pid control - good tunning - a pocket guide

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Volume EMC 27.01

Good Tuning:A Pocket Guide

By Gregory K. McMillan



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 2000670.42’75--dc21

00-036958

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TABLE OF CONTENTS 7

Table of Contents

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

1.1 Introduction ................................. 1

1.2 Actions Speak Louder than Words2

1.3 Controller à la Mode..................... 6

1.4 Is That Your Final Response? ....... 7

1.5 The Key to Happiness................ 30

1.6 Nothing Ventured, NothingGained ....................................... 34

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

2.1 First Ask the Operator................ 43

2.2 Default and Typical Settings....... 43

2.3 The General-purpose Closed-loopTuning Method............................ 47

2.4 The Shortcut Open-loop Method 53

2.5 Simplified Lambda Tuning ......... 58

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

3.1 Watch Out for Bad Actors .......... 63

3.2 Deadly Dead Band...................... 64



8 TABLE OF CONTENTS

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



BEST OF THE BASICS 1

1.0—Best of the Basics

1.1 Introduction

Welcome 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, let’s 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 control

valves makes this implausible. Anyeffort 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



2 BEST OF THE BASICS

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 Words

The 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 the

opposite of process action to provide feedback correction, you should use a direct-acting con-




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 control

valve, 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 AC2, 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




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 PID

and 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.




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




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 à la Mode

The 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 locallysets 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).




• 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 thesupervisory mode.

• ROut (remote output) – The output isremotely set, often by a sequence or by

another 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




(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 itdoesn’t know the process variable should bechanging initially and that the brakes shouldonly be applied to the process when itapproaches set point. Using derivation action

that 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




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 loop’s 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 c∗ En




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

as follows:Pn = K c∗ Dn

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

In = K c ∗ 1/Ti ∗ (En∗ Ts ) + In-1

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

In

= K c ∗ 1/T

i ∗ (D

n∗ T

s) + I

n-1

The 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 / Ti




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 PIDcontroller (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-




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



BEST OF T

HE BASICS 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




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.



BEST OF T

HE BASICS 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 ) .




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.



BEST OF T

HE BASICS 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




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




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 to

achieve 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.




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 as

1.5, 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.




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-




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




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 )




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.




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.




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 )




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 to

use 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




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




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 used

in 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.




1.5 The Key to Happiness

When I was four years old and sitting on my

daddy’s 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 it

will slow down the divergence of the measure-ment from the set point during an upset andgive the controller a chance to catch up. All




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.



32 BEST OF T

HE BASICS

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




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 amazed

at 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 loopvariables

Delays controller ’s ability to see and react

to upset




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 are

usually nonlinear High steady-state gain causes overreactionand oscillations

Low steady-state gain causes loss of sensitiv-ity and wandering

1.6 Nothing Ventured, NothingGained

There 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 study

the relationships revealed by the equations pre-sented in this section, you should skip ahead toSection 2.0 on Tuning Settings and Methods.




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<< 1),then the controller gain is proportional to justthe inverse of the open loop gain:




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 versus

reagent-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-




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.




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 o∆AI

∆AO-------------

∆MV∆AO--------------

∆FR ∆MV--------------

∆PV∆FR -----------

∆AI∆PV-----------•••= =

K fr 1Ff

----=




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•

----------------------------------=




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

(%/pph)(%/ft)∆AO = change in the controller ’s analog

output (%)∆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 equations

used 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



BEST OF T

HE BASICS 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




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.



TUNING SETTINGS AND METHODS 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 Settings

Tables 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



44 TUNING SETTINGS AND METHODS

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 level

loops, 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.




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 ; λ

= 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 )

λ λ λ λ

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 )

λ λ λ λ

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 )

λ λ λ λ

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




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 ;

λ = 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 )

λ λ λ λ

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 )

λ λ λ λ

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 )

λ λ λ λ

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




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.




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

S e t r e s e t t i m e = 1 0 * o s c i l l a t i o n p e r i o d

t r u e

f a l s e




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




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 loopstarts 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.




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-




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

2.4 The Shortcut Open-loop Method

The 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




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




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




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

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

K i∆%PV2 ∆t ⁄ ( ) ∆%PV1 ∆t ⁄ ( )–

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

K cK x

K i TDo•-----------------------=

TDv

DB

K x ∆%AVP•

--------------------------------- TDo

•=

∆%AVP ∆%AODB2

--------–=

Ti ci TDv TD0+( )•=

Td cd TDv TD0+( )•=




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 deadband (sec)

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

(seconds/repeat)




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 Tuning

If 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 98

percent of the final response (T98). Thissimplified form of the equation for Lambda




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




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 the

controller 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 process

variable (∆%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).




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(λ = 4).

The equation for reset time setting is as follows:

Ti = T98 / 4 = TDo/ 4 + TC (seconds/repeat)

The equation for gain setting is as follows:

K c = ( ∆ %AO / ∆ %PV ) ∗ ( 1/ λ )

(λ 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.




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

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

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



MEASUREMENTS AND VALVES 63

3.0—Measurements and

Valves

3.1 Watch Out for Bad Actors

The 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



64 MEASUREMENTS AND VALVES

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 Band

According 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 five

times larger for pneumatic positioners than for digital positioners. Figure 14 shows that it is




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




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 minimize

this 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.




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

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

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




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 ( s e c )

S t e p S i z e ( % )

1 2

3

4

5

6 7

1

- s l i d i n g s t e m v a l v e w i t h d i a p h r a g m a c t u a t o r a n d d i g i t a l p o s t i o n e r w i t h p u l s e w i d t h m o d u l a t e d s o l e n o i d s .

2

- s l i d i n g s t e m v a l v e w i t h d i a p h r a g m a c t u a t o r a n d d i g i t a l p o s i t i o n e r w i t h n o z z l e f

l a p p e r

3

- s l i d i n g s t e m v a l v e w i t h d i a p h r a g m a c t u a t o r a n d p n e

u m a t i c p o s i t i o n e r

4

- r o t a r y v a l v e w i t h p i s t o n a c t u a t o r a n d d i g i t a l p o s i t i o n e r

5

- r o t a r y v a l v e ( t i g h t s h u t o f

f ) w i t h p i s t o n a c t u a t o r a n d

p n e u m a t i c p o s i t i o n e r

6

- v e r y l a r g e r o t a r y v a l v e ( >

6 ” ) w i t h a n y t y p e o f p o s i t i o n e r

7

- s l i d i n g s t e m v a l v e w i t h a

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




Table 4 — Dynamic Classes of Control Valves (Four classes A → D for each of the four categories 1 → 4)

Referring to Table 4, consider a DACB classcontrol valve. It will respond to signals larger than 0.2 percent and smaller than 5.0 percent inless than 2 seconds above a position of 20 per-cent. If you don’t care about how well a valveresponds, specify class AAAA--almost any valvewill meet it.

A general-purpose application would be BAAB.Examples of other classes for various types of

1-Minimum StepClassesClass A - 3.0% ± 0.3%Class B - 1.0% ± 0.1%Class C - 0.5% ± 0.1%Class D - 0.2% ± 0.1%

2-Maximum StepClasses

Class A - 5% ± 0.5%Class B - 10% ± 1.0%Class C - 20% ± 2.0%Class D - 50% ± 2.0%

3-Response TimeClassesClass A - 15 secClass B - 5 secClass C - 2 secClass D - 1 sec

4-Minimum PositionClassesClass A - 30%Class B - 20%Class C - 10%Class D - 0%

Note: The response time is the time it takes the trim(not the actuator) to stay within 10 percent of stepor within 0.1 percent of span, whichever is largest.(Overshoot is OK if recovery is within this offsetfrom the desired position of the trim)




control loops are given in the following list. Tochoose a typical class, use the loop type that

actually throttles the control valve. For cascadeloops, you should use the slave loop.

• Vessel or Column Temperature Control=> CABC

• Exchanger Temperature Control =>CACC

• Pipeline Temperature Control => CCCC• Liquid Pressure or Flow Control => CACC• Vessel Level Control => CABC• Gas or Steam Pressure Control => CBDC• Compressor Surge Control => CCCD• Vessel pH Control => DABD

• Pipeline pH Control => DBCD• Pressure Relief => BCCD• For split range, use class D for last category

(minimum throttle position)

The best way to see if the flow actually changed

for a small change in controller output is tomake a sensitive flow measurement with verylow noise. This is particularly important for rotary valves or pneumatic positioners. Another clue that the valve has a problem is if the controlloop oscillations are smaller in manual than inauto (this assumes you have tuned the control-ler). If it is a critical rotary valve and there is noflow measurement, you need to take the valve




out of the pipeline. In the shop, you need tothen attach a travel indicator to the butterfly

disk or ball to check whether they track thechanges in the actuator shaft.

Finally, the change in the flow measurement for a change in controller output will also show if the control valve is on a portion of the installedcharacteristic that is too steep or flat. If there is

no flow measurement, ask the valve manufac-turer to generate an installed valve characteristicfor your piping system. Signal characterizationto linearize the valve will decrease valve deadtime from its resolution limit for the flat portionof the curve, but it will increase this dead time

for the steep portion of the curve.

Figure 15 summarizes the maintenance tests for a good or bad valve. The change in PV can beany process variable, but it works best if it is afast measurement such as flow or pressure. Slowprocess variables such as temperature and levelrespond much too slowly, especially for smallchanges in controller output, to make it practicalto determine valve dead band.

Rule 20 – To achieve the tightest control (i.e., least variability), use

sliding stem valves and digitalpositioners. If you use rotaryvalves, you should have a flow




F i g u r e 1 5 — M

a i n t e n a n c e T e s t s f o

r a G o o d o r P o o r C o n t r o l V a l v e

c r i t i c a l

v a l v e ?

b e t t e r i n

m a n u a l t h a n

a u t o ?

s l i d i n g s t e m

t h r o t t l i n g

v a l v e ?

∆ ∆ ∆ ∆ P V f o r

∆ ∆ ∆ ∆ A O O K ?

f a s t p r o c e s s

r e s p o n s e ?

S t e p

r e s p o n s e t e s t

O K ?

D o e s b a l l

o r d i s k t r a c k

s h a f t ?

i n s t a l l e d

c u r v e * s l o p e

O K ?

t r u e

t r u e

t r u e

t r u e

t r u e

f a l s e

t

r u e

t r u e

g o o d

v a l v e

g o o d

v a l v e

p o o r

v a l v e

p o o r

v a l v e

p o o r

v a l v e

p o o r

v a l v e

f a l s e

f a l s e

f a l s e

f a l s e

f a l s e

t r u e

f a l s e

f a l s e

( v a l v e

d y n a m i c s a r e O K )

( l o o p t u n i n g

i s a s s u m e d

t o b e O K )

( a c t u a t o r

s h a f t p o s i t i o n

r e f l e c t s t r i m

p o s i t i o n )

* C h e c k s l o p e o n a c t u a l c u r v e

t h a t i n c l u d e s t h e v a r i a t i o n i n

p r e s s u r e d r o p a v a i l a b l e t o t h e

c o n t r o l v a l v e d u e t o c h a n g e s

i n s y s t e m d r o p a n d p u m p h e a d




measurement, splined shaft connections, and ashort large-diameter shaft.

Rule 21 – If you must operate onthe flat portion of an installedvalve characteristic, use signalcharacterization to make the valvemore sensitive. Be careful to avoid

increasing the valve dead time from dead bandon the steep portion of the curve. Also makesure you don’t eliminate an equal-percentagecharacteristic used to compensate for a flow ratiogain.



CONTROL CONSIDERATIONS 75

4.0—Control Considerations

4.1 Auto Tuners

The relay method auto tuner shown in Figure 16is effective and simple. It keeps the loop under control by constantly forcing the PV back and

forth across the starting point of the test. Itseffectiveness depends upon the noise bandbeing set correctly so that fluctuations fromnoise are not measured as loop oscillations. Fig-ure 17 shows a single step in controller outputthat uses the shortcut tuning method to providean estimate of tuning settings and then a seriesof successive steps to provide an automatic iden-tification of valve dead band.

4.2 Uncommonly Good Practices for Common Loops

For flow and pressure loops, first make sure thescan time is fast enough. For gas pressure, thegain must be maximized. For level loops it ismost important that you decide whether thelevel control must be tight or loose and that youminimize the reset action. For temperature loops

it is critical that you use a narrow calibrationspan and slow scan time. For concentrationloops you must make sure that the sensor is not



76 CONTROL CONSIDERATIONS

F

i g u r e 1 6 — R e l a y M

e t h o d A u t o T u n e r

T i m e

( m i n )

M e a s u r e m e n t

( % )

U l t i m a t e P e r i o d

T u

0

S e t P o i n t

O u t p u t ( A O )

( % )

d

a

U l t i m a t e G a i n

4 ∗ ∗ ∗ ∗ d

K u = − − − −

− − − −

− − − −

− − − −

π ∗

π ∗

π ∗

π ∗ e

n

e = s q r t ( a 2 -

n 2 ) I f n = 0 ,

t h e n e

= a

a l t e r n a t i v e t o

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

o t h P V




F i g u r e 1 7 — E n h a n c e d

P r e t e s t a n d P r e t u n e

M e a s u r e m e n t

( % )

I n i t i a l P V

O u t p u t ( A O )

( % )

T i m e

( s e c s )

T D o

v a l v e d e a d b a n d i d e n t i f i c a t i o n

R a m p t i m e i d e n t i f i c a t i o n

a n d s h o r t c u t e s t i m a t e o f

c o n t r o l l e r t u n i n g s e t t i n g s

T D m a x

∆ ∆ ∆ ∆

A O

D B / 2




have Scotty and warp drive, you are stuck withthe dead time caused by equipment, piping,

instrumentation, and control valves in your loop.

A dead-time compensator is very sensitive to anoverestimate of the dead time. A dead time thatis 25 percent larger than actual can cause insta-bility. A major source of dead time is a transpor-tation delay, which can be computed for apipeline as the volume divided by the flow or for a sheet as the distance divided by the speed.Overestimates of the process gain and underesti-mates of the time constant are also problems butto a lesser degree.

To derive the full advantage of a Smith Predic-tor, you should increase the controller gain andthe reset action. For a negligible time constant,the reset time can be set equal to one-fourth of the uncorrected dead time to provide a reset

action that is an order of magnitude greater. Adead-time compensator is most effective ondead-time-dominant loops where the dead timecan be accurately calculated and updated in thepredictor.

Most dead-time compensators can be reduced tosome form of the Smith Predictor shown in Fig-ure 18. The PID controller output passes




through a dead time, single time constant, andsteady-state gain model of the valve, process,

and sensor dynamics. The model output withand without the loop dead time is subtractedfrom and added to the measurement of the pro-cess variable, respectively. This leaves the modeloutput without the dead time as the controlledvariable. The dead time has been removed fromthe loop as far as changes in the controller out-put are concerned. Note that the controlled vari-able is no longer the actual process variable.

Rule 22 – To maximize the sta-bility of a dead-time compensator,update the dead time as quickly

and accurately as possible andmake sure you always underesti-

mate the dead time and process gain and over-estimate the time constant. You should includethe change in dead time resulting from a changein a transport delay by using a computation in

which the dead time is inversely proportional toflow or speed.




F i g u r e 1 8 — S m

i t h P r e d i c t o r

c o n t r o l l e r

K c

T i T d

v a l v e

p r o c e s s

m e a s u r e m e n t

T C s

T D s

K s S

m i t h P r e d

i c t o r

s e t p t .

∆ ∆ ∆ ∆

+ + + +




Rule 23 – The reset time shouldbe set to be about one-fourth (¼)

of the uncompensated dead timeto get the most out of a dead-timecompensator. The reset time can

be decreased by an order of magnitude by add-ing a dead-time compensator that has just a 10percent underestimate of the dead time.

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

A feedforward signal that is accurate both ingain and in timing can make an impressiveimpact on control loop performance, especially

for unit operations with large dead times such asdistillation columns and large reactors. Ideally,the compensating effect from the feedforwardsignal should arrive in the process at the sametime as the load change and be equal but oppo-site to the upset. For fast loops, the timing is

tight, and the feedforward signal may arrive earlyand cause an inverse response. If it is too late,the feedforward signal creates a second distur-bance. For fast loops, the timing is more criticalthan the gain, but dynamic compensation isoften neglected. Figure 19 shows the patterns of response that are a clue to how you shouldadjust the feedforward gain and timing.




F i g u r e 1 9 — F e e d

f o r w a r d T u n i n g

t o o

e a r l y !

t o o m

u c h !

P V

P V

T i m e

T i m

e

t o o l a t e !

n o t e n

o u g h !

P V

P V

T i m e

T i m

e

n o n e !

p e r f e c

t !

P V

P V

T i m e

T i m

e




You can greatly improve a loop’s set pointresponse by adding the percentage change in set

point into the controller output as a feedforwardsignal that has a gain of about half of the con-troller gain, an action opposite to the controlaction, and a slight filter. This provides the kick you would normally get from a high gain setting.The loop can then rely on reset action to makethe rest of the transition to the new set point.

Rule 24 – Both the feedforward gain and the dynamic compensa-tion (dead time and lead lag) must be set properly to get the most benefit. For fast processes the tim-

ing is more critical. It is better for the signal toarrive a little late than too early because inverseresponse is extremely disruptive.

Rule 25 – Add a feedforward sig-nal of a set point in percent to the

controller output with a gainabout half of the controller gain,an action opposite of the control-

ler action, and a small filter. The feedforwardaction is opposite the controller action becausethe controller action works on error, which is themeasurement minus the set point. For nonlinear valves, you may need to add signal characteriza-tion.




4.5 Cascade Control Tuning

Cascade control is a type of control in which a

secondary (slave or inner) loop is added that getsa set point from a primary (master or outer)loop. If the secondary loop response (both deadtime and time constant) is five times faster thanthe primary loop response, there is no interac-tion between the loops, and the secondary loop

can correct for upsets it can measure before theyaffect the primary loop. If the secondary loop isnot fast enough, you must increase the scan timeand the PV filter time of the primary loop or youwill have to decrease the controller gain and rateaction of the primary loop to reduce the interac-

tion. Besides catching an upset quicker, the sec-ondary loop may also help linearize the responseof the primary loop. For example, in the cascadeof reactor temperature to coolant jacket exit tem-perature, the secondary loop of jacket tempera-ture will make the process gain for reactor temperature linear in addition to sensing coolanttemperature disturbances before they affect thereactor temperature. Similarly, the cascade of exit coolant temperature to a flow loop on cool-ant makeup will remove the nonlinearity of theinstalled characteristic and dead band of thevalve in addition to reducing the effect of cool-

ant pressure changes. The most common type of secondary loop is the flow loop. It can consider-ably improve the performance of a primary loop




for concentration, level, and temperature con-trol. The flow loop is not generally recom-

mended for liquid pressure control because thespeed of response of the liquid pressure and floware about the same. Another type of cascadecontrol that should be used more frequently isthe cascade control of still, reactor, or evapora-tor temperature to steam pressure control. Inthis kind of control, the steam pressure loopcompensates not only for steam supply pressureupsets but also for changes in the condensingrates (heat load and transfer) as reflected in thesteam coil or jacket pressure.

You should tune the secondary loop for an

immediate response before tuning the primaryloop. An offset in the secondary loop is usuallyof no consequence since the sole purpose of thesecondary loop is to meet the demands of a pri-mary loop. You should tune the secondary loopwith maximum gain action and minimum reset

action and use a feedforward of the set point.This is particularly important for cascade controlof gas pressure control to flow. If the abruptchanges in the secondary loop output upsetanother important loop, then you may need touse Lambda tuning to make the secondary loopresponse smoother and more gradual.




The most common mistake is to forget to prop-erly set the output limits of the primary loop.

You must set the output limits on the primaryloop so they match the set point limits on thesecondary loop. Also, the primary loop must notwind up when the secondary loop output is at itsoutput limits.

Rule 26 – If the dead time andtime constant of the primary loopare not five times slower thanthey are for the secondary loop,the primary loop must be slowed

down. The scan time and filter time must beincreased or the controller gain and rate action

must be decreased in the primary loop.

Rule 27 – You must tune the sec-ondary loop first and use gainand/or set point feedforwardaction in it so the secondary loop

can immediately respond to theset point changes from the primary loop. Resetaction is too slow to be the major source of con-trol action in the secondary loop. If you use afeedforward of the set point, make sure it isscaled properly. If the secondary loop fights withother important loops, use Lambda tuning tominimize the interaction.




Rule 28 – Make sure the output limits of the primary loop match

the set point limits of the second-ary loop. In a fieldbus-based sys-tem, the primary loop output limits

use the engineering units of the secondary loop.In older systems, the primary loop output limitsare usually expressed as a percentage of the sec-ondary loop scale.



TROUBLESHOOTING 89

5.0— Troubleshooting

5.1 Patience, Heck, I Need to Solve theProblem

Figures 20 and 21 show some diagnostics for loops in manual and auto. In these diagrams,

reset action (repeats per minute) is referencedrather than reset time (seconds per repeat). If there are fewer oscillations with the loop in man-ual, the problem is either a poor control valve or controller tuning. If there are also fewer oscilla-tions in other loops, then they are probably

caused by an interaction between this loop andother loops. If the oscillations persist and arefast, they are probably due to electromagneticinterference (EMI), sensor noise, pressure waves,or resonance. If the oscillations persist and areslow, then they are periodic upsets from other loops that have poor tuning or valves or arecaused by on-off actions (level switches), steamtraps, pressure regulators, burps (column flood-ing), or flashing. If the oscillations dissipatewhen the valve is closed, the oscillations werecaused by pressure fluctuations at the valve.

With a loop in manual, you can find the valvedead band by making a step change of 0.25 per-



90 TROUBLESHOOTING

cent in the valve and then waiting more than thedead time to see if the actual process variable

responds to the change in the controller output.For slow processes or in situations where you arereasonably sure the valve is really lousy, you canincrease the step size to 0.5 percent or even 1.0percent. This will allow the test to be completedbefore your patience wears thin. If there is noresponse, repeat the step. The steps should all bein the same direction until there is response of the process variable that is outside of the noiseband. Then repeat test for the opposite direc-tion. The absolute magnitude of the total num-ber of step changes needed to get a response inboth directions is a measure of the valve dead

band.

Rule 29 – If the oscillation goesaway when you put the loop inmanual, then the loop is the causeof the oscillation. The culprit

could be the control valve, tuning,or loop interaction.

Rule 30 – If the oscillation only goes away when you close thevalve, then it was caused by pres-sure fluctuations at the valve. Theculprit could be an oscillating pres-



TROUBLESHOOTING 91

sure loop, on-off actions, or oscillating users onthe same header.

Rule 31 – To track down thesource of an oscillation, put eachloop in manual and stop each on-off action one at a time. When theoscillation stops, you know the cul-

prit was the last loop you put in manual or thelast on-off action you stopped.

If the loop is in automatic and there are fast peri-odic upsets, the oscillations are probably causedby EMI, sensor noise, pressure waves, or reso-nance. If you experience slow periodic upsets

and a period much greater than four times thedead time, then you should suspect on-off actions, steam traps, pressure regulators, burp-ing, or flashing as the source. Otherwise, tuningis probably the culprit. When PV wanders inautomatic it is a symptom of the control loop

operating on the flat portion of an installedvalve characteristic. If the PV falters for a dead-time-dominant loop (see Figure 3b), it is an indi-cation of too much gain action. If the PV stair-cases (see Figure 5), it is an indication of toomuch rate action. If the PV overshoots anddevelops a slow oscillation whose period varieswith the reset setting (see Figure 4), it is a sign of too much reset action (i.e., the reset time too



92 TROUBLESHOOTