[pid] pid control - good tuning - a pocket guide

8/6/2019 [PID] PID Control - Good Tuning - A Pocket Guide

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Volume EMC 27.01

Good Tuning:A Pocket Guide

By Gregory K. McMillan


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Copyright 2001 ISA The Instrumentation, Systems,and Automation Society67 Alexander DriveP.O. Box 12277Research Triangle Park, NC 27709

All rights reserved.

Printed in the United States of America.10 9 8 7 6 5 4 3 2 1

ISBN 1-55617-726-7

No part of this work may be reproduced, stored in a retrievalsystem, or transmitted in any form or by any means,electronic, mechanical, photocopying, recording or otherwise,without the prior written permission of the publisher.

Library of Congress Cataloging-in-Publication Data

McMillan, Gregory K., 1946-Pocket guide to good tuning / by Gregory K. McMillan.

p. cm.ISBN 1-55617-726-71. Automatic control--Handbooks, manuals, etc. I. Title.

TJ213.M352 2000670.4275--dc21

00-036958

ISA wishes to acknowledge the cooperation of thosemanufacturers, suppliers, and publishers who grantedpermission to reproduce material herein. The Society regrets

any omission of credit that may have occurred and will makesuch corrections in future editions.


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NoticeThe information presented in this publication is for the

general education of the reader. Because neither the author

nor the publisher has any control over the use of theinformation by the reader, both the author and the publisher disclaim any and all liability of any kind arising out of suchuse. The reader is expected to exercise sound professional

judgment in using any of the information presented in aparticular application.

Additionally, neither the author nor the publisher haveinvestigated or considered the effect of any patents on theability of the reader to use any of the information in aparticular application. The reader is responsible for reviewingany possible patents that may affect any particular use of theinformation presented.

Any references to commercial products in the work arecited as examples only. Neither the author nor the publisher endorses any referenced commercial product. Any trademarksor tradenames referenced belong to the respective owner of themark or name. Neither the author nor the publisher makes anyrepresentation regarding the availability of any referencedcommercial product at any time. The manufacturer'sinstructions on use of any commercial product must befollowed at all times, even if in conflict with the informationin this publication.


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Editors Introduction

This mini-book is available both in down-loadable form, as part of the ISA Encyclopediaof Measurement and Control, and bound in aprint format.

Mini-books are small, unified volumes,from 25 to 100 pages long, drawn from the ISAcatalog of reference and technical books. ISAmakes mini-books available to readers who neednarrowly focused information on particular sub-

jects rather than a broad-ranging text that pro-vides an overview of the entire subject. Eachprovides the most recent version of the mate-

rialin some cases including revisions that havenot yet been incorporated in the larger parentvolume. Each has been re-indexed and renum-bered so it can be used independently of the par-ent volume. Other mini-books on relatedsubjects are available.

To order: Internet: www.isa.orgPhone: 919/549-8411Fax: 919/549-8288Email: [email protected]


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T ABLE OF C ONTENTS 7

Table of Contents

Chapter 1.0 Best of the Basics................................ 1

1.1 Introduction ................................. 11.2 Actions Speak Louder than Words21.3 Controller la Mode..................... 61.4 Is That Your Final Response? ....... 71.5 The Key to Happiness ................ 301.6 Nothing Ventured, Nothing

Gained ....................................... 34

Chapter 2.0 Tuning Settings and Methods ........... 43

2.1 First Ask the Operator................ 432.2 Default and Typical Settings....... 432.3 The General-purpose Closed-loop

Tuning Method............................ 472.4 The Shortcut Open-loop Method 532.5 Simplified Lambda Tuning ......... 58

Chapter 3.0 Measurements and Valves ................ 63

3.1 Watch Out for Bad Actors .......... 633.2 Deadly Dead Band ...................... 64


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8 T ABLE OF C ONTENTS

Chapter 4.0 Control Considerations .................... 75

4.1 Auto Tuners................................ 75

4.2 Uncommonly Good Practices for Common Loops........................... 75

4.3 Dead-Time Compensation and Warp Drive.................................. 78

4.4 I Have So Much Feedforward,I Eat before I Am Hungry .......... 82

4.5 Cascade Control Tuning............. 85

Chapter 5.0 Troubleshooting............................... 89

5.1 Patience, Heck, I Need to Solvethe Problem................................ 89

5.2 Great Expectations and PracticalLimitations................................... 97Index .................................................................... 103


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B EST OF THE B ASICS 1

1.0Best of the Basics

1.1 IntroductionWelcome to the wonderful world of proportional-integral-derivative (PID) controllers. This guide will cover the key points of good tuning and provide more

than thirty rules of thumb. First, lets blow away some myths:

Myth 1 It is always best to useone controller tuning method. False; the diversity of processes, con-

trol valves, control algorithms, andobjectives makes this impractical.

Myth 2 - Controller tuning settingscan be computed precisely. Not so.The variability and nonlinearity innearly all processes and controlvalves makes this implausible. Any

effort to get much more than one significantdigit is questionable because any match to theplant is momentary. If you run a test for an autotuner or manually compute settings ten times,you should expect ten different answers.

Roughly 75 percent of process control loopscause more variability running in the automatic


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2 B EST OF THE B ASICS

mode than they do in the manual mode. A thirdof them oscillate as a result of nonlinearities

such as valve dead band. Another third oscillatebecause of poor controller tuning. The remain-ing loops oscillate because of deficiencies in thecontrol strategy. A well-designed control loopwith proper tuning and a responsive controlvalve can minimize this variability. Because thismeans you can operate closer to constraints,good tuning can translate into increased produc-tion and profitability.

1.2 Actions Speak Louder than WordsThe very first settings that must be right are the

controller and valve actions. If these actions arenot right, nothing else matters. The controller output will run off scale in the wrong directionregardless of the tuning settings.

The controller action sets the direction of a

change in controller output from its propor-tional mode for every change in the controller sprocess variable (feedback measurement). If youchoose direct action, an increase in process vari-able (PV) measurement will cause an increase incontroller output that is proportional to its gainsetting. Since the controller action must be theopposite of process action to provide feedback correction, you should use a direct-acting con-


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troller for a reverse-acting process except asnoted later in this guide. Correspondingly, you

should select reverse control action for a direct -acting process so an increase in process variablemeasurement will cause a decrease in controller output that is proportional to its gain setting,except as noted later. A direct -acting process isone in which the direction of the change in theprocess variable is the same as the direction of the change in the manipulated variable. Areverse-acting process is one in which the direc-tion of the change in the process variable isopposite the direction of the change in themanipulated variable. The manipulated variableis most frequently the flow through a controlvalve, but it can also be the set point of a slaveloop for a cascade control system or variablespeed drive.

The valve action sets the display. For example, itdetermines whether a 100 percent output signal

corresponds to a wide open or a fully closedvalve. It also determines the direction of achange in the actual signal to the control valvewhen there is a change in the controller s out-put. In some analog controllers developed in the1970s, such as the Fisher AC 2, the valve actionaffected only the display, not the actual signal.To compensate for this lack of signal reversal for a reverse-acting valve (i.e., an increase-to-close or


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fail-open valve), the control action had to be theopposite of the action that would normally be

appropriate based on process action alone. For-tunately, the valve action corrects both the dis-play and the actual valve signal in moderncontrollers, so the control action can be basedsolely on process action. However, the user should verify this before commissioning anyloops. In control systems that use fieldbusblocks, the valve action should be set in the ana-log output (AO) block rather than in the PIDcontroller block. This ensures that the back-cal-culate feature is operational for any functionblocks (split range, characterization, and signalselection) that are connected between the PIDand AO blocks. The signal can also be reversedin the current-to-pneumatic transducer (I/P) or in the positioner for a control valve. Before theadvent of the smart positioner, it was preferablefor the sake of visibility and maintainability thatany reversal be done in the control room rather

than at the valve. It is important to standardizeon the location of the signal reversal to ensurethat it is done and done only once. Table 1 sum-marizes how the controller action depends uponboth the process and valve actions and on thesignal reversal.


