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-------------------- Tune LoopModule 12416

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Instrument Trainee Task Module 12416

TUNE LOOP-

Objectives

Upon Completion of this module, the trainee will be able to:

1. Identify and list the advantages and disadvantages of variousmethods of open loop tuning.

2. Identify and list the advantages and disadvantages of variousmethods of closed loop tuning

Prereuisites

!uccessful completion of the follo"ing #as$ Modules is reuired beforebeginning study of this tas$ module% &''() #as$ Modules 124*1 through1241+.

)euired !tudent Materials

1. !tudent Module2. )euired !afety (uipment

Instrument #rainee #as$ Module 12416 2

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'ourse Map Information

#his course map sho"s all of the Wheels of Learning tas$ modules in thefourth level of the Instrument curricula. #he suggested training orderbegins at the bottom and proceeds up. !$ill levels increase as a trainee

advances on the course map. #he training order may be adjusted by thelocal #raining Program !ponsor.

,(-(, 4 'OMP,(#(

#une ,oop Module 12416 3

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#/0,( O 'O(!

Section Topic .Page

1.*.* Introduction. 62.*.* actors /ffecting !tability. 3.*.* 'losed ,oop Methods.. 3.1.* &otch Method.. 5.2.* ltimate Period Method.. 1+..* 7ampened Oscillation Method. 18

4.*.* Open ,oop Methods. 2*4.1.* #ime 'onstant Methods.. 224.2.* )eaction )ate Method. 2+


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#rade #erms Introduced In #his Module

Approximation: / calculation "hich is not precise9 bug very close.

Closed loop: / combination of control units in "hich the controlleduantity is measure and compared "ith a standard representing thedesired performance.

Dampened Oscillation et!od: / decrease in the amplitude of an

oscillation pr "a motion "ith time.

Dead Time: #he time bet"een a change actually occurring and thecontroller sensing the change.

Deca" #atio:#he ratio of one oscillation to the previousoscillation.

Empirical: 7ata "hich is gathered from actual physical test9 notcalculations.

$ain:#he ratio of output to input of any section of a control system.

%ntegral Time: #he setting of the integrator in an integral controller.sually set as minute%:% pr repeats per minute.

eas&red 'aria(le:#he part of the process "hich is being measured bya control system.

Notc! et!od: / method of controller tuning that utili;es the freuencyresponse of a controller to determine the point "hen the loop gain is lessthan one at the critical freuency.:

Open Loop: / system in "hich the controlled uantity is allo"ed to varyin accordance "ith the inherent characteristics of the control system.

Oscillations: / uality that fluctuates above and belo" a set value.

Oscillator": / process more prone to oscillate.

Proportional pl&s reset pl&s rage controller: #ype of controller thatincorporates all three methods of control.

Stepping: / setting of a controller "here the process is desired tostabili;e. !tepping is9999 usually determined manually.

#age:)ate is the name of the section of a controller "hich responds to a


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process rage of change. /lso called derivative.

#age Time:#he setting of a rage controller. sually in minutes.

#eaction #age et!od: of tuning a controller "here the basis is ho" fastthe process changes from one steady state to another.

#eset: )eset is the part of a controller "hich responds to the magnitudeand the time an error signal e99 that are located on the controller. Informationconcerning the controller9 measuring element and the final controlelement is usually available from the manufacturer. If not9 it is easilyobtained through simple calculations and measurements.

Items such as gain9 dead time and time constant are not difficult todetermine for the control system components.

?o"ever9 the same characteristics for the process are e

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proportional plus reset plus rate controller. #his "as chosen since itis the most common controller in use.

2.*.* /'#O)! /('#I&A !#/0I,I#B=

One of the primary points of interest in the overall performance of acontrol system is the response of the control loop and process actingtogether. C)esponseC is usually used to describe the dynamic behavior ofthe entire system after a disturbance "hich may be either demand orsupply. #he overall uality of the response is judged by the speed "ith"hich the controlled variable returns to the setpoint9 by the amount ofovershoot that occurs and by the stability of the system during thetransient condition.

