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INSTITUTE

Distributed in A~.,:- :·".&Sia by: OF INSTRUMENTATION AND CONTROL

AUSTRALIA,

INC.

CONTROLLER TUNING AND CONTROL LOOP PERFORMANCE

Is E c o No

E o I TI

o NI

A Primer By David W. St. Clair

PUBLISHED BY: STRAIGHT-LINE CONTROL COMPANY, INCORPORATED

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BACKGROUND THIS BOOKLET WAS ORIGINALLY ISSUED IN 1983 AS AN INTERNAL REPORT IN THE DUPONT COMPANY TO HELP ENGINEERS AND TECHNICIANS,

WHO HA VE

NO SPECIAL TRAINING IN FEEDBACK CONTROL, UNDERSTAND

THE BASIC

',

. . ;

CONSIDERATIONS

AND LIMITATIONS. IT HANDILY BROKE ALL RECORDS AT .

•

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THE DUPONT COMPANY FOR NUMBER OF REQUESTED COPIES (OVER 1200) WHEN

ISSUED.

THAT

REPORT

WAS

RELEASED

TO

THE

PUBLIC

AND

.

PUBLISHED DUPONT

IN 1990. IT SUBSEQUENTLY

REQUESTED

A MANUAL

SOLD OVER 16,000 COPIES. IN 1992

TO BE WRITTEN

SPECIFICALLY

FOR

TRAINING, EXPANDING ON THE ORIGINAL REPORT. THIS SECOND EDITION IS BASED PERHAPS 80% ON THAT TRAINING MANUAL.

ABOUT THE AUTHOR THE AUTHOR RETIRED · AFTER 40 YEARS OF PRACTICE INSTRUMENTATION

IN THE FIELD OF

AND CONTROL IN THE PROCESS INDUSTRIES

(8 YEARS

WITH EASTMAN KODAK AND 32 YEARS WITH DUPONT.) HE TOOK IN 1947 WHAT HE UNDERSTOOD TO BE THE FIRST COLLEGE COURSE OFFERED IN THE THEORY OF FEEDBACK CONTROL, A CHANCE EVENT AT MIT THAT STARTED HIS CAREER IN THE FIELD. HE ARGUABLY HAS APPLIED THE SCIENTIFIC METHOD TO SOLVING CONTROL PROBLEMS IN THE PROCESS INDUSTRIES LONGER T

ANYONE, OR AT LEAST THAT WAS PROBABLY TRUE WHEN

HE RETIRED IN 1987. HE HAS BEEN EXPLAINING THE CONCEPTS TO THE NONSPECIALIST FOR MOST OF THAT TIME. HE RELISHES THIS OPPORTUNITY SPREAD THE WORD TO A LARGER AUDIENCE.

HENCE THIS PUBLICATION

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Copyright© 1989, 1993 by David W. St. Clair. Straight .. Line Control Company, Inc, .

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PREFACE .

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This second edition of Controller Tuning and Control Loop Performance has been extended in both directions :fmtn ,the first. Sections have been added for the very beginner and for the somewhat more experienced. It is about twice the size. Sections have been added on the what-to-do and how-to-do-it of tuning, to help the person who may have never done it before. Then interspersed throughout are paragraphs that extend some of the non-math concepts to the realm of math, or at least algebra. These sections explaining concepts in math (sometimes frequency response terms) are clearly identified to make them easy to skip. This second printing of the second edition · also has expanded part of chapter 2 and has added two pages to chapter 8, as compared with the first printing. It still stands on its . . own, of explaining the essence of feedback control, without referring to math. I hope these new references will help any reader who wants to bridge the gap from the nonmath to the math. .

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· The first edition was essentially a verbatim copy of a report written for DuPont in 1983, which I was allowed to make public in 1990. This second edition is perhaps 80% based on a 1992 update of that original report, written for a training course for DuPont instrument technicians and engineers. The new version was to have . specific references to the DuPont situation, and was co-authored by Paul S. Fruehauf (of DuPont) and myself (DuPont retired). I am very appreciative of the permission from William X. Alzos (of DuPont) to use what I wished from those course notes.· .

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I am particularly grateful to Paul S. Fruehauf who has worn two hats ·in. the preparation of this second edition, first as co-author. of the DuPont report, and second· as critical reviewer of my modifications and additions to that report. Most of the material in chapter 2 is his. The first draft of much of that material was his, and he persuaded me to include it in this booklet. He is currently an employee of Applied Control Engineering, Inc., a consulting firm in Delaware. .

