laboratory AHU that is quippd with thr prssur-indpndnt VAV boxs. Th laboratory VAV boxs us lctrical controls, thus, th prformanc indics ar computd at th cntral workstation. This ngats th bnfit of rducd ntwork traffic that rsults from implmnting th indics in local digital controllrs, but maks it possibl to dmonstrat th utility of th prformanc indics. A block diagram dpicting th control systm for th laboratory VAV boxs and th 8

9 implmntation of th prformanc indics to monitor th boxs is shown in Figur 8. This control systm is slightly diffrnt from th block diagram rprsntation in Figur 4. Th VAV boxs do not control th tmpratur in individual zons; thy dlivr th supply air to a common zon. Thus, rathr than using room thrmostat signals and th tmpratur controllr to adjust th stpoint to th flow controllr, this stpoint is stablishd artificially by snding a voltag signal from th oprator workstation (via a data acquisition and control unit) to th + Flow Stpoint - Flow Controllr Oprator Workstation Motor & Dampr Position Snsor Flow Rspons Flow Snsor Computs Prformanc Indics Figur 8 Block diagram rprsnting th implmntation of airflow rror and dampr position prformanc indics in prssur-indpndnt VAV boxs in a laboratory AHU. individual VAV boxs. In addition, th laboratory VAV boxs ar ach quippd with a potntiomtr for masuring th dampr position. This dos not affct th control of th VAV boxs; howvr, dampr position will b usd to monitor th opration of th VAV boxs. Th first fault considrd was a stuck dampr in a VAV box. This fault causs th rror signal to th airflow controllr to incras as th zon load changs. Th zon load profil for th occupid priod of th day is rprsntd by th stpoint voltag signal snt to th VAV boxs. Th stpoint voltag signal is shown in Figur 9a. Th sam signal is snt to all VAV boxs for th initial two and on-half hours of th tst, howvr, th signal snt to VAV box 3 is thn hld constant ovr th rmaindr of th tst to simulat a stuck dampr fault. For this fault, th opration of th VAV boxs was monitord using a prformanc indx for th airflow rror of ach box. Th absolut airflow rror prformanc indx is givn by whr ( ) t = t T + λ t - t-t (4) t = Q st - Qt is th absolut valu of th diffrnc in th stpoint and actual airflow rats at tim t t = EWMA of absolut airflow rror at tim t Th sampling tim for controlling th VAV boxs was 1.5 sconds, hnc, t was updatd vry 1.5 sconds. Th smoothing constant was st to 02. Th normalizd absolut airflow rror prformanc indx for ach of th thr VAV boxs is shown in Figur 9b at fiftn minut intrvals for ight hours of a nin hour tst priod. Th initial hour is not prsntd bcaus th rsults ar ovrly influncd by startup transints that ar much mor svr than normal load or stpoint changs. Normalizd valus wr obtaind by dividing th airflow rrors by th maximum stpoint airflow rat for th tst. Th xistnc of a fault 9

10 in VAV box 3 is vidnt from Figur 9b. Th scond fault is an unstabl supply air prssur controllr. Bcaus th airflow controllrs in th prssur-indpndnt VAV boxs attmpt to maintain th airflow rats at th stpoint valus, this fault can lad to th constant adjustmnt of th dampr positions and thrfor, xcssiv war of th actuators. To implmnt this fault, th proportional gain for th proportional plus intgral controllr that controls th supply fan was incrasd by a factor Zon Load VAV Box Voltag Input for Normal Opration VAV Box Voltag Input for Stuck Dampr Figur 9a Voltag inputs to th VAV box flow controllrs Flow Error VAV Box 1 VAV Box 2 VAV Box Figur 9b Voltag inputs to th VAV box flow controllrs. of 4.5 aftr two and on-half hours of opration, and th supply prssur stpoint was incrasd from 249 to 274 Pa aftr four hours of opration. To isolat th ffct of th unstabl supply prssur from othr ffcts that would tnd to mak th VAV box damprs opn and clos, a constant stpoint voltag was snt to th thr VAV boxs, thrby simulating constant loads for ach zon. Th movmnt of th VAV box damprs is quantifid using an EWMA of th absolut valu of th chang in th potntiomtr signal for ach dampr. Th supply air prssur is plottd in Figur 10a for a six hour priod and th 10