#he performances that describe the uality of response for a controlsystem tend to counteract each other. Aenerally an increase in the speedof response decreases the stability of the system. /n attempt at achievingtoo fast a speed of response may actually create a totally unstable system./ control system that is stable is one that is undergoing oscillations thatare constant or decreasing in amplitude. /n unstable control system is onein "hich the oscillations are increasing in amplitude. #hese oscillationsnormally occur at a certain freuency called the critical freuency. #hiscritical freuency is the one at "hich there e

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.*.* ',O!(7 ,OOP M(#?O7!=

Procedures for adjusting controllers fall into one of t"o categories. irst9there are a fe" methods based upon characteristics determined from the

closed loop response of the system. #hese methods reuire that thecontroller be in automatic. !econd9 some methods are based upon thecharacteristics determined from the open loop response. #he processreaction curve is used to determine these characteristics. #he open loopmethods do not even reuire that the controller be installed.

.1.* &O#'? M(#?O7

One of the simplest methods of tuning a controller is the notch method.#his method utili;es the freuency response of a controller to determinethe point "hen the loop gain is less than one at the critical freuency.

0y plotting the gain of a three mode controller against the freuency ofthe signals to "hich it must respond9 some rather interesting and usefulpieces of information can be obtained. / plot of this type is $no"n as afreuency response curve. Figure 1 sho"s the freuency response curvefor a three mode controller.

#he curve can be divided into three major sections. #hese sections areproportional9 reset and rate.

#he gain in the middle portion of the curve is controlled by theproportional adjustment%9 &ormally this gain is the lo"est of the threesections. #he gain at the lo"er freuencies=D is controlled by the resetadjustment. #his gain starts at the proportional value and increase in alinear manner until a ma

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igure 1. reuency )esponse 'urve for a #hree Mode 'ontroller

/djustment of proportional band of the controller causes the curve tochange as sho"n in Figure 2.#he curve sho"n in the upper dotted line isthe result of the proportional adjustment. #he upper adjustment that issho"n in the figure is $no"n as ma$ing the notch shallo"er. #he notch isthe area bet"een the reset and rate gain lines. Ma$ing the notchshallo"er is the same as increasing the gain or narro"ing the proportionalband. Increasing the proportional band or decreasing the gain has theeffect of deepening the notch. #his is sho"n as the lo"er dashed line inFigure 2. It should be noted that the length of the proportional portion ofthe curve is unaffected9 only the position of the curve is changed. /nother"ay of stating this is the "idth of the notch remains the same.

igure 2. /djustment of Proportional Portion of the 'urve

#he "idth of the notch is controlled by the reset and rate adjustments ofthe controller. #he effects of these adjustments are sho"n in Figure 3.#heleft side of the notch is controlled by the reset adjustment. Increasing thereset adjustment9 "hich is increasing the number repeats per minute ordecreasing the integral time, causes the reset portion of the curve shiftto the right. #he reset gain has been increased. / left shift of the curve is adecrease the reset gain. 0oth of these adjustments are sho"n as dotted

lines on the left side of Figure 3. /djustment of the rate adjustment hassimilar effects. /n increase in rate time produces an increase in rate gain.

#he increase in rate gain is sho"n as a movement of the to portion of thecurve to the left. Movement to the right is a decrease in rate gain. Figure 3sho"s these adjustments as dotted lines on the right side of the figure.


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igure . (ffect of /djusting the )eset and )ate Portions of the 'urve

#he final result is that the si;e and shape of the notch can be changed bythe adjustments. on the side of the controller. #he depth of the notch iscontrolled by the proportional or gain adjustment. #he "idth of the notchis manipulated on the left by the reset adjustment andE on the right bythe rate adjustment.

#he problem of matching the controller to the process is no" a matter ofhaving the loop gain less than one at the critical freuency. If the gain ofthe controller is sufficiently less than one9 then the loop gain is less thanone. #he notch method of tuning strives to place the critical freuency"ithin the notch. Fith the critical freuency "ithin the notch9 the gain ofthe controller is reduced to insure stability.

#he notch tuning procedure is normally performed "ith the controller inservice. Figure 4 sho"s a bloc$ diagram of a control loop upon "hich thenotch tuning method is being employed. #he bloc$ diagram has beenmodified by the addition of a recorder. #he recorder is indicating thevalue of the setpoint and the measured variable. #he reuiredinformation needed for the tuning process is obtained from the recorder.

igure 4. 0loc$ 7iagram of a Process 0eing &otched #uned


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#he initial step is to broaden the notch. #his is accomplished bydecreasing the reset and rate gains "ith the controller in manual. #hereset adjustment is set to either minimum repeats per minute orma

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igure 6. 'ontroller Aain at the Aain ,imit 7ue to Proportional /djustment