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Which brings us to rule of thumb number one.

Rule 1 The controller actionshould be the opposite of the pro-cess action unless there is anincrease-to-close (fail-open) con-trol valve for which there is no

reversal of the valve signal. This means thatyou should use reverse and direct-acting control-lers for direct and reverse-acting processes,

Table 1 Controller Action

Process Action Valve Action SignalReversal Controller Action

Direct Increase-Open

No Reverse

Reverse Increase-Open

No Direct

Direct Increase-Close

Yes Reverse

Reverse Increase-Close

Yes Direct

Direct Increase-Close No Direct

Reverse Increase-Close

No Reverse


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respectively. The valve signal can be reversed for a fail-open valve at many places, but it is best

done in the AO block of the control system.1.3 Controller la ModeThe names for the operational modes of the PIDvary from manufacturer to manufacturer. Thus,the Foundation Fieldbus modes listed next pro-

vide a uniformity that can be appreciated by all. Auto (automatic) The operator locally

sets the set point. PID action is active(closed loop). In older systems, this mode isalso known as the local mode .

Cas (cascade) The set point comes fromanother loop. PID action is active (closedloop). This is also known in older systemsas the remote mode or remote set point( RSP ).

LO (local override) PID action is sus-pended. The controller output tracks anexternal signal to position the valve. Thismode is typically used for auto tuning or tocoordinate the loop with interlocks. Inolder systems, it is also known as output tracking .

Man (manual) The operator manually setsthe output. PID action is suspended (openloop).


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IMan (initialization manual) PID actionis suspended because of an interruption in

the forward path of the controller output.This is typically caused by a downstreamblock that is not in the cascade mode. Thecontroller output is back-calculated to pro-vide bumpless transfer.

RCas (remote cascade) The set point is

remotely set, often by another computer.PID action is active (closed loop). Thismode is also known in older systems as thesupervisorymode.

ROut (remote output) The output isremotely set, often by a sequence or byanother computer. PID action is suspended(open loop). In older systems, this mode isknown as direct digital control (DDC ).

1.4 Is That Your Final Response?

The contribution that the proportional actionmakes to the controller output is the error multi-plied by the gain setting. The contribution madeby the integral action is the integrated error mul-tiplied by the reset and gain setting. The resetsetting is repeats per minute and is the inverse of integral time or reset time (minutes per repeat).Foundation Fieldbus will standardize the resettime setting as seconds per repeat and the rate


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(derivative) time setting as seconds. The contri-bution made by derivative mode is the rate of

change of the error or process variable inpercent (%), depending upon the type of algo-rithm, multiplied by the rate and gain settings.

When derivative action is on the process vari-able instead of on the control error, it worksagainst a set point change. (The control error isthe difference between the process variable andthe set point.) The reason for this is that itdoesnt know the process variable should bechanging initially and that the brakes shouldonly be applied to the process when itapproaches set point. Using derivation actionthat is based on the change in control error willprovide a faster initial takeoff and will suppressovershoot for a set point change. This is particu-larly advantageous for set points driven for batchcontrol, advanced control, or cascade control.The improvement can translate into shorter

cycle or transition times, an enhancement of theability of slave loops to mitigate upsets, and lessoff-spec product because overshoot has beendiminished.

When derivative action is used with a time con-stant there is a built-in filter that is about one-eighth (1/8) of the rate setting. However, youshould use set point velocity limits to prevent a


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jolt to the output when there is a large stepchange in error from a manually entered set

point. This is particularly important when youare using large gains or derivative action basedon control error.

The PID algorithm uses percentage (%) inputand output signals rather than engineering units.Thus, if you double the scale span of the input(error or process variable), you effectively halvethe PID action. Correspondingly, if you doublethe scale span of the output (manipulated vari-able), you double the PID action. In fieldbusblocks, both input and output signals can bescaled with engineering units. Using output sig-nal scaling will facilitate the manipulation of theslave loops set point for cascade control. For controllers that use proportional band, you needto divide the proportional band into 100 percentto get the equivalent controller gain. Propor-tional band is the percentage change in error

needed to cause a 100 percent change in output.Proportional mode is expressed by the followingequation (note that adjustments are gain or pro-portional band):

Pn = K cEn


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When the derivative mode acts on the processvariable in percent (%PV), the equation becomes

as follows:Pn = K cDn

Integral mode is expressed by the followingequation (note that adjustments are integral timeor reset):

In = K c 1/T i (EnTs ) + In-1

When the derivative mode acts on %PV, theequation becomes as follows:

In

= K c 1/T

i (D

nT

s) + I

n-1The equation for derivative mode is as follows(adjustments are derivative time or rate):

Dn = K c Td (En - En-1)/ Ts

Or for derivative mode on %PV:Dn = K c Td (%PVn - %PVn-1) / Ts

Note the inverse relationships across controllers!

Gain (K c) = 100% / PB

Reset action (repeats/minute) = 60 / T i


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Where:

En = error at scan n (%)K c = controller gain (dimensionless)PB = controller proportional band (%)Pn = contribution of the proportional mode

at scan n (%)%PVn = process variable at scan n (%)In

= contribution of the integral mode atscan n (%)

Dn = contribution of the derivative mode atscan n (%)

Td = derivative (rate time constant) timesetting (seconds)

Ti = integral time or reset time setting(seconds/repeat)Ts = scan time or update time of PID

controller (seconds)

Rule 2 If you halve the scale

span of a controlled (process)variable or double the span of amanipulated variable (i.e., set point scale or linear valve size),

you need to halve the controller gain to get the same PID action. For controlled variables,

the PID gain is proportional to the measurementcalibration span. Often these spans are narrowedsince accuracy is a percentage of span. For con-


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trol valves, the PID gain setting is inversely pro-portional to the slope of the installed valve

characteristic at your operating point. If a valveis sized too small or too large, the operatingpoint ends up on the flat portion of the installedvalve characteristic curve. For butterfly valves,the curve gets excessively flat below 15 percentand above 55 percent of valve position.

Figure 1 shows the combined response of thePID controller modes to a step change in theprocess variable (%PV). The proportional modeprovides a step change in the analog output(%AO1). If there is no further change in the%PV, there is no additional change in the out-put even though there is a persistent error (off-set). The size of the offset is inverselyproportional to the controller gain. Integralaction will ramp the output unless the error iszero. Since the error is hardly ever exactly zero,reset is always driving the output. The contribu-

tion made by the integral mode will equal thecontribution made by the proportional mode inthe integral time ( %AO2 = %AO1). Hence,the integral time setting is the time it takes torepeat the proportional contribution (secondsper repeat). The contribution made by the deriv-ative mode for a step change is a hump becauseof the built-in filter, which is about one-eighth(1/8) of the rate


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B EST OF T

HE B ASICS 13

F i g u r e 1

P

I D R e s p o n s e

% % % % A O

2 =

% % % % A

O 1

% % % % P V

s e c o n d s / r e p e a t

% % % % A O

1

s e t p o i n t T i m

e

( s e c s )

S i g n a

l

( % )

0 % % % % P V


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setting. Otherwise, there would be a spike in theoutput.

If the temperature is below set point for a reac-tor, as shown in Figure 2, should the steam or water valve be open? After looking at a faceplateor the digital value for temperature on a graphicdisplay, most people think the steam valve isopen when the temperature is below set point.Reset provides a direction of action that is con-sistent with human expectation. However, theproper direction for a change in controller out-put and the split-ranged control valve dependsupon the trajectory of the process variable (PV).If the temperature is rapidly and sharply increas-ing, the coolant valve should be opening. Gainand rate action will recognize that a set point isbeing approached and position the valves cor-rectly to prevent overshoot. In contrast, reset hasno sense of direction and sacrifices future resultsfor immediate satisfaction. Most reactors, evapo-

rators, crystallizers, and columns in the processindustry have too much reset. On two separateapplications in chemical plants, for example, itwas reported that the controller was seriouslymalfunctioning because the wrong valve wassupposedly open, when in reality it was just gainand rate doing their job to prevent overshoot.