11 corrsponding EWMA's for th absolut airflow rror and th absolut valu of th chang in position (indicatd by a chang in voltag from a potntiomtr) of ach VAV box dampr ar plottd in Figurs 10b and 10c. A smoothing constant of 02 was usd for ths rsults. Figur 10a shows that th supply air prssur bgins to oscillat shortly aftr th chang in th proportional gain at t = 2.5 h, whr t dnots tim. Th oscillations ar lss svr just prior to th stpoint chang; howvr, aftr th chang thr wr sustaind oscillations with a pak to pak amplitud of approximatly 120 Pa. Figurs 10b and 10c show that th instability of Supply Air Prssur (Pa) Flow Error Figur 10a Unstabl supply air prssur rspons. VAV Box 2 VAV Box 3 VAV Box 1 Figur 10b Normalizd absolut airflow rror for th thr VAV boxs. 11

12 Chang in Dampr Position VAV Box 2 VAV Box 1 VAV Box 3 Figur 10c Normalizd absolut chang in dampr position for th thr VAV boxs. th supply air prssur is manifstd in continuous movmnt of th damprs in th VAV boxs. Th largr th amplitud of th oscillations of th supply air prssur, th gratr th valu of th EWMA's for both th absolut airflow rror and th absolut chang in th VAV box dampr position. As th oscillations ar supprssd, th EWMA's also dcras. For this cas, th chang in dampr position is a mor rliabl indication of th prsnc of a fault than th absolut airflow rror. Howvr, for th stuck dampr fault, th opposit would b tru. Th rsults in Figur 10 dmonstrat a straightforward mthod of dtcting an unstabl supply air prssur controllr. For VAV boxs with digital controllrs, th absolut valu of th chang in th control signal to th dampr actuator could b usd instad of th potntiomtr voltag to dtct this fault, as wll as unstabl VAV box flow controllr faults. Control Prformanc Monitoring of a Laboratory VAV AHU L t al. (1996a, 1996b) studid th symptoms of ight complt faults for a VAV AHU and traind an artificial nural ntwork (ANN) to idntify an idalizd pattrn of th symptoms for ach fault. In this study, EWMA's for th control signal u, th absolut valu of th chang in th control signal u, th procss rror, and th absolut valu of th procss rror for th supply fan, rturn fan, and cooling coil valv control loops wr usd to xamin six of th faults considrd by L t al. (1996a, 1996b). Control loops for th hating coil valv and mixing box damprs wr not considrd. Th six faults xamind wr as follows: Complt failur of th supply fan Complt failur of th rturn fan Stuck cooling coil valv Complt failur of th supply air thrmocoupl Complt failur of th supply air flow station Complt failur of th rturn air flow station Unlss notd othrwis, faults wr introducd thr hours aftr th commncmnt of a tst and opration continud for two hours aftr th occurrnc of a fault. With th xcption of th supply air thrmocoupl fault, all faults wr introducd by disconncting or turning off th powr to snsors or actuators. Th supply air thrmocoupl fault was introducd through softwar changs. In th rsults that follow, only EWMA's ar prsntd. Tim sris rsponss of th actual control signal, procss rror and rlatd variabls ar not prsntd. 12

13 Th EWMA's rspond at a much slowr rat than th actual variabls that ar usd by th controllrs. For all rsults prsntd in this sction, th smoothing constant for th cooling coil valv controllr, supply fan controllr, and rturn fan controllr ar 00333, 05, and 025, rspctivly. Figur 11 shows th volution of th prformanc indics for a complt failur of th supply fan. During normal opration th supply fan was controlld to maintain a static prssur of 249 Pa in th supply air duct and th rturn fan was controlld to maintain a flow diffrnc of 72 m 3 /s btwn th supply and rturn air ducts. Th fault causd th supply fan rotational spd to dcras to zro. Figur 11a shows th prformanc indics for th cooling coil valv controllr. Bcaus thr was no air flow, th supply air tmpratur gradually incrasd, as vidncd by th dcras in. Two hours aftr th occurrnc of th fault, th EWMA of th cooling coil valv procss rror was approximatly -2 C. Th ris in th supply air tmpratur causd th cooling coil valv control signal to incras to its maximum valu, although u did not saturat in th tim allottd for this tst. If th tst lngth was xtndd, u would vntually saturat. Th absolut valu of th chang in th control signal u initially incrasd rapidly aftr th fault occurrd; howvr, onc th controllr saturatd, u dcayd toward zro. This typ of rspons was also sn for u for th othr control loops. Figur 11b shows th prformanc indics for th supply fan controllr for Control Signal u 000 u Chang in Control Signal Procss Error ( o C) Figur 11a Cooling coil valv prformanc indics for a complt supply fan failur. Control Signal u u Chang in Control Signal Procss Error (Pa) Figur 11b Supply fan prformanc indics for a complt supply fan failur. 13