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I have tried to make this second edition appeal to readers whose background may not be the chemical processing industries. I know I can only partly succeed in this broadened scope, for all of my 40 years in the automatic control business were in that industry. .

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I hope this booklet meets what I perceive as a need for more information on the beginning end of training on the subject of controller tuning and control loop performance.

ENJOY

This booklet on controller tuning and controt loop performance stops where most books and courses on the subject begin. Too • often the subject IS introduced with math unfamiliar to-the reader. That does not have to be there are simple concepts to help those unschooled in the math to know and understand the basics, to appreciate the limitations and to know· what can be expected.

My field for 40 years was industrial process control. The basic concepts of control are the same, regardless of the field. The examples will change, but the concepts, principles, and much of thevocabulary won't. For readers whose field. is different from mine I hope you will gain some useful insight into . your situation.

scapegoat, being blamed for problems that are not related to tuning, with the result that time and energy are spent needlessly. Meanwhile a proper solution goes unsought. While I will give ruJes · for tuning, the rules themselves are only' part of ;the picture. The ''tuner'' needs to know what the desired performance is and what to expect-when the system is responding as well as can be ex• pected, and when is it not. If it ts not, then the rules may not apply, or should be modified. This booklet teaches not only the rules, but· what can and cannot be expected from tuning. It is also to teach some of the common pitfalls. Why do the tuning rules not seem to work sometimes? In addition, tuning is often done to fix some problem. You· cannot use or fix anything unless you know how it should work, and that includes control loops.

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Not everyone needs to know about controller tuning. Many businesses, like banking and insurance, probably need no one. Other businesses, like the automotive business, probably need only a few. But that still leaves many businesses that do need to know, and you wouldn't be reading this if you didn't feel a need to know! In many industries proper tuning is vital to quality, and often decisions are made to take expensive steps when better tuning might do the job. On other occasions controller tuning is the

Tuning rules presume that the desired result is a "tight" system, one that does the best job of reducing the effects of disturbances, . and/or one that responds quickly to setpoint • changes. This may not always be what IS desired. Many level controls are often deliberately detuned (made more sluggish than the tuning rules would make it), a condition referred to as averaging level control. Many • loops Ill a plant do not have a very vital

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2

Chapter 1, Getting Started

bearing on quality or other business considerations, so whether they are tuned tightly or not is not all that important. How many new operations are started up and have all the loops on automatic for the' first product

made? Not many. Quite possibly not any. Usually there are at least a few loops that stay on manual for some time, sometimes • even years. It IS hard to argue that these loops need tight tuning.

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Controller tuning is mostly science, Tuning rules are based on mathematically clean and simple models that approximate the real

world. the If real world were mathematically clean and. simple.. then • controller .tuning would . . be all science (provided of course, therewas agreement on what was desired from the tuning). Happily, .. experience (and higher math) has shown that the real world can be simplified without sacrificing accuracy enoughto worry about, • It IS known, with .a reasonable degree of • certainty, when this simplification lS invalid, and therefore when the rules for tuning will break down, .

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mathematically pure and simple models are used to represent the ''typical'' process. Don't worry about that, certainly not at this stage, The differences are relatively small compared with what I consider realistic goals in tuning. We will not be concerned about determining settings to within 1% ' and generally not within 10 or 20%. For instance, if the tuning rules determine that a controller setting should be 1.00, it doesn't really matter · if it is set for 1.01 or 1.10. .

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Even if· set for 1.20 you would be hard • pressed to see the difference ID most practical cases. Determining settings within 30 to 50% is a more realistic expectation. Two specialists in tuning will almost surely come up with different settings in any given situation. They are far more likely to, indeed will .almost . certainly, come up with the same analysis of what m.ay be wrong with a loop. They are less likely to agree on what the best solution is. It is rather like politics • Ill that regard . . .

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There are ··numerous publications givmg tuning rules, and, as you might expect, they • don't all. give exactly the same rules. This IS because different .criteria are used for what constitutes "proper" tuning. Different .