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B EST OF T

HE B ASICS 15

F i g u r e 2

R

e s e t G i v e s T h e m W h a t T h e y W

a n t

S P

P V

I V P

5 2

4 4

?

T C - 1

0 1

R e a c

t o r

T e m

p e r a

t u r e

s t e a m

v a l v e

o p e n s

w a

t e r

v a l v e

o p e n s

5 0 %

s e t p o

i n t ( S P )

t e m p e r a

t u r e

t i m

e

P V

P r o p o r

t i o n a

l a n d r a

t e a c

t i o n s e e

t h e

t r a j e c

t o r y v

i s i b l e i n a

t r e n

d !

B o t

h w o u

l d w o r

k t o o p e n

t h e

w a t e r v a

l v e

t o p r e v e n t o v e r s h o o

t .

R e s e t a c

t i o n

i n t e g r a

t e s

t h e n u m e r

i c

d i f f e r e n c e

b e t w e e n

t h e

P V a n

d S P

s e e n

b y o p e r a t o r o n a

l o o p

f a c e p l a t e

R e s e t w o r

k s t o o p e n

t h e s t e a m v a

l v e

( r e s e t

h a s n o s e n s e o f

d i r e c t

i o n ) .


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Figures 3a and 3b show the effect of gain settingon a set point response. If the gain is too small,

the approach to set point is too slow. If the gainis too large, the response will develop oscilla-tions. If the dead time is much larger than thetime constant and the gain action is too largecompared to the reset action, the response willmomentarily flatten out (falter or hesitate) wellbelow the set point. Loops that are dead-timedominant tend to have too much gain and notenough reset action. For nearly all other loops inthe process industry, the opposite is true. Thesize of the dead time relative to the time con-stant and the degree of self-regulation (ability toreach a steady state when the loop is in manual)determine which tuning methods you shouldemploy.

It is particularly important to maximize the gainso you can achieve tight control of loops thatcan ramp away from set point, such as gas pres-

sure. Maximizing the gain is also important for loops that can run away from set point, such asan exothermic reactor temperature. Finally, gainmust be maximized to speed up the set pointresponse for advanced control, batch control,and cascade control as well as for startupsequences. However, gain readily passes variabil-ity in the process variable to the output, whichcan increase overall variability and interaction.


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B EST OF T

HE B ASICS 17

F i g u r e 3 a E

f f e c t o f G a i n S e t t i n g o n S e t P o i n t R e s p o n s e

f o r a T i m

e C o n s t a n t M u c h L a r g e r

t h a n D e a d T i m e

1 2 3

1 - l o w c o n t r o

l l e r g a

i n

2 - m e d

i u m c o n t r o

l l e r g a

i n

3 - h

i g h c o n t r o

l l e r g a

i n


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F i g u r e 3 b

E

f f e c t o f G a i n S e t t i n g o n S e t P o i n t R e s p o n s e

f o r a D e a

d T i m e M u c

h L a r g e r

t h a n

T i m e C o n s t a n t ( D e a

d T i m e D o m i n a n t )

1 2 3

1 - l o w c o n t r o

l l e r g a

i n

2 - m e d

i u m c o n t r o

l l e r g a

i n

3 - h

i g h c o n t r o

l l e r g a

i n


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You must set the process variable filter to ensurethat fluctuations from measurement noise stay

within the dead band of the control valve. Thevariability amplification by gain can be particu-larly troublesome if there is inadequate smooth-ing because of insufficient volumes or mixing.These loops tend to be dead-time dominant, andthey exhibit abrupt responses (i.e., no smoothingby a time constant). Thus, you should reducethe gain setting for loops on pipelines, desuper-heaters, plug flow reactors, heat exchangers,static mixers, conveyors, spinning (fibers), andsheets (webs).

Rule 3 Increase the gain toachieve tight level, stirred reactor,or column control and to speedup the set point response foradvanced, batch, cascade, and

sequence control. For high gains it is especiallyimportant that you set a process variable filter to

ensure that fluctuations in the PID output aresmaller than the valve dead band. You shouldalso establish set point velocity limits so the out-put doesn t jerk when the operator changes theset point.


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Rule 4 Decrease the gain toprovide a smoother, slower, and

more stable response; reduceinteraction between loops; andreduce the amplification of vari-

ability. Pulp and paper, fiber, and sheet pro-cesses use less gain (higher proportional band)and more reset action (smaller reset time). Theyalso are much more sensitive to variability fromvalve dead band. The dead time is larger thanthe process time constant for most of theseloops.

Rule 5 For level control of surge tanks, use a gain, such as1.5, that is just large enough toavoid actuating the alarms set tohelp prevent the tank from over-

flowing or running dry. You can estimate thegain as follows: it is the maximum neededchange in controller output divided by the dif-

ference between the high- and low-level alarms.For example, if a 60 percent change in controller output will always keep the level between 30 per-cent and 70 percent, the correct controller gainis 1.5. You can add an error-squared algorithm,where gain is proportional to error, to effectivelyattenuate control action near the set point. Thisis a generally effective way to reduce the effect of noise for all types of level control loops.


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Rule 6 - For residence time con-trol and for material balance con-

trol, use as high a gain for levelcontrol as possible, such as 5.0,that does not wear out the valves

or upset other loops. Continuous reactors,evaporators, crystallizers, and thermosyphonreboilers often need to maintain a level accu-rately, particularly if they are being pushedbeyond nameplate production rates. Level con-trol also needs to be tight when it manipulates areflux flow for a column or a reactant makeupflow for a recycle tank.

The Ziegler-Nichols (J. G. Ziegler and N. B.Nichols, Optimum Settings for AutomaticControllers, Transactions of the ASME, vol. 64,Nov. 1942, p. 759) tuning method depicts a goalof quarter-amplitude response where each subse-quent peak in an oscillatory response of the PIDcontroller is one-fourth of the previous peak.

This goal will generally provide a minimum peak error, but the controller is too close to the edgeof instability. An increase of just 25 percent inthe process gain or dead time can cause severeoscillations. By simply cutting the controller gain in half you will make Ziegler-Nichols tun-ing sufficiently robust. You will also make itlook more like Internal Model Control (IMC)tuning for stirred reactors, evaporators, crystal-


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lizers, and columns. If the controller manipu-lates a control valve instead of a flow set point,

you need to reduce the gain for the steepest partof the installed valve characteristic curve.

For loops that will reach a steady state when putin manual, decreasing the gain will alwaysimprove their stability. For exothermic reactorswhere a runaway condition can develop, there isa window of allowable gains in which instabilitycan be caused by a gain that is too small or toolarge. For level loops with reset action, there isalso a window in which a gain that is too smallcan cause slow, nearly sustained oscillations.

Rule 7 If you have a quarter-amplitude response, you shoulddecrease the gain to promote sta-bility. Generally, halving the con-troller gain is sufficient. This

assumes that the reset action is not excessive

(i.e., integral or reset time is too small). If themanipulated variable is a control valve and theoperating point moves from the flat to the steepportion of the installed characteristic, you mayneed to cut the gain by a factor of three or four.

Figure 4 shows the effect of reset setting on a setpoint response. If the reset action is too small(i.e., the reset time too large), it takes a long time


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F i g u r e 4

E f f e c t o f R e s e t S e t t i n g o n S e t P o i n t R

e s p o n s e

1 2 3

1 - l o w r e s e

t a c t

i o n ( h

i g h r e s e

t t i m e )

2 - m e d

i u m r e s e

t a c t i o n

3 - h

i g h r e s e

t a c t

i o n (

l o w r e s e

t t i m e )


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to eliminate the remaining error or offset.Whereas insufficient gain slows down the initial

approach, inadequate reset action slows downthe final approach to set point. If the reset actionis too large (reset time is too small), there isexcessive overshoot. The addition of reset actionreduces controller stability and is dangerous for exothermic reactor temperature loops. Polymer-ization reactors often use proportional-plus-derivative temperature controllers (i.e., no inte-gral action). For level loops, using a reset time of fewer than 3,000 seconds per repeat makes itnecessary to use relatively high gains (5.0 for large volumes) to prevent slow, nearly sustainedoscillations.

Both reset and gain can cause oscillations, and ahigh gain setting can aggravate an overshootcaused by reset action. For this reason, checkingthe ratio of the reset time to the oscillationperiod can help you distinguish the main culprit.

You will need to decrease the reset action (i.e.,increase the reset time) of the loop if the ratio ismuch less than 0.5 for vessel or column tempera-ture, level, and gas pressure control or if it ismuch less than 0.1 for flow, liquid pressure,pipeline, spin-line, conveyor, or sheet (web) con-trol.


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Rule 8 If there is excessiveovershoot and oscillation,

decrease the reset action (increasethe reset time). If the current resettime setting is less than half the

oscillation period for loops on mixed volumesor less than a tenth of the period for any loop,there is too much reset action. If the oscillationperiod changes by 25 percent or more as youchange reset action, it is a sign that the oscilla-tion is caused or aggravated by reset action.

Rule 9 For level loops with lowcontroller gains (< 5.0), reset action must be greatly restricted(i.e., reset time increased to 50 ormore minutes) to help mitigate

nearly sustained oscillations. Level loops arethe opposite of most other loops in that you canincrease the reset action (decrease the reset time)as you increase the gain (see page 99 for more

detail).Figure 5 shows the effect of rate setting on a setpoint response. A rate setting that is too smallincreases any overshoot caused by reset action.A setting that is too large causes the approach toset point to staircase and if large enough it cancause fast oscillations.


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F i g u r e 5

E

f f e c t o f R a t e S e t t i n g o n S e t P o i n t R e s p o n s e

1 2 3 1 - l o w

d e r i v a

t i v e

( r a t e )

2 - m e d

i u m

d e r i v a

t i v e

( r a t e

)

3 - h

i g h d e r i v a

t i v e

( r a t e )


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Rate can be used whenever there is a smoothand slow open-loop process response. Rate can-

not be used where there is excessive noise, chat-ter, inverse response, or an abrupt response. Itcan be used primarily on temperature loops thatmanipulate heating or cooling where there is atemperature transmitter with a narrow calibra-tion span (large spans cause analog/digital [A/D]chatter). Analyzers that have a cycle time (sam-ple and hold) have signals that are too noisy andabrupt for derivative action. Continuous con-centration measurements made by electrodes or inline devices (such as capacitance, conductivity,density, microwave, mass spectrometry, pH, andviscosity for mixed volumes) may allow you touse derivative mode if you add a filter to attenu-ate the high-frequency measurement noise.

If the measurement is continuous but is used for pipeline control, the control response is tooabrupt. This is because the loop dead time is

large compared to the largest time constant.There is noise in every process variable. If thenoise is greater than the measurement resolutionlimit, the loop sees it. If it causes an outputchange greater than the final element or controlvalve resolution limit, loop variability will beworse in auto than in manual, particularly if there is any rate action. While it is true that


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increasing the measurement and valve resolutionlimit reduces the loop s sensitivity to noise, it

also degrades its ability to recover from loadupsets. If the measurement doesn t see or correctan upset because the control error is smaller than a resolution limit, the control loop perfor-mance deteriorates.

Poor control valve resolution is a problem for any loop. If the valve doesn t move, there is nocorrection. On the other hand, poor measure-ment resolution is primarily a problem for PIDtemperature loops. The large-span ranges foundin computer input cards or transmitter calibra-tion can result in a resolution limit of 0.25 F or more. It is impractical to expect control that istighter than twice the resolution limit or 0.5 F.Also, for a change of 0.25 F per minute, an addi-tional minute of dead time is introduced intothe loop. Short scan times also introduce chatter because the actual temperature change is small

compared to the noise (i.e., the signal-to-noiseratio is too small). The scan time for most tem-perature loops is too short. Poor measurementresolution and fast scan times are the main rea-sons why rate cannot be used in temperatureloops. Constrained Multivariable PredictiveControllers (CMPC) are much less sensitive tomeasurement resolution because the scan time islarge and the move in the manipulated variable


37/120


is based on the complete trajectory and not thecurrent measurement like the PID controller.

Poor valve resolution is as much a problem for the CMPC as for the PID, unless you set theminimum size of a move to exceed the resolu-tion limit. The resolution limit is unfortunatelya function of direction and position.

Rule 10 Rate is primarily usedin temperature loops that havenarrow span transmitters and slowscan times. However, it is also usedfor continuous analytical measure-

ments such as capacitance, conductivity, den-sity, mass spectrometry, microwave, pH, and

viscosity for concentration control of mixed vol-umes. If the temperature control is not intendedfor a mixed volume, the rate setting is very small(6 seconds) and is mostly used to compensatefor the thermowell lag. In every case, you mustset the measurement filter large enough to keep

output fluctuations within the valve dead band. Rule 11 Most temperature andlevel loops chatter because thePID scan time is too small. Thetrue temperature or level changewithin the scan time must be large

compared to the A/D resolution limit (0.05%);otherwise, the signal-to-noise ratio is too small.


38/120


1.5 The Key to HappinessWhen I was four years old and sitting on mydaddys knee, he said, Son, I have just onething to say to you dead time. Well, it took meforty years to appreciate the significance of hiswords of wisdom. If a loop has no dead time or noise, perfect control is possible and an infinitegain permissible. There is no tuning issue. With-

out dead time, I would be out of a job.

Dead time is that period of time from the startof a disturbance until the controller makes a cor-rection that arrives at the same point in the loopat which the disturbance entered. The controller

needs to see the upset, react to it, and get thecorrection to the right place. To appreciate deadtime imagine that you go to a party and startdrinking. The period of time between the firstdrink and when you eventually bypass the nextround is dead time.

While zero dead time is not possible, a decreasein dead time reduces the effect of nonlinearities,such as changes in the time constants andsteady-state gains of the loop, and makes theloop easier to tune. It is desirable that the largestloop time constant be in the process because itwill slow down the divergence of the measure-ment from the set point during an upset andgive the controller a chance to catch up. All


39/120


other time constants are undesirable and createadditional dead time. The major time constant

can be approximated as follows: it is the time ittakes to reach about 63 percent of the final valueafter the dead time. It takes one dead time andfour time constants for a response to reach 98percent of its final value.

The open-loop steady-state gain is the percent-age change in the process variable for a percent-age change in output after all transients havedied out. The controller is in manual. A highsteady-state gain is both a curse and blessing. Itcan improve the control of the true process vari-able by making the measurement more sensitive.This is particularly important for inferring com-position from temperature or concentrationfrom pH. However, a high steady-state gain canmake it more difficult--and sometimes impossi-ble--to control the measured variable. For exam-ple, excessive oscillation can result from a small

amount of stick and slip in a reflux valve for anacrylonitrile and water distillation or in a reagentvalve for sulfuric acid and sodium hydroxideneutralization. A low steady-state gain oftenresults when a throttle position is on the exces-sively flat portion of the installed valve charac-teristic. The process variable will often wander and respond to the conditions of a related loopmore than from the manipulated variable.


40/120

32 B EST OF T

HE B ASICS

F i g u r e 6

L

o o p B l o c k D i a g r a m

T C

p 1

T D

p 2

T C

p 2

K p v

T D p

1

T C

c 1

T C

m 2

T D

m 2

T C

m 1

T D

m 1

K a i

T D

c 1

T C

c 2

K c

T i T d

V a l v e

P r o c e s s

C o n t r o

l l e r

M e a s u r e m

e n t

K m v

T C

v

T D

v

K L

T L L

T D

L

L o a d

U p s e t

S e t P o i n t

K i

A I ( % % % % P V )

A O

M V

P V

F R

F L

F r

O p e n

L o o p

-

l o o p

i s i n m a n u a l

( P I D a l g o r i

t h m

i s s u s p e n

d e d

)

C l o s e d

L o o p

-

l o o p

i s i n a u

t o ( P I D a l g o r i

t h m

i s a c

t i v e

)

P I D


41/120


The block diagram in Figure 6 shows all the deadtimes, time constants, and steady-state gains in a

control loop. Feedback control corresponds tothe signal making one complete circle aroundthe block diagram. The total dead time isapproximately the sum of all the pure deadtimes and small time constants as you traversethe loop. The dead time from valve dead band isinversely proportional to the rate of change of the controller output, and the dead time fromtransportation delays is inversely proportional tothroughput. The diagram in Figure 6 has manyuses--including preventing guests from overstay-ing their welcome. Just show this slide and starttalking about dead time and you will be amazedat how quickly the place empties. There is asafety issue, however, in that guests can get tram-pled in the rush for the door.

The following list summarizes the three key vari-ables and their relationship to loop perfor-

mance:1. Dead Time or Time Delay (TD)

The most important of the three key loopvariablesDelays controller s ability to see and reactto upset


42/120


Perfect control is possible for zero deadtime

Nonlinearities become less important as thedead time decreases

2. Time Constant (TC)Better control is possible for a large process time constant

Time constants in series create dead timeMeasurement time constants give the illu-sion of providing better control

3. Steady-State Gain (K)The valve and process steady-state gains areusually nonlinear High steady-state gain causes overreactionand oscillationsLow steady-state gain causes loss of sensitiv-ity and wandering

1.6 Nothing Ventured, NothingGainedThere is a lot to be gained from having a better understanding of the overall open-loop gain(K o). However, if you don t have time to studythe relationships revealed by the equations pre-sented in this section, you should skip ahead toSection 2.0 on Tuning Settings and Methods.


43/120


The controller gain is inversely proportional tothe open-loop gain for all types of loops. For

loops that are dead-time dominant (i.e., deadtime is much greater than the largest time con-stant), the controller gain can be simply set asone-fourth of the inverse of the open-loop gain.For these same loops the reset time can be set asone-fourth of the dead time. The result is asmooth stable response similar to what youwould get from Lambda tuning, which will bediscussed (see Section 2.5) as one of the pre-ferred tuning methods for dead-time dominantloops. For loops with a healthy time constant,the controller gain is also proportional to theratio of the time constant to the dead time. For these loops, the smooth response that is pro-vided by a large time constant (i.e., residencetime) of a mixed volume enables you to use ahigher controller gain for tighter concentration,gas pressure, and temperature control.

If the loop time constant is much larger than thedead time (TC / TD >> 1), then the controller gain is proportional to this ratio besides theinverse of the open loop again:

K c 0.25 TC / (TD K o)

If the loop is dead-time dominant (TC/TD


44/120


K c = 0.25 1 / K o

The manipulated variable gain is linear for avariable speed drive (VSD). For a control valve itis the slope of the installed characteristic curveand is typically very nonlinear. For operatingpoints on the upper part of the installed charac-teristic curve of a butterfly valve, the slope can

be so flat that the valve gain approaches zero.Note that for concentration and pressure loops,the process variable should be plotted against aflow ratio (e.g., column temperature versus distil-late-to-feed ratio, heat exchanger temperatureversus coolant-to-feed ratio, and pH versusreagent-to-feed ratio). The process gain is theslope of this curve and is highly nonlinear. Athigh flow ratios, the slope can be so flat that theprocess gain approaches zero. The open-loopgain has a flow ratio gain that is inversely pro-portional to the feed flow, which is an additional

source of nonlinearity for pipeline, desuper-heater, static mixer, and exchanger temperatureor concentration control. In these applications,an equal-percentage valve characteristic is desir-able since the valve gain is proportional to flowand cancels out the flow ratio gain. However, for

loops on agitated vessels and columns the con-troller gain is proportional to the process timeconstant (residence time), which is inversely pro-


45/120


portional to feed flow. Since, as we mentionedpreviously, the controller gain is also inversely

proportional to the open-loop gain, the intro-duction of an equal-percentage valve characteris-tic is bad news because the flow ratio gain wascancelled out by the process time constant for the controller gain.

The process gain for flow loops is 1. For pressureloops downstream of a compressor, fan, or pump, the process gain is the slope at the operat-ing point on the characteristic curve of the com-pressor, fan, or pump. At low flows, the slopecan be so flat that the process gain approacheszero.

The analog input gain is the inverse of the cali-bration span for the controlled variable. It is lin-ear except when a square root extractor is notused on a differential head meter.

Rule 12 For dead-time-domi-nant loops, set the gain equal toabout one-fourth of the inverse of the open-loop gain and the reset time (seconds per repeat) equal to

about one-fourth of the dead time. Rate actionis not used. This provides a smooth stableresponse similar to Lambda tuning.


46/120


Rule 13 Use equal-percentagevalve trim for pipeline, desuper-

heater, static mixer, and heat exchanger control to make theloop more linear. This assumes

that the installed characteristic is close to theinherent equal-percentage trim characteristic.

For concentration and temperature loops, theopen-loop gain is a steady-state gain that has aflow ratio gain K fr , which is the inverse of thefeed flow:

K o = K mv K fr K pv K ai

For flow loops, the open-loop gain is a steady-state gain that has a unity process gain and noflow ratio gain (K fr omitted and K pv = 1):

K o = K mv K ai

For pressure loops, the open-loop gain is asteady-state gain with a process gain K pv, which is the slope of the pump or compressor curve,

K oAI

AO-------------

MVAO--------------

FR MV--------------

PVFR -----------

AIPV-----------= =

K fr 1Ff ----=


47/120


and no flow ratio gain (K fr omitted and K pv =curve slope):

K o = K mv K pv K ai

For level loops, the open-loop gain is a ramp rateand uses K i instead of K pv to denote an integra-tor gain. K i is the inverse of the product of fluid

density and the vessel s cross-sectional area.There is no flow ratio gain (K fr omitted):

K o = K mv K i K ai

Where:

Ff = feed flow (pph)K i = level loop integrator gain (ft/lb)K o = overall open-loop gain (one per hour

for level, otherwise dimensionless)K mv = manipulated variable (valve or VSD)

steady-state gain (pph/%)K fr = flow ratio steady-state gain (inverse of

feed flow) (1/pph)

K pv = process variable steady-state gain(wtfrac/%) (degC/%) (psi/%)

K i1

density area----------------------------------=


48/120


K ai = analog input steady-state gain(%/wtfrac) (%/degC)(%/psi)

(%/pph)(%/ft)AO = change in the controller s analogoutput (%)

AI = change in the controller s analog input(%)

PV = change in the process variable (wtfrac)(degC) (psi) (pph) (ft)

FR = change in the flow ratio (pph/pph)MV = manipulated variable or valve flow

(pph)

Figure 7 shows the dead time, time constant,and steady-state gain for a process that reaches asteady state (i.e., self-regulating) and for an inte-grator such as level. In both cases, the processvariable response is to change the controller out-put with the loop in manual (open-loopresponse). Figure 7 also shows the equationsused to approximate an integrator gain as equalto the initial ramp rate of a self-regulatingresponse. This initial ramp rate is approximatelythe steady-state gain divided by the dominanttime constant. Auto tuners that compute set-tings from an open-loop response use this

approximation to convert an integrator into anequivalent


49/120

B EST OF T

HE B ASICS 41

F i g u r e 7

I n

t e g r a t o r G a i n ( R a m p R a t e )

L o a

d

U p s e t T

D o

T C

p

T i m e

( m i n )

P

r o c e s s

V

a r i a b l e

( % )

0

% % % % P V

% % % % P V / / / / t

K o

K i = =

=

=

=

% % % % A O

T C

p

T 9 8

t

% % % % P V

o

K o

=

% % % % A O

% % % % P V

o

6 3 %

o f % % % % P V

o


50/120


time constant and steady-state gain because theycannot handle integrator gain. This method

works well when the dead time is small com-pared to the ramp rate. The dead time is thetime required for the PV to get out of the noiseband.