14 Control Signal u u Chang in Control Signal Procss Error (m 3 /s) - Figur 11c Rturn fan prformanc indics for a complt supply fan failur. th supply fan fault. Th fault causd th supply air prssur to dcras to zro. This yildd valus of and qual to 249 Pa for th supply fan controllr. As vidncd by th rspons of u, th fault also causd th control signal to th supply fan to incras to its maximum valu in an attmpt to offst th dcrasing supply air prssur. Th prformanc indics for th rturn fan controllr ar shown in Figur 11c. Bcaus thr is no air flow in th supply duct, th rturn fan controllr quickly shut down th rturn fan in an attmpt to maintain th flow diffrnc btwn th supply and rturn air ducts at th stpoint valu. Th fault causd for th rturn fan controllr to approach th procss stpoint valu of 72 m 3 /s, whil u saturatd at its minimum valu. Plots of th rturn fan controllr prformanc indics for a complt failur of th rturn fan ar shown in Figur 12. For this and th rmaining faults, only th prformanc indics for th controllrs that ar significantly affctd by a givn fault ar prsntd. Th fault causd th rturn fan rotational spd to dcras to zro. This causd th flow diffrnc btwn th supply and rturn ducts to incras, which yildd a larg ngativ valu of. In addition, th ngativ rror causd th control signal to th rturn fan to incras to its maximum valu, thus causing u to saturat at its maximum valu. Aftr incrasing rapidly aftr th occurrnc of th fault, u dcayd to zro onc u saturatd. Plots of th cooling coil valv controllr prformanc indics for stuck cooling coil valv ar shown in Figur 13. Th fault was introducd thr hours into th tst, and nar normal opration continud until a zon load incras was imposd on th thr VAV boxs at t = 4 h. Th load incras causd th dampr of ach VAV box to opn, thus dcrasing th static prssur in th supply duct. This causd th supply fan spd to incras to bring th static prssur back up to th stpoint valu and, consquntly, th supply air tmpratur incrasd. Th rsultant ffct of th fault is that is approximatly qual to - C at th nd of th tst. In an attmpt to compnsat for th incrasing supply air tmpratur, th control signal 14

15 Control Signal u u Chang in Control Signal Procss Error (m 3 /s) Figur 12 Rturn fan prformanc indics for a complt rturn fan failur. Control Signal u u Chang in Control Signal Procss Error ( o C) Figur 13 Cooling coil valv prformanc indics for a stuck cooling coil valv. to th cooling coil valv incrasd toward its maximum valu and vntually saturatd, and u approachd unity. Givn additional tim, u would also saturat and would rmain saturatd until a significant load dcras occurrd. In addition, th fault causd a rathr obvious chang in th valu of u. At first u incrasd as th control signal incrasd. Howvr, onc th control signal saturatd, u bgan to dcras toward zro. Prformanc indics for th cooling coil valv controllr ar plottd in Figur 14 for a supply air thrmocoupl failur. A complt thrmocoupl failur typically rsults in a voltag signal that varis randomly btwn larg positiv and larg ngativ valus. If th snsd valu of th supply air tmpratur is outsid of th rang of normal oprating conditions (0 to 40 C, for xampl), th tmpratur could b automatically st to zro so that th tmpratur would not fluctuat. This failur was simulatd by ovrwriting th masurd supply air tmpratur with a valu of 0 C. This causd and to incras and approach th supply air stpoint valu of 14.5 C, whil u dcrasd to its minimum valu. Bcaus of th abrupt chang in th supply air tmpratur causd by stting it qual to 0 C, u incrasd vry rapidly and thn bgan to dcay toward zro sinc u was saturatd at its minimum valu. Rturn fan prformanc indics ar plottd in Figur 15 for a complt failur of th supply fan flow station. This fault causd th rturn fan to shut down bcaus th supply flow station indicatd that thr was no flow in th supply duct. Thus, th control signal u to th rturn fan dcrasd to its minimum valu in an attmpt to maintain th flow diffrnc 15

16 Control Signal u u Chang in Control Signal Procss Error ( o C) Figur 14 Cooling coil valv prformanc indics for a supply air thrmocoupl fault. Control Signal u u Chang in Control Signal Procss Error (m 3 /s) Figur 15 Rturn fan prformanc indics for a complt supply flow station failur. btwn th supply and rturn ducts at th stpoint valu. Th procss rrors and wr approximatly qual to 0.37 m 3 /s at th conclusion of th tst, whil u dcayd to zro. As in all cass whr a controllr saturatd, u also dcayd to zro aftr a rapid incras immdiatly following th fault. Rturn fan controllr prformanc indics ar plottd in Figur 16 for a complt failur of th rturn fan flow station. Whn this fault occurrd, a zro rading was obtaind for th rturn flow station. Thus, th control signal u to th rturn fan incrasd to its maximum valu in an attmpt to maintain th flow diffrnc btwn th supply and rturn ducts at th stpoint valu. Th rspons of th prformanc indics for th rturn fan controllr for this fault ar almost idntical to thos obsrvd for th rturn fan failur. Control Prformanc Monitoring of Ral Building VAV Boxs Th tru valu of th prformanc indics is bttr undrstood if on considrs th task of simultanously monitoring tns or hundrds of VAV boxs. For that scal of a systm, th prformanc indics must b computd in th individual digital controllrs and plots such as Figur 9b prsnt only th currnt valus of th prformanc indics for ach of th VAV boxs. This tchnology xists today in ral buildings. Currntly, ovr 100,000 digital VAV controllrs hav th capability of dtrmining th following thr prformanc indics: duty cycl, EWMA of absolut valu of th flow rror, and EWMA of th absolut valu of th tmpratur rror. Th VAV controllrs ar commissiond by a building oprator, who 16

17 rsponds to quris from commissioning softwar to slct th prformanc indics to b computd. In on particular building, a subcontractor installd nw digital controllrs for 24 dualduct VAV boxs (Wang, 1993) that wr locatd on th 21st floor of a 28 story offic building. Th digital controllrs sampld th controlld variabls vry 1.5 sconds. Th smoothing constant for th flow rror was and th smoothing constant for th tmpratur rror was An avrag duty cycl was dtrmind from th last tim th controllr was rst. Th subcontractor and building nginr wr confidnt that th VAV controllrs wr corrctly installd and oprating proprly. Figur 17a shows th normalizd flow rror for th 24 VAV boxs. Th flow rrors wr normalizd by dividing th EWMA of th absolut valu of th flow rror by th dsign maximum flow rat for cooling. Th normalizd flow rrors for boxs 16 and 18 ar significantly largr than th flow rrors for th othr boxs. Aftr furthr invstigation, th Control Signal u u Chang in Control Signal Procss Error (m 3 /s) Figur 16 Rturn fan prformanc indics for a complt rturn flow station failur. building nginr dtrmind that th lctric motor for box 16 had a dfctiv capacitor. Also, it was dtrmind that th lctric actuator for box 18 was incorrctly installd. Spcifically, th lctric dampr actuator had bn lockd to th dampr shaft 90 dgrs from th corrct position. This causd th VAV box to b wid opn whn th VAV controllr issud a closd command, and to b compltly closd whn th VAV controllr issud a command for full flow. A dtaild dscription of th VAV box dampr actuator installation is providd in th Appndix. For th fault fr VAV boxs (i.., boxs 1 to 15, 17, and 19 to 24), th avrag normalizd flow rror was 47 and th standard dviation was 27. For VAV boxs 16 and 18, th normalizd flow rrors wr 66 and 1.136, rspctivly. Ths flow rrors ar 30 and 40 standard dviations largr than th avrag valu for fault fr boxs. Figur 17b shows th duty cycl for th 24 VAV boxs. Thr appars to b no significant outlir in th duty cycl for th VAV boxs. If a control systm for on of th VAV boxs was unstabl, a high duty cycl and a larg normalizd flow rror would b xpctd for that particular box. Figur 17c shows th EWMA of th absolut valu of th tmpratur rrors for th 24 VAV controllrs. Notic that although four boxs hav tmpratur rrors abov 1ºC, th rrors ar not dmd to b significant nough by thmslvs to warrant furthr attntion from th building oprator. Figur 17d is a plot of th EWMA of th tmpratur rrors vrsus th EWMA of th normalizd flow rrors. Both boxs 16 and 18 hav larg flow 17