#his results in the system once again becoming stable. #he result of thisadjustment is sho"n in Figure 7. #he gain of the controller is no"sufficiently lo" that the loop gain is less than one.

igure 3. 'ontroller Aain /fter inal /djustment of Proportional 0and

Once the proportional band has been adjusted9 the ne

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igure 5. 'ontroller Aain at the Aain ,imit 7ue to the )eset /djustment

Figure 8 sho"s the results of the notch being narro"ed until the reset

gain is at the limiting value for the gain. #he controller gain is again largeenough to provide a loop gain of on Ee Once this condition is reached9 thenumber of repeats per minute is reduced to a value that is one third of theone that placed the reset gain portion of the curve at the gain limit.adjustment ma$es the system stable. #he reset portion of the responsecurve is no sufficiently to the left of the gain limit so that the gain of thecontroller is lo" enough ensure that the loop gain is less than one at thecritical freuency. #he control system no" in a stable condition. #he resultof this adjustment is sho"n in Figure 9. #he reset gain portion of theresponse curve is no" closer to the critical freuency than the rateportion.

igure 8. 'ontroller Aain /fter inal !etting of the )eset /djustment

?aving completed adjustment of the proportional band and the repeatsper minute leaves9 Eonly the rate adjustment. #his time the rate time isincreased. #his action increases the :: rate gain portion of the responsecurve. / small disturbance9 a setpoint change9 is introduced / into theprocess. #he effect of the disturbance on the measured variable ismonitored by the recorder. /s before9 the process responds sluggishly.

?o"ever9 as the rate time is increased9 the response of the processbecomes more oscillatory. #he increasing of the rate time follo"ed by


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introducing a disturbance is continued until the measured variable brea$sinto continuous oscillation. /s this part of the procedure is beingperformed9 the notch is being narro"ed. Figure 10 sho"s the effect of thenotch being narro"ed until the rate gain is at the limiting value of thegain. #he gain of the controller is no" large enough to establish a loopgain of one.

igure 1*. 'ontroller Aain at the Aain ,imit 7ue to the )ate /djustment

/fter this condition is reached9 the rate time is reduced to a value that is

one third of the value that placed the rate gain portion of the curve at thegain limit. #his adjustment ma$es the system stable again. #he rateportion of the response curve has no" been moved far enough to the rightof the gain limit so that the gain of the controller is lo" enough at thecritical freuency to ensure the loop gain is less than one. Figure 11 sho"sthe position of the rate portion of the response curve after the rateadjustment is completed.


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igure 11. 'ontroller Aain /fter inal !etting of the )ate /djustment#he final result is that the freuency response curve is symmetricallyplaced about the critical freuency. 7ue to the proportional portion of theresponse curve9 the gain of the controller is lo" enough to ensure that theloop gain is less than one at this point. In order to improve performance9the loop gain should be high belo" and above the critical freuency. #hisis accomplished by narro"ing the notch as far as possible and stillmaintain stability. #he narro"ing of the notch is achieved by the resetand rate portions of the response curve. pon completion of the notchtuning method9 the response of process to a disturbance appears as a oneuarter dampened "ave in the value of the measured variable.

One of the main disadvantages of the notch tuning method is that theprocess must be placed into continuous oscillation three times. #here areprocesses that cannot tolerate being placed into continuous oscillationthis many times. /nother closed loop tuning method is available that onlyreuires placing the process into continuous oscillation once. #his is the

ultimate period method.

.2.* ,#IM/#( P()IO7 M(#?O7

#he ultimate period method for tuning controllers "as first proposed byGiegler and &ichols in the early 184*:s. #he term CultimateC is used "iththis method because it reuires the determination of the ultimate gain orproportional band and the ultimate period. #he ultimate gain9 Hu9 orultimate proportional band9 P0u9 is the ma

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sho"s the ultimate period. #he ultimate period in this case is the timeperiod from "hen the controlled variable is at its ma

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igure 1. )esponses of the Measured -ariable to a !upply 7isturbance

sing the ultimate gain or proportional band and the ultimate period9 thefollo"ing euations are used to determine the settings that provide a oneuarter dampened "ave of the measured variable.

Proportional

Hp *.+ HuP0 2 P0u

Proportional and )eset

Hp *.4+ HuP0 2.2 P0u

#i PuJ1.2)PM 1.2JPu

Proportional and )ate

Hp *.6 Hu P0 1.66 P0u

#d PuJ5

Proportional and )eset and )ate

Hp *.6 Hu P0 1.66 P0u

It should be noted that these euations are empirical. / controlsystem tuned using these euations is a very close appro

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18

igure 14. #est 7ata for ltimate #uning Method

/s an e

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Hp *.6 Hu P0 1.66 P0u

Hp *.6 L4 2.4 P0 1.66 L2+K 41.+K

#i PuJ2 )PM 2JPu

#i 16 minJ2 5 min )PM 2J16 min *.12+repeatsJmin

#d PuJ5

#d 16 minJ5 2 min

/s noted earlier these settings give a close appro

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)eset#i PJ1.+ )PM 1.+JP

)ate#d PJ5

Once the reset and rate adjustments are made9 the gain or proportionalband is readjusted to provide a one uarter dampened "ave response ofthe measured variable.

In general9 there are t"o obvious disadvantages to these methods. irst9both are in actuality trial and error. #his is because many values of gain orproportional band must be tested before the gain limit9 ultimate gain orthe gain that gives a one uarter dampened "ave is determined. #o ma$ea test9 especially at values of gain near the desired one9 it is oftennecessary to "ait for the completion of several oscillations before it can bedetermined if the trial value of gain is the desired one. !econd9 "hile one

loop is being tested in this manner9 its output may affect several otherloops. #his may produce unstable operation of an entire control system9especially a comple< one. /ll tuning methods reuire upsetting the controlloop9 ho"ever9 other techniues reuire only one test.

4.*.* OP(& ,OOP M(#?O7!=

In contrast to closed loop methods9 the open loop techniues reuire thatonly one disturbance be imposed upon the process. In actuality thecontroller is not in the loop during the testing of the process. #hesemethods see$ to determine the characteristics of the process.

rom the process characteristics9 the proper values for the controllersettings are obtained. In general9 most processes are multiple capacity.

#his reuires the use of an approximation. #he most commonappro

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igure 16. 0loc$ 7iagram of a Process 0eing Open ,oop #uned

#he other change is that besides indicating the measured variable9 therecorder indicat controller output rather than setpoint. /n arrangement ofthis type can be used to obt%: the process reaction curve for a process.

#o determine the process reaction curve the process is brought to asteady state level. Ideall the steady state level should be one "here thecontrolled variable is at the setpoint. #h. controller may then be placed inmanual. / supply disturbance is introduced by changin. the manual outputof the controller. #he response of the process to the supply disturbance: isrecorded. #his is done by the recorder that receives the measured variablesignal. #he output of the controller is also recorded to provide a referencefor "hen the disturbance "as9 initiated. /fter the process reaction curvehas been recorded9 the controlled variable should: be returned to thesetpoint by manual operation. It is obviously easier to obtain a processreaction curve than it is to determine the ultimate gain.

Figure 17 sho"s a typical process reaction curve for a process that hasbeen open loop tested. #he curve is one for a multiple capacity process.

#his curve is appro

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igure 13. Process )eaction 'urve for a Open ,oop #ested Process

igure 15. #ime 'onstant Method for a !ingle 'apacity "ith 7ead #ime/ppro

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because a change of 2*@ for a 1**@ span is greater than a change of2*@ for a 2**@ span. #herefore9 a 2*@ change in the measured variabledoes not indicate the magnitude of the change9 as "ell as the percentageof span does. / 2*@ change for a 1**@ span is 2*@K of span9 "hereas a2*@ change for a 2**@ span is 1*K of span. #he 2*K span change is alarger change "ith respect to the measuring span of the instrument thanthe 1*K change even though both changes are 2*@. #he input change isthe percent of span change in the controller output. sing the K of spanreuirement for the output change9 the process gain may be "ritten asfollo"s%

spanfKinoutputcontrollerin'hange

spanofKinvariablemeasuredin'hangeIH

"here%

HProcess Aain

#he dead time determination is done the same "ay as presented earlier.#he dead time sho"n in the figure as td.

sing this information the follo"ing euations are utili;ed to tune thecontroller for a one uarter dampened "ave response of the measuredvariable.

Proportional

H p tJLtdHP0 1**KJHp


Hp*.8 tJLtdHP0 1**KJHp#i. td)PM 1J. td


Hp1.2 tJLtdHP0 1**KJHp#i 2.* td)PM 1J2 td#d *.+ td

/s an e

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sing euation 8=89 the process gain can be determined.

igure 18. #est 7ata for Open ,oop #ime 'onstant Method

spanfKinoutputcontrollerin'hange

spanofKinvariablemeasuredin'hangeIH

H 4*KJ5.K 4.5*

sing the information obtained from the process reaction curve the

follo"ing settings can be made. #hese are Giegler=&ichols euations.

Proportional

HP t JLtdH P0 1**KJH PHP1.6 minJL*.2 minL4.5* 1.63 P0 1**KJ1.63 6*K


HP*.8 t JLtdH P0 1**KJH pHP*.8 L1.6 minJL*.2 minL4.5* 1.+ P0 1**KJ1.+ 66.63K

#i. td)PM 1J. td#i. L*.2 min *.666 min )PM 1J.L*.21.+repeatsJmin


HP1.2 t JLtdH P0 1HP1.2 L1.6 minJL*.2minL4.5*2.*

P0 1**KJ2 +*K#i2.* td )PM 1J2.* td#i2.* L*.2 *.4 min )PM 1J2.*L*.2 min2.+

repeatsJmin#i*.+ td


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#d*.+ L*.2 min *.1 min

4.2.* )eaction )ate method

#he second method of open loop tuning is $no"n as the Reaction Rate

Method and is sho"n9 in Figure 20. In this method the informationreuired from the process reaction curve is the slope of the ma

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Proportional

Hp 1JL)rtd P0 1**KJH p


Hp *.8JL)rtd P0 1**KJH H#i . td )PM 1J. td


Hp 1.2J')r#d P0 1**KJHP#i 2.* td )PM 1J2.* td#d *.+ td

28

igure 21 #est 7ata for Open ,oop )eaction )ate Method

/n e

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#he supply disturbance is the change in the controller output of 5.K ofspan. #he time period for the 1*@ change is *.+ min. #his time isdetermined by using the ma

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!ummary

#"o major factors are reuired to produce instability in a control loop.#hese are a loop gain:9 that is greater than one and a 6** phase shiftaround the control loop. #he loop gain is adjustable. It is adjusted bychanging the gain of the controller. #he 6*@ phase shift depends:E on thecharacteristics of the components that comprise the control loop. #hecharacteristics are generally not adjustable and often are difficult todetermine. #his is especially true for the process. #he 6*@ phase shiftnormally occurs at a certain freuency "hich is the critical freuency.

#herefore9 in tuning a control loop the loop gain must be less than one atthe critical freuency for stability and higher at other freuencies toensure sensitive control.

#"o methods are available for control loop tuning. #hese are the closedloop and open loop methods. (ach has its o"n advantages anddisadvantages.

#he closed loop methods are the notch tuning9 ultimate period anddampened oscillation. (ach method is performed "ith the controller inautomatic.

7isturbances are introduced into the process until sustained9 constantamplitude oscillations are achieved. Information is obtained from theseoscillations. #he information is then used in euations to determine the

controller settings.

#he open loop methods are the time constant and reaction rate methods.(ach of these methods is performed "ith the controller in manual. Onlyone test is performed. #his test is used to obtain the process reactioncurve. (ach method uses different information from the process reactioncurve to determine the controller settings. /gain the information obtainedis used in euations to calculate the controller settings. .

0oth the closed loop and the open loop methods are designed to producea one uarter dampened "ave in the measured variable after adisturbance. In either case9 a very close appro

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#ro"ess $ontrol Instrumentation Te"hnolog% &ohn Wile% and !ons9 18339&e" Bor$!(,='?('H )(-I(F J P)/'#I'( N(!#IO&!

1. Fhat term identifies the dynamic behavior of the system after adisturbancea. 7ampenedb. Aainc. Oscillationsd. esponse

2. Fhat method of timing has the disadvantage of having the processin continuous oscillation three timesa. &otchb. ltimate periodc. #ime constant

d. )eaction rate

. 7escribe the &otch method of tuning.

4. 7escribe the ltimate Period method of tuning.

+. 7escribe the #ime 'onstant method of tuning

6. 7escribe the )eaction )ate method of tuning.

P()O)M/&'( J ,/0O)/#O)B (()'I!(!

1. 7escribe the steps used in tuning a loop using any of the methodsdiscussed.a. &otch methodb. ltimate period methodc. 7ampened oscillations methodd. #ime constant methode. )eaction rate method


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/&!F()! #O !(,='?('H )(-I(F N(!#IO&!

1. d2. a. /ns"er is found on pages 6=144. /ns"er is found on pages 1+=2*+. /ns"er is found on pages 22=236. /ns"er is found on pages 23=*

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