51/120

T UNING S ETTINGS AND M ETHODS 43

2.0 Tuning Settings and

Methods

2.1 First Ask the Operator You should test new tuning settings by changing

the set point in both directions and observingwhether the response is smooth and fast enoughfor these set point changes and load upsets.Don t leave these new settings over night untilyou are sure they are right. Before entering newsettings or trying tuning methods, ask the opera-tor for permission to tune the loop. Also ask him or her what the maximum allowable sizecan be for each direction of a step change in thecontroller set point and output without causinga problem. You should put most analog control-lers and some digital controllers in manualbefore entering a change in gain to avoid bump-ing the controller output.

2.2 Default and Typical SettingsTables 2 and 3 show the default and typical tun-ing settings for controllers whose reset setting isin repeats per minute and seconds per repeat,respectively. The number in front of the paren-theses in each column is a default setting, a


52/120

44 T UNING S ETTINGS AND M ETHODS

number that can be used for a download or for aguess if nothing is known about the loop and no

test can be performed. The numbers within theparentheses represent a range of typical values. If your tuning setting falls outside the suggestedrange, this doesn t necessarily mean the tuningsetting is wrong. It does suggest that the loop isunusual or has some problems such as interac-tion, noise, a coated sensor, or a sticky controlvalve. The last column shows the tuning meth-ods that generally give the best results. The gen-eral-purpose tuning method logic shown inFigure 8 is the closed-loop method (CLM),which is referenced in Tables 2 and 3. While thismethod is best for gas pressure, reactor, and levelloops, it can be used for most other loops aswell, particularly if the loop s set point is beingdriven for advanced, batch, cascade, or sequencecontrol and there are no interaction issues.


53/120


T a b l e 2

D

e f a u

l t a n

d T y p i c a l P I D S e t t i n g s

( s c a n i n s e c , r e

s e t i n r e p / m i n , a n d r a t e i n

m i n u t e s ;

= L a m

b d a , C

L M = C l o s e

d - l o o p m e t

h o d ; S C M = S h o r t c u t m e t

h o d )

A p p

l i c a t

i o n

T y p e

S c a n

G a i n

R e s e t

R a t e

M e t

h o d

( s e c o n

d s )

( r e p e a

t s )

( m i n u t e s

)

L i q u i

d F l o w

/ P r e s s

1 ( 0

. 2 - 2

)

0 . 3 ( 0

. 2 - 0 . 8

)

1 0 ( 5 - 5

0 )

0 . 0 ( 0

. 0 - 0 . 0 2 )

T i g h t L i q u i

d L e v e l

5 ( 1

. 0 - 3

0 )

5 . 0 ( 0

. 5 - 2 5

) * 0 . 1 ( 0

. 0 - 0 . 5

) 0 . 0 ( 0 . 0 - 1 . 0

)

C L M

G a s

P r e s s u r e

( p s i g )

0 . 2 ( 0

. 0 2 - 1 ) 5 . 0 ( 0

. 5 - 2 0

)

0 . 2 ( 0

. 1 - 1 . 0

)

0 . 0 5 ( 0 . 0 - 0 . 5 )

C L M

R e a c t o r p H

2 ( 1

. 0 - 5

)

1 . 0 ( 0

. 0 0 1 - 5 0 ) 0 . 5 ( 0

. 1 - 1 . 0

) 0 . 5 ( 0

. 1 - 2 . 0

)

S C M

N e u

t r a l

i z e r p H

2 ( 1

. 0 - 5

)

0 . 1 ( 0

. 0 0 1 - 1

0 ) 0 . 2 ( 0

. 1 - 1 . 0

)

1 . 2 ( 0 . 1 - 2 . 0

)

S C M

I n l i n e p H

1 ( 0

. 2 - 2

)

0 . 2 ( 0

. 1 - 0 .

3 )

2 ( 1 - 4

)

0 . 0 ( 0 . 0 - 0 . 0

5 )

R e a c t o r

T e m p e r a

t u r e 5 ( 2

. 0 - 1

5 )

5 . 0 ( 1

. 0 - 1 5

)

0 . 2 ( 0

. 0 5 - 0 . 5 ) 1 . 2 ( 0 . 5 - 5 . 0

)

C L M

I n l i n e

T e m p e r a

t u r e

2 ( 1

. 0 - 5

)

0 . 5 ( 0

. 2 - 2 . 0

) 1 . 0 ( 0

. 5 - 5 . 0

)

0 . 2 ( 0 . 2 - 1 . 0

)

C o l u m n

T e m p e r a

t u r e 1 0 ( 2

. 0 - 3

0 )

0 . 5 ( 0

. 1 - 1 0

)

0 . 2 ( 0

. 0 5 - 0 . 5 ) 1 . 2 ( 0 . 5 - 1

0 )

S C M

* A n e r r o r / s q u a r e a

l g o r i t

h m

o r g a

i n s c

h e

d u

l i n g s h o u

l d b e u s e

d f o r

l e v e

l l o o p s

w i t h g a

i n s

< 5


54/120


T a b l e 3 D

e f a u

l t a n

d T y p i c a l P I D S e t t i n g s ( s c a n i n s e c , r e

s e t i n

s e c / r e p , a

n d r a t e i n s e c ;

= L a m

b d a , C L

M = C l o s e

d - l o o p m e t

h o d ,

S C M = S h o r t c u t m e t

h o d )

A p p

l i c a t

i o n

T y p e

S c a n

G a i n

R e s e t

R a t e

M e t

h o d

( s e c o n

d s )

( s e c o n

d s )

( s e c o n d s )

L i q u i

d F l o w

/ P r e s s

1 ( 0

. 2 - 2

)

0 . 3 ( 0

. 2 - 0 .

8 )

6 ( 1 - 1

2 )

0 ( 0 - 2

)

T i g h t L i q u i

d L e v e l

5 ( 1

. 0 - 3

0 )

5 . 0 ( 0

. 5 - 2 5

) *

6 0 0 ( 1 2 0 - 6

0 0 0 )

0 ( 0 - 6

0 )

C L M

G a s

P r e s s u r e

( p s i g )

0 . 2 ( 0

. 0 2 - 1 ) 5 . 0 ( 0

. 5 - 2 0

)

3 0 0 ( 6 0 - 6 0 0 )

3 ( 0 - 3

0 )

C L M

R e a c t o r p H

2 ( 1

. 0 - 5

)

1 . 0 ( 0

. 0 0 1 - 5 0 ) 1 2 0 ( 6 0 - 6 0 0 )

3 0 ( 6 - 3 0 )

S C M

N e u

t r a l

i z e r p H

2 ( 1

. 0 - 5

)

0 . 1 ( 0

. 0 0 1 - 1

0 ) 3 0 0 ( 6 0 - 6 0 0 )

7 0 ( 6 - 1

2 0 )

S C M

I n l i n e p H

1 ( 0

. 2 - 2

)

0 . 2 ( 0

. 1 - 0 .

3 )

3 0 ( 1 5 - 6 0 )

0 ( 0 - 3

)

R e a c t o r

T e m p e r a

t u r e 5 ( 2

. 0 - 1

5 )

5 . 0 ( 1

. 0 - 1 5 )

3 0 0 ( 3 0 0 - 3

0 0 0 ) 7 0 ( 3 0 - 3 0 0 )

C L M

I n l i n e

T e m p e r a

t u r e

2 ( 1

. 0 - 5

)

0 . 5 ( 0

. 2 - 2 . 0

)

6 0 ( 1 2 - 1 2 0 )

1 2 ( 1 2 - 6

0 )

C o l u m n

T e m p e r a t u r e 1 0 ( 2

. 0 - 3

0 )

0 . 5 ( 0

. 1 - 1 0 )

3 0 0 ( 3 0 0 - 3

0 0 0 ) 7 0 ( 3 0 - 6 0 0 )

S C M

* A n e r r o r / s q u a r e a l g o r i t

h m

o r g a

i n s c

h e

d u

l i n g s h o u

l d b e u s e

d f o r

l e v e

l l o o p s

w i t h g a

i n s

< 5


55/120


2.3 The General-purpose Closed-loop Tuning MethodA closed-loop (controller in auto) method hasthe following advantages over open-loop (con-troller in manual) methods:

1. It forces the user to find the maximum con-troller gain to minimize peak error anddead time from dead band. It also forcesthe user to find out whether reset and rate iseven needed, and it ensures rapid set pointresponse and gets inside the window of allowable controller gains for integratingand runaway loops.

2. Loops stay in automatic, which is safer for difficult or very fast loops.

3. It includes the effects of valve hysteresisand dead band.

4. It includes the dynamics and peculiar fea-tures of controller algorithms.

5. It includes nonlinearities that are depen-dent on direction and rate of change.


56/120


6. It facilitates the tuning of the master (outer)loop of a cascade system for an oscillating

inner (slave) loop.This closed-loop procedure uses rapidly decay-ing oscillations as shown in Figure 9 instead of the sustained oscillations proposed by the origi-nal Ziegler-Nichols method. The measuredperiod will be larger for damped oscillations inindustrial applications mostly because of valvedead band, but the error will be in the safe direc-tion in terms of a larger, more stable reset timesetting. The closed-loop procedure should alsoresult in about half of the gain estimated by theZiegler-Nichols method.

Rule 14 Use the general-pur-pose closed-loop method if theloop must stay in auto or if it isparticularly important to maxi-mize the gain for tight control and

a fast set point response. However, for dead-time-dominant loops, you should substantiallydecrease the factor for the reset time. This willprevent the set point response from falteringbecause of too much gain action and notenough reset action. For temperature and pres-sure loops on exothermic reactors, it is especiallyimportant to use this method to prevent a run-away.


57/120


F i g u r e 8

G

e n e r a l - P u r p o s e C l o s e

d - l o o p M e t

h o d

C h e c k

l o o p s c a n

t i m e

G e t

l o o p

i n a u

t o n e a r n o r m a l s e

t p o i n t

S e t f i l t e r

t i m e =

t w i c e s c a n

t i m e

A d j u s

t g a i n

t o g e

t s l i g h t o s c i

l l a t i o n

S e t r e s e t

t i m e =

0 . 5 * o s c i

l l a t i o n p e r i o d

A d j u s t g a

i n t o g e

t d e s

i r e d

d e g r e e o f s m o o

t h n e s s o f

b o t h P V a n

d M V

I n t e g r a t i n g

o r r u n a w a y

r e s p o n s e

?

F o r

t e m p e r a

t u r e , s

e t r a

t e t i m e =

0 . 1 * o s c i


S e t r e s e t

t i m e =

1 0 * o s c i


t r u e

f a l s e


58/120


F i g u r e 9

S l i g

h t O s c i l l a t i o n

S e t P o i n t

T i m e

( s e c s )

P V ( % )

O f f s e

t

O s c

i l l a t

i o n

P e r

i o d T

o

0


59/120


A list of steps for the Closed Loop Method isas follows:

1. Put the controller in automatic at normalset point. If it is important not to make bigchanges in the manipulated variable (analogoutput), narrow the controller output limitsto restrict valve movement.

2. For level, gas pressure, and reactor loopsdecrease the reset action (i.e., increase thereset time) by a factor of ten if possible andtrend-record the process variable (PV) andanalog output (AO).

3. Add a PV filter to keep output fluctuationswithin the dead band of valve caused bynoise.

4. Bump the set point and increase the con-troller gain if necessary to get a slight oscil-

lation.5. Stop increasing the gain when the loop

starts to oscillate or the gain has reachedyour comfort limit. Then note the period.For gain settings greater than 1, the oscilla-tion will be more recognizable in the ana-log output (AO). Make sure AO stays onscale within the valve s good throttle range.


60/120


6. Reduce the gain until the oscillation justdisappears so recovery is smooth.

7. For a temperature loop with a smoothresponse (no chatter, inverse, square wave,or interaction), use rate action. If the gain islarger than 10, reset and rate action are notneeded. If the manipulated flow will upsetother loops, decrease the gain or use error-squared control. If a high gain is used, set avelocity limit for the set point and config-ure the set point so it tracks the PV in man-ual and DDC (ROUT). This will enable theloop to restart.

8. If rate action is used, set the rate time equalto one-tenth (1/10) of the period and setreset time equal to half the period. If rateaction is not used, cut the gain by 50 per-cent. If the loop is clearly dead-time domi-nant, increase the reset action so the reset

time is about one-eighth (1/8) of the loopperiod. Make another set point change andadjust the gain to get a smooth response.Do not become any more aggressive than aslight oscillation.

9. If you select gains smaller than 5 for level,decrease the reset action (i.e., increase thereset to more than 3,000 seconds), add feed-


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forward, and add rate if there is no inverseresponse or interaction.

2.4 The Shortcut Open-loop MethodThe shortcut method is ideally suited for veryslow responses such as column temperaturewhere there is a good control valve and posi-tioner and you need to get a quick estimate of the controller tuning settings. This methodlooks at the change in ramp rate of the %PV asshown in Figure 10 for about two to three deadtimes. It doesn t require the loop to be at steadystate. However, if there is an upset that causesthe ramp rate to change, the results will be inac-

curate. In general, you should repeat this test inboth directions and use the most conservativesettings. Also, if the bump in controller output ismuch larger than the dead band, the shortcutmethod doesn t include the dead time fromvalve dead band. If the changes in controller

output per scan approach the control valve deadband in size, you should add the additional deadtime from the valve dead band to the observeddead time.

The shortcut method is also effective for pHloops because it can keep the test near the oper-ating point on the titration curve. The use of aclosed-loop method can get confusing for pH


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F i g u r e 1 0

C

h a n g e i n R a m p R a t e

f o r N o n - S t e a d y S t a t e

T i m e

( m i n )

P r o c e s s

V a r

i a b l e

( % )

s t e p c h a n g e

i n t h e

c o n t r o

l l e r o u

t p u t

T D

o

% % % % P V

1

t

% % % % P V 2

t


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particularly if the oscillations develop into alimit cycle after being bounced back and forth

between the flat ends of the titration curve. Theperiod of such a limit cycle is extremely longand variable, and it will occur for a large range of controller gains.

A list of steps for the Shortcut Method are asfollows:

1. Adjust the measurement filter to keep thecontroller output fluctuations caused bynoise within the valve dead band.

2. Note the magnitude of output change for each reaction to typical upsets. With thecontroller in manual near set point, make astep change in the controller analog output(%AO) of about the same magnitude asthe output change you noted, but larger than twice the valve dead band.

3. Note the observed dead time and thechange in ramp rates. If the process waslined out before the test, then the startingramp rate is zero (%PV1 / t = 0).

4. Divide the change in ramp rate by thechange in valve position to get the pseudo


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integrator gain (K i). Then compute thedead time from the dead band.

5. Use the following equations. For a master or supervisory loop, omit TD v.

K i%PV2 t ( ) %PV1 t ( )

%AO-----------------------------------------------------------------------------=

K cK x

K i TD o-----------------------=

TDv

DB

K x %AVP--------------------------------- TD

o=

%AVP %AO DB2

--------=

Ti ci TD v TD 0+( )=

Td cd TD v TD 0+( )=


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Where:

%AVP=change in actual valve position (%)%AO= change in the controller analog output

(%)DB = dead band from valve hysteresis (%)K c = controller gain (dimensionless)cd = rate time coefficient (1.0 for back-

mixed and 0.0 for plug flow volumes)ci = reset time coefficient (4.0 for back-

mixed and 0.5 for plug flow volumes)K x = gain factor (1.0 for Ziegler-Nichols, 0.5

for IMC, and 0.25 for Lambda)K o = open-loop gain (dimensionless)

K i = pseudo integrator open-loop gain(1/sec)%PV = change in process variable (%) t = change in time (sec)TC = largest loop time constant (sec)TDo = dead time seen in open-loop test (sec)TDv = dead time from control valve dead

band (sec)Td = derivative (rate) time setting (seconds)Ti = integral (reset) time setting

(seconds/repeat)


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Rule 15 Use the shortcut method when you want a quick

estimate for a very slow or nonlin-ear loop, provided that the valvedead band is 0.25 percent or less

and the step size keeps you near the operatingpoint. Make sure there are no load upsets duringthe test and that you measure the new rate of change of the PV for at least two dead times.You should repeat the test for both directionsand use the most conservative tuning.

2.5 Simplified Lambda TuningIf the loop is dead-time dominant, Lambda

tuning is the best method. It also helps tominimize interactions and suppress oscillations.Lambda tuning is an open-loop method that isparticularly effective for relatively fast loops,such as in pipelines, desuperheaters, staticmixers, exchangers, conveyors, spin lines, and

sheet (web) lines, or wherever there is plug flow.It provides a closed-loop time constant thatapproximates the open-loop time constant.Figure 11 shows the step change in controller output and the open-loop response of theprocess variable. The user simply needs to notethese changes and the time required to reach 98percent of the final response (T 98). Thissimplified form of the equation for Lambda


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F i g u r e 1 1

L a m

b d a T e s t

T 9 8

T

i m e

( m

i n )

S i g n a l

( % )

0

% % % % A O

% % % % P V

o


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tuning is only suitable for self-regulatingprocesses. EnTech has expanded the actual

Lambda tuning rules to cover a wide variety of processes.

The following is a list of steps for the Simpli-fied Lambda Tuning Method :

1. Adjust the measurement filter to keep thecontroller output fluctuations caused bynoise within the valve dead band.

2. Note the magnitude of output change todetermine the reaction to typical upsets.With the controller in manual near set

point, make a step change in the controller analog output ( %AO) of about the samemagnitude as the output change you noted,but larger than twice the valve dead band.

3. Note the observed dead time as the time ittook to reach the first change in the processvariable (%PV) outside of the noise band.

4. Note the open-loop gain (the percentagechange in measurement divided by the per-centage change in controller output).

5. Note the response time (the time from thebump to 98 percent of the final value).


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6. The reset setting (repeats/minute) is setequal to the inverse of one-fourth of the

response time.7. The controller gain is adjusted to be one-

fourth of the inverse of the open-loop gain( = 4) .

The equation for reset time setting is as follows:

Ti = T 98 / 4 = TD o/ 4 + TC (seconds/repeat)

The equation for gain setting is as follows:

K c = ( % AO / %PV ) ( 1/ )

( is a tuning factor that is increased to provide aslower and smoother response.)

Rule 16 Use the Lambda tun-ing method for dead-time-domi-nant or fast loops that can be left in manual. You should repeat thetest for both directions and use the

most conservative tuning.


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Rule 17 In Lambda tuning,decrease to speed up the con-

troller s response to upsets andset point changes (minimize PV) and increase to slow down

the response and reduce loop interaction(minimize %AO). This simplifies tuning to asingle knob.


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M EASUREMENTS AND V ALVES 63

3.0Measurements and

Valves

3.1 Watch Out for Bad ActorsThe analog/digital converter (A/D) chatter from

large temperature measurement spans and shortscan times is the factor most frequently cited toexplain why derivative action cannot be used inPID controllers. It is also a considerable sourceof dead time because the measurement must getout of the noise band if the PID controller is todiscern a true load change from the chatter.There is a similar signal-to-noise ratio problemfor level measurements, particularly if the signalis noisy due to sloshing or bubbles.

The next most frequent problem is sensor coat-ing and drift. Resistance temperature detectors(RTDs) and smart transmitters can reduce driftby an order of magnitude. Keeping the velocitythat is passing a sensor above 5 fps is the mosteffective way to keep a sensor clean.

Rule 18 Narrow span ranges

and slow scan times should beused for temperature and levelmeasurements to minimize the


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64 M EASUREMENTS AND V ALVES

dead time and chatter from the analog/digitalconverter (A/D). For level measurements, you

should minimize sensitivity to bubbles,sloshing, and coating.

Rule 19 Use RTDs and smart transmitters to reduce drift andcalibration requirements. Theywill more than pay for themselvesthrough lower maintenance costs

and more accurate process operating points.

3.2 Deadly Dead BandAccording to EnTech studies, most loop

variability is caused by poor tuning and controlvalve resolution. Figure 12 shows the dead bandthat occurs whenever a control valve changesdirection and the staircasing that is the result of stick-slip action. The dead band and stick slipare usually largest near the valve seat. Valve

resolution is the minimum change in signal inthe same direction that will result in a flowchange and is usually about half of the valvedead band. As you approach the resolution limitthere is a dramatic increase in the loop deadtime from dead band, as illustrated in Figure 13.This additional dead time can be about fivetimes larger for pneumatic positioners than for digital positioners. Figure 14 shows that it is


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F i g u r e 1 2

D

e a d T i m e

f r o m t h e V a l v e

d e a d

b a n d

d e a d

b a n d

S t i c k - S l i p

S i g n a l

( % )

0

S t r o

k e

( % )

d i g i t a l p o s i

t i o n e r

w i l l f o r c e v a

l v e

s h u t a t

0 % s

i g n a

l

p n e u m a t

i c p o s i

t i o n e r

r e q u

i r e s a n e g a

t i v e

s i g n a l

t o c l o s e v a

l v e


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worse for piston actuators and rotary valves.Most valve manufacturers will choose a valve

position and step size that is near the minimumshown in Figures 13 and 14. For large step sizes,the time required to move large amounts of air into or out of the actuator increases the responsetime.

Another problem with rotary valves is that thefeedback to the positioner is from the actuator shaft. What might seem to be minor gaps in key-lock connections and twisting in long shaftsactually means that the butterfly disk or ballmay not move, even though the positioner seesa movement of the actuator shaft. To minimizethis problem, you should use splined connec-tions and short large-diameter shafts, and youshould conduct actual flow tests on all rotaryvalves. All tests on control valves should use stepsizes that approximate what is expected to occur as changes in the controller output from one

scan to another (< 0.5%). You should also usevery large step sizes for pressure-relief valves andfor compressor antisurge valves. There is noth-ing in a valve specification that requires that thevalve will actually move. To ensure that a valvewill respond to meet the needs of a control loop,you should add the dynamic classes in Table 4to the valve specification sheet when purchasinga control valve.


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F i g u r e 1 3

D

r a m a t i c R i s e i n R e s p o n s e T i m e a s Y o u A p p r o a c h t h e R e s o l u t i o n L i m i t

0 . 1

0 . 1

1 . 0 1

. 0

1 0 . 0

1 0 . 0

1 0 0

1 0 0

4 0 0 4 0 0

4 0 . 0

4 0 . 0

4 . 0 4 . 0

0 . 4 0 . 4

d e a d

t i m e

d e a d

t i m

e

f r o m

f r o m

d e a d

b a n d

d e a d

b a n d

p r e s t r o

k e

p r e s t r o

k e

d e a

d t i m e

d e a

d t i m e

l a g f r o m

l a g f r o m

s t r o k i n g

s t r o k i n g

t i m e t i m e

R e s p o n s e

R e s p o n s e

T i m e

( s e c

)

T i m e

( s e c

)

S t e p

S i z e

( % )

S t e p

S i z e

( % )

G u e s s w

h a t s t e p

s i z e

t h e v e n d o r w

i l l c h o o s e

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h a t s t e p

s i z e

t h e v e n d o r w

i l l c h o o s e

t o d e t e r m

i n e t h e r e s p o n s e

t i m e o f

t h e v a

l v e

t o d e t e r m

i n e t h e r e s p o n s e

t i m e o f

t h e v a

l v e


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F i g u r e 1 4

R

e s p o n s e T i m e D e p e n

d s u p o n t h e V a l v e , S

h a f t , S i z e a n

d C o n n e c t i o n s ,

A c t u a t o r , a n

d P o s i t i o n e r

0 . 1

1 . 0

1 0 . 0

1 0 0

4 0 0

4 0 . 0

4 . 0

0 . 4

R e s p o n s e

T i m e

[pid] pid control - good tuning - a pocket guide

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