18 rrors. This figur can hlp a building oprator prioritiz maintnanc for boxs with th high normalizd flow rrors by stablishing which of th boxs has th highst tmpratur rror and thrfor, th highst liklihood of uncomfortabl occupants. Although box 18 has a largr flow rror than box 16, box 16 should probably b xamind and fixd first bcaus of th larg tmpratur rror associatd with this box. CONCLUSIONS This papr prsntd a nw mthod for monitoring th prformanc of control loops. Th mthod dtrmins prformanc indics using rcursiv rlationships. This maks th mthod computationally fficint, and minimizs th computr mmory rquirmnts bcaus only prvious valus of th prformanc indics ar stord. Consquntly, th mthod can b implmntd in low-cost digital controllrs, thus rducing ntwork traffic causd by monitoring variabls at th cntral workstation. Building oprators can us th prformanc indics to quickly assss th prformanc of a larg numbr of controllrs. This papr prsntd laboratory and fild tst rsults dmonstrating th utility of th prformanc indics for prformanc monitoring and fault dtction in variabl-air-volum air-handling units with prssur-indpndnt variabl-air-volum boxs. Fault dtction could b furthr automatd by combining th prformanc monitoring mthod with thrsholds obtaind through xprt knowldg or by application of th principls of statistical quality control. ACKNOWLEDGMENTS This rsarch was partially supportd by th Offic of Enrgy Efficincy and Rnwabl Enrgy, U. S. Dpartmnt of Enrgy EWMA of flow rror maximum flow rat VAV box numbr Figur 17a Normalizd flow rrors. Duty Cycl (Prcnt) VAV box numbr Figur 17b Duty cycl. 18

19 EWMA of Tmp. Error ( o C) VAV box numbr Figur 17c Tmpratur rrors. EWMA of Tmp. Error (oc) Box 16 Box EWMA of flow rror maximum flow rat Figur 17d Tmpratur rrors vrsus normalizd flow rrors. REFERENCES Åström, K. J. and T. Hägglund, PID Controllrs: Thory, Dsign, and Tuning, 2 nd Edition, Instrumnt Socity of Amrica, Rsarch Triangl Park, North Carolina, Box, G. E. P., and G. M. Jnkins, Tim Sris Analysis: Forcasting and Control, Rvisd- Edition, Holdn-Day, San Francisco, Hartman, T. B., Dirct Digital Controls for HVAC Systms, McGraw-Hill, Huntr, J. S., "Th Exponntially Wightd Moving Avrag," Journal of Quality Tchnology, Vol. 18, No. 4, pp , Octobr L, W. Y., C. Park, and G. E. Klly, "Fault Dtction of an Air-Handling Unit Using Rsidual and Rcursiv Paramtr Idntification Mthods," ASHRAE Transactions, Vol. 102 Pt. 1, pp , 1996a. L, W. Y., J. M. Hous, C. Park, and G. E. Klly, "Fault Diagnosis of an Air-Handling Unit Using Artificial Nural Ntworks," ASHRAE Transactions, Vol. 102 Pt. 1, pp , 1996b. Montgomry, D. C., Introduction to Statistical Quality Control, Scond Edition, John Wily & Sons, Nw York, Pandit, S. M, and S. M. Wu, Tim Sris and Systm Analysis with Applications, John Wily & Sons, Inc., Nw York, Sborg, D. E., T. F. Edgar, and D. A. Mllichamp, Procss Dynamics and Control, John Wily & Sons, Nw York, Wang, S. K., Handbook of Air Conditioning and Rfrigration, McGraw-Hill, Inc., Nw York, NOMENCLATURE 19

20 Symbols d duty cycl of an lctric motor procss rror, y st - y S numbr of starts, stops, and rvrsals of an actuator T sampling tim of analog-to-digital convrtr t tim t s sttling tim of a controllr u control signal u chang in control signal X prformanc indx X EWMA of prformanc indx X y procss output δ tolranc limit for procss output λ xponntial smoothing constant Subscripts j tim indx st stpoint valu 20

21 OUT GND IN APPENDIX: PROCEDURE FOR INSTALLING ELECTRIC DAMPER ACTUATOR TO THE VAV BOX Figur A.1 shows th lctric dampr and VAV box. Th following procdur should b usd to attach th motor to th dampr: 1. Plac th dampr blad in th closd position. 2. Slip th coupling for th lctric dampr actuator ovr th dampr shaft. 3. Attach lctric dampr actuator to VAV box. 4. Us an Alln wrnch to scur th st scrw in th coupling to th dampr shaft. Whn installing th dampr actuator for VAV box 18, th dampr blad was in th opn position instad of th closd position aftr stp 1. This causd th dampr blad to b 90 dgrs out of position. VAV Box Dampr Elctric Dampr Actuator Alln Wrnch Dampr Shaft UP DPT-2015 Coupling (-) L O Figur A.1 Dampr and lctric actuator. 21

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