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was a quantum leap. forward in the science and/or art of tuning industrial controllers. It took perhaps /10 years or more after that before subsequent authors started to hone and refine . their: recommendations, .. but . the essence of their approach has remained un.·

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scathed to this day! . Ziegler and Nicholsnot only brought. order out .of chaos; but· they presented . it · in · a simple, understandable way. They· presented two ways· 'of· determining controller settings. One was based on closed-loop tests, the other on open-loop tests. . · They were both based on sound mathematics, though their peers did not recognize oraccept it at the time. A 1991 con- . versation wi.th each of . them revealed· that Nichols, with a mathematical bent, was primarily responsible for verifying the math of the closed-loop formulas, while: Ziegler; of ·a more empirical bent, conceived the open-

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know about: Automatic Control, aassical Linear Theory, edited by George J.· Thaler, Naval Postgraduate School. It was published by Dowden, Hutchinson and Ross .Inc., Stroudsbµrg,11-~A./.:in_ ~l'.9Jfl~, It is qui of ·:ptint . .... now, :biit~can·;t,e·-9i,ttfn.ed frqm ·major technical· ··Iibraties. )-/The :iibook "is .one ··.of the "Benchmark Papers in Electrical. Engineer.mg. anc d .Computer . 'Science, . '' v. 7, wit. h Library of Congress Catalog .Number: 742469, ., and . ISBN: · 0-87933-083-X,._ ·It ·• is a photographic· reproduction .of .milestone papers. on the math of· the feedback control . loop, with-editorial ·comments on .the contribution. each made from-a historical: viewpoint.··•·. The British· papers by Callender, Hartree.. Porter (and Stevenson); 1936· and 1937, from which Nichols was able to confirm the formulas presented by himself and Ziegler, are also containedin it, as well as . the original Ziegler and Nichols paper.

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64, Nov. 1942; · p7.S.:.?)., :_ Their contribution

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Controllers,•·Transactions··;of the ASME,· v

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loop· method. · Nichols . then verified . the mathematical validity of; the ·open-loop approach.

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No reasonably thorough writing -on controller tuning would be complete without paying tribute to J . .G. Ziegler and N. B .. Nichols (Optimum Settings ..

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,r.,ath . "(a.P.l{!BIIY~ fA/gel:>~fJ) ;· : and :-:'Jejy. ·. . . . . quickly forget ~aboiit· tfiti· ~bias,: 'B~ ·as· it . · · : · .

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used. This is simply a change that continues at a fixed rate, rather than all at once, as for a .step change. The derivative· function· adds to the output that would normally occur, in effect advancing the response by an amount in time . equal to the derivative . time. Actually the advance in time is notquiteas large. as the derivative time, . which is a result of the· deliberate . imperfection in the function. .

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derivative would have a transfer function of: ·. · · . . :.,~!.}, ,; :JJ: . .;: ft' ? ·.... :., . . .

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You already know that the; derivative .. function is not mathematically perfect. Actually the way the algebra is written is to. write it as a proportiBn,al-plus-derivative function, with the proportional part having a gain of one. Here is the transfer function typically used to describe the (proportional-plus-) derivative function:

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Derivative action has the potential to improve performance but is unlike proportional or integral action in one important aspect. Withthose, it is· mostly amatter of using enough but not too much. If you did not use enough there would still be beneficial action, and performance would be better than if you did not use them at· all. With derivative the problem is ·. still one of using enough but not too much, ·but -if you do not use enough, there is no benefit at all and there could be some harm. If you use just a little bit too . much the troubles increase a lot faster. than the benefits. IF .

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USED AT ALL,.. IT. HAS TO BE SET INTELLIGENTLY.

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The numerator is the ideal part and the · denominator is · the practical necessity. The-denominator tstne transfer function of a lag, which will be discussed more in ·.· the next secion · on. filter time. · The new. parameter, Kd, is known as .th,e _deriva~ . tive gain .. It determines the .height of the . peak in.Figure 1.5. If the derivative gain is 10, a typical figure, then the maximum the derivative function can magnify any rate of change is 10.·· .

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It should be remembered that j\vsually the derivative function on a digital controller is set up to act only on the controlled variable, not on the error.

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contaminate the product Y ou.may think -of other examples. So again, you are back to the tuning rules .. · · ·. · . . _

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These .. rules . are;.:..J degraded . polymer . that

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If y~u need to be Jnore precise than the above generalities yield, then continue with the closed-loop approach to tuning, trying . small setpoint changes to test for stability. ~ The open . . loop, response Is usually too ,fast . ' to ~APWI'~ a9~urately on typical . co~t,()J . i : roolll' :llionitoring equi,pment, so ~~the. open- .• : .· loop ···approach:,. is··usually not•·. u·sablei'··ae . . ·• • aware · though.·· of one factor when; tuning · ·• flow loops. T,hat is tha~ ~he· ope.11~,~9.p gain .. · . is likely to be .higher at high flows than at. · · low flows. The open-loop gain is how much the ('low moves (in percent ()f scale), . . ill response. to a· change in t~e .con~roller output (in p~rcent of seal~)~ If this is higher at higµ flows,. as it often is, then tµ.n~g done a.t low flows may become unstable at high flows. .

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28

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. Chapter 2, Tuning Rules and Procedures

Occasionally a flow will be controlled indirectly. That is; the valve .and the flow meter are not in the same line. In these cases the typical flow-loop dynamics do not exist so the typical tuning settings do not exist either. Tune these loops as you would any other, choosing between the open and closedloop methods . · ·. based · on considerations discussed elsewhere.

Level and flow are examples of classes of loops that only rarely justify being tuned to be tight. There will be many other individual loops which need only to be stable and perform reasonably well. They do not need to run the four-minute mile. But supposing you do want to, how fast can · you reasonably be expected to run the mile?

Pause a moment to think about it.Processes come in a virtually limitless variety, while controllers come with only two adjustments to fit them . Oh yes, in truth there are three, ~roportional, Integral and Derivative (PID), but integral and derivative are determined by the· same process parameter, so having set one, the setting for the other is also determined. Broadly conceived, the task of tuning is concerned with fitting the time and amount parameters of the controller to the . time and amount. parameters of the process. This is similar to fitting clothing (shoes are a good example) to a human being (also coming in a virtually limitless variety), by specifying only two parameters, like width and length. In both cases it turns out not all that badly.

could be worse than if a less customized ap- . proach had been used.

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The reset time, the derivative time and the filter time · are all keyed into the . time parameter of the process. Unfortunately the controller gain is not uniquely tied to an amount parameter of the process; it is tied to both time and amount parameters of the process. Actually it is tied to a time-dependent amount, but that is getting· too complicated at this stage. Just · remember that the time· settings · of a controller are tied to a time parameter in the process, so the time settings all have a relationship to each other. .

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The reason a· controller, having essentially only two adjustments, can fit a process that might be temperature, pressure, flow, composition or an almost limitless variety of controlled variables (when given a name such as these), is that the controller doesn't care what physically is being controlled. It cares only about the time and amount features of the process. It doesn't care about units at all. It is true though, that processes by name often have time and amount •

With computers it is possible, of course, to build a controller to "custom fit" the process, much the same as a tailor would custom fit clothes to a particular person. Let the process, or person, then change. The result

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Chapter 2, Tuning Rules and Proeedures . .

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Part of an overview on these tuning rules is to realize that notonly are .: th~y designed to give tight control, ;but that they :lite .predi-

. · -. inverse .response ,Pr be. :open-loop un-

cated on a few assumptions.

Remember that the rules· are· approximate~They will get. you nicely in :tho; ballpark for· tight control. The. calibrattOJl.,f~ll · . 'e . knobs for analog controllers .· is · :freqlently poor: ·

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Noise can:1,c,.~(j~jlt of ils bwdt$irfli>Ie · variations .· in the· measurement; either not · . meaningful ·. · · variations · and/or . . variations . too fast for. the: controller to · . do inyth~gabQllt. > · · i . . . · •· . .

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· . . · · : I will. venture at this point to introduce a · · : · · concept you· must understand if ·you are to get into the math I algebra of control · loops. The key is to think of wne: is .. . happe(iin.n . WfJ•n · .:~e:i,:· '.:loofi::· _ .,; . ,;,;;Nin• .g·· ·- .· . . ' . ·.. .: : ....... -~•-, ,,,?f;. ..; :. . - -~f:l:.. :. :~>,, ... 'If.;,:;,,,;,:~-""-: : .,,,,,,;r.;J.iilti •·.

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Probably all pure dead time lags . involve a distance and a, velocity. · Generally both distance and velocity are well know, so the dead time is well known, The velocity may change>. with process .eonditions, but a· new deadtime can be calculated. 'One example would be coating weight.on .a moving film. Another would . be -the actual. weight -, after casting or forming 'Jtlte, · sheet" i• ~ the _ first . place; such as in: polyester sheetmaterialor in paper making. These dead times wndr~ run tominutes, because- ofthe distanbes~~d~ velocities involved. · , Jt', · · · .· ·.. · · . , . · ·• · ~:: .

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Another example is in fluid flow. Imagine a brine recirculating system around a jacketed reactor. Colder brine is introduced in the loop and frequently the circulating brine temperature is measured. The distance from the point of fresh brine entrance to the temperature measurement point creates a dead time. With a typical design velocity

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Samplelines.for analyzers·,._such-as,for.lR or chromatography, Introduce .a dead .time. If the flow is turbulent, then there is ,.Jittle ldngifudillal mixing and. the dead time of eomJ)Ositioj:t •: to::: ithe:' ,; :analyzer .is . ·Virtu.ally pure .. If the:7.flow is. iaminar,;;suchi;;:as:in. ·a sample line-taken off for a viscometer ' then· ·there ·is substantial longitudinal mixirig and the dead time is not pure. It has a pure dead time component which is shorter than that computed from average velocity because the velocity in the center of the pipe is higher than the average velocity. Then the response has a lag beyond that as the material along the edge of the pipe comes along, but this is .

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general _concept _to the actual syste.m.. The organization ., of material is: 'mixed ·between type · of .· lag · and · .of •.• equipment . or

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this dead time is usually only afew seconds; but it is still a pure dead time. · Well almost. Actually · the lag · from· brine entrance to temperature measurement is more complex than this. It has that pure dead time element, but then it also has more delay because of the need. to change the. pipe temperature. The pipe absorbs some of the energy which would otherwise be physically transported. I am not aware of any quick estimating technique . to determine how much lag this might . add; ·. · it· · would · depend·.. · on • the parameters .ofthe system. Generally·.. it. is small ·• .relative •.:'· to .·· .typieal · . temperature

This. section will present specific examples of lags tohelp transcend the·. .gapfrom the

process.

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Chapter 5, Examples of Actual Lags

52

not pure dead time. Generally, in the viscosity case, you won't be far wrong by assuming pure dead time, calculated from distance and average velocity. The consequences of this simplification depend on what other lags are in the loop. Typically it would be a conservative assumption. _ . ·

connection with Figure 3.3, it may tum out that the lag is too long relative to the upsets expected. The point I want to make is that the dead time, per se, is no problem. It is the speed and severity of the upsets relative to the dead time that are important. .

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While on the subject of analyzers, what is

the effective lag of a chromatograph if used Most controllers are so fast that their lags in a control loop? For illustration_:,:.~sume can be igllor~, even pneumatic controllers. the unit has a cycle tun~ of l'Q,minu:is-. Thi~-. In ·-loops .op8fating · with natural periods of introduces a minimum · effective dead time one second and less this may not be true, of half that, or S minutes, But that is not .all, ·- but in· that 'region you will likely need to To this must be. added the .time .between knowmore thanthesenotes will teach you when the sample valve opens. and when· the . >'' anyway. Most and possibly all instrument peak being controlled gets measured and manufacturers "oan now give you the held. If this were 3 minutes· · then the dynamic ··characteristics of a11· _ their chromatograph should be _ considered as equipment. If a pneumatic controller is adding aneffective dead time of·s minutes operatinga valve without a positioner, or is to the loop dynamics. And this excludes any having . to fill a comparably large volume, lag in the sampling line. The very· act of the controller might have a small lag. In all sa.mpl-ing introduces other dynamic cases I can think of where there was interest considerations but these are discussed under in dynamic performance, the valve was Sampling Frequency and Loop· Performance equipped with. a· positioner (small volume in chapter 9 . ·_ · for the controller and transmission line to fill) so . the . controller's . lag was made A quick word· about processes which have a irrelevantly short. pure dead time as a dominant lag. Many people who are not in · the field of control When_ I say that the lags in a controller can think that if a process has "a lot of dead usually be ignored I mean the proportionaltime'' it is uncontrollable, ·Not so. It - is just action part of the controller. 'The integral as controllable as any other process. Indeed, action is .in .itself a lag, but it is under our an argument can be · made that it . is more control. . The derivative action· is the controllable, since the natural period may be opposite, a lead, but it is also under· our closer . to 2L than 4L. The view that control. In analyzing the lags in a complete processes with pure dead time are hard to control system .I prefer to. think of the control derives from the fact that frequently· controller as having no lags ( or leads), since pure dead times are long . several minutes. their contribution is part of the tuning Then in applying the concepts explained in considerations. .

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Chapter 5, Examples of Actual Lags·

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Lags of transmission lines are ~':·fifMel~~;( : :·'~ matically very_ complex, · depending not ---+--· only on lengthand inside diameter, but 4 .. . . ~ : '. . . 'V , . · ' .- ·" . : also . on absolute pressure and · tempera,,• 3 . .. . ' ture· and on termination volume. If the 2-------........ -........ ...-~+++-+-------f termination volume -actually increases · m V4" TUBING. L.--:-- rt 3/•".TUBING with pressure, as. With .: an unpositioned !J 1.0 ·' ..... · . . . . _..... : .... · . .-··. . . . valve operator, the lag is even longer. 0.8 ·. You need molecules · to increase the 0.6 ...........•... 7;...,- +-- .........+--tl-+-~~-----1 o.s----. . _ . . . .. pressure of the existing volume · and to 0.4 __.......,_....._~l-loo+-+-+---fill . the ... incrementally . new volume, 0~3 ..... --- ~--- ,. · ·-·: ....._......................', .......+-....... -.---Realize that· the incrementally new vol0.2 - -··-· · ..,__· ume needs molecules to· fill it from zero / ' V. absolute pressure, notjust to change an . 0.1._ ............._....................... _ incremental .- amount. · . This can be a 100 · · 200 300 400 : reoo · 1,000 · 2,000 significant part of the - total · effective Tubing Length, Feet.· · · · volume. Except for unpositioned valves, termination , · volumes · · of pneumatic · F.1gure 5• 1 • -·The Iag of : transm1ss10 · · n tu b"1ng · may be equipment are generally small enough to approximated by a first order lag,,. . be ignored. · .. · · · ·

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Chapter 7, Derivative Action

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tl)J]\]:):I::;J!:~''''''~:;;~,~~~:-~··; . . .... ·,,'.:;~itt'=f ~ pa,ts, firSt . .· the··•cPhtr · ·. one loop. to become unstable if the other used, it might be practical to program or . . · · ·. loop js switched from automatic to manual, configure decoupling terms to .reduee • ".· · . or vice versa. This section on interactions is the · cross talk. Again, this may be too . . more to alert you io the potential problems complicated for the novice to undertake. , · than to equip you to solve them. Basically, unless the problem deserves a more elegant Almost implicit, when · there is · a problem approach, I recommend tuning for the worst with interactionisthat the natural periods of caseIthose.conditions that are most likely to the .two loops are 'similar. If one loop has a produce cycling), and accepting the pernatural period of one second and the other formance ·at other conditions. · . . · · .. · of one minute, · it is highly · unlikely that . . ·..

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Chapter 9, Potpourri

Sometimes, sometimes. Sometimes the disturbance to a control ·. loop is known, and sometimes it is not. · Sometimes the effect of the disturbance is known and sometimes it is not. All of which makes an otherwise almost exact science · · into something of an art. How is it possible to look at some recording charts and decide anything about ·anything?· Well, sometimes it's easy and sometimes it's next to impossible. . .

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typically slow loops.: Frequently the source of a disturbance is a mystery or cannot be agreed upon,. and the measurement itself may be suspect. It would be very difficult to determine whether a loop is performing as well as it can without retuning. If the natural period is already known, then perhaps some judgment could be made using the concept presented in figure 3 .3 . Between these two extremes is a lot of territory; · Experience can be a · . key ingredient. . If. a control system has been giving . excellent .performance and then it is poor, the, . temptation is . to look for a coincident cause. If a control· system· has been drawing straight lines and then appears · to be drawing somewhat . Jess straight lines · .. · . · well, it just is hard to make any general comment. · You .' need to use · all • the knowledge you have . gained on what affects the performance of a loop. .

Let's take an. easy one · first. Consider a

simple flow control loop. The· only. process reasons for flow changing are a change in either· .. upstream· or downstream pressure (unless the flow is "critical," in which· case · · only· ·.the· · upstream pressure applies). Frequently there is knowledge. aboutthese changes, or the potential for change; so there is knowledge about. the upset · or potential for upset. Since the flow loop will be fast, any effects that last very long can be judged as unnecessary and fixable by tuning or by hardware improvements.

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; Probably the first consideration Isto put the loop Oli IJlanual, to see if things. get better or ·. worse. . This ; is easier . to do in some situations than· others. It· is an alternative to . keep in mind .. It is particularly helpful in . situations where interaction is suspected. ..

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Occasionally. the desirdf~;1-iM;.7.1;_f9r:,;:/tb~ in filtering or dampening noisy controller cannot be set because:·:c,f.~a acij~y.\' '.: - .measurements is to reduce what you. don't measurement. If the desired gain were used, · ·: · ·_· want andkeep what you.do want, The first the valve- would move too . much and order lag is calleda "low pass'' filter. It actually make things worse instead of better. passes (does not dampen) a low frequency In addition there· is excessive wear - and tear variation; it attenuates high frequencies. So on the .. valve and excessive . instrument air if a decision .is made to use a first order lag consumption. Sometimes this is an easy for dampening noisy measurements, this problem to solve .end. sometimes it isn't. involves an. .implied decision . that a This section will . deal with the use .· of the separation can be made between desired first order lagand with the Moore Products signal and undesired signal on the basis of inverse derivative . unit to. _ combat this frequency (period). problem .. : Elegant options that might be available with a . computer are omitted. The This separation between what is attenuated filter time setting is a first order lag, and and what is not is not abrupt. That is, the therefore Is · not -_• considered elegant. It is filter does not, for instance, ''pass'' one cycle almost specifically for this purpose. per minute and greatly attenuate 1.1 cpm. The noise usually is not composed of a single frequency anyway, but rather has several components. For the uninitiated, try to think of filtering sections of the noise signal with sections of sine waves of different frequencies. This will usually give an· adequate feel· to make· the necessary decisions. The first order lag is widely used because it is relatively easy to implement and is well A .· simplified · formula for. the attenuation understood. Some - instruments, especially characteristic of a first order-lag is: · transmitters, are built with adjustable dampening, and this is almost always a first Output amplitude P ...... order lag. It is very easy to approximate Input amplitude 6.28T with digital equipment, requiring minimal storage and operations. To appreciate the · · · ·_ Where: . P = Period, same time units as T dampening characteristics of a first order T = Time constant of filter lag it is desirable apd- almost necessary to think in terms of frequency or period. While This is not the whole story, for the ratio its behavior has been explained in its time cannot be greater than one. So this formula response (figure 4.5), it is far more helpful applies only if P is less than 6.28T. Even to understand its response to cyclic upsets. that is not the whole story, but if all you are interested in is getting some meaningful In the time domain the observed reading is attenuation, that is all you need to know. always changing at a rate such that it The full story is in the equation for would get to the true value in one time amplitude ratio given in chapter 4, in the constant. That says it all, but it is math/algebra section for the first order lag. information that is hard to apply. The trick It is repeated in this section. The problem .

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· is.·that·'to get tlie.atienuation· . you also······· .. ·· If your loop··is.dfthepn.eumatic vintage you . . . . · introduce · a lag. that will affect the; ·:: , : .might consider : · the; Moore Products ·. apparent . dead time and : hence the ·. pneumatic ·relay, Model 59~rr~1Whicli they · · . · performance efthe loop. . . . . call a reverse action derivative}telay.' Itwill ' . reduce the high frequencyamplitudes by .a In summary, it is generally acceptable to use . factor of 6. A time adjustment -on it: is then a first order lag to dampen noise when the setto-determine what frequencies are .not periodicity of the noise is much shorter than attenuated. Its advantages are hard to the · natural· . period. As · these periods explain without· recourse . to·. · .frequency approach· each other, the disadvantages may response analysis. It is included in: this outweigh the advantages. Incidentally, there discussion because it is easily implemented. is no objection to dampening ·a- recording. It is normally .placed in the outputof the only, to make a chart mote , readable. contro Iler; but occasionally ·on. the input. · It Dampen it as much . as:· · you "like; but can, under special situations, · minimize the remember that the truthisworse than meets effect the filter has on the natural period, ;If the eye. · · ,. you. are. in the versatile world ·of· digital control ·: other · options · are available that· ,are beyond·the scope ofthis booklet, · > •

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What · can be done · when the periodicity of the noise i's near the . natural period? Frequently a good compromise is to reduce the gain and integral time together. If the normal tuning rules wouldhave called for a gain of 5 and an integral time .·. of IO minutes, try a gain of 3 · and 6 minutes of integral action .. Maybe even a gain of 1 and an. integral time ·of 2 minutes would. be a .. good compromise. Reduce the gain to make the effect of noise acceptable, decrease the . integral time until stability· prob lems arise. Or you could also· use an integral-only controller. This approach · is not recommended for· level loops or other nonself-regulating loops, as it will get you into cycling troubles in a hurry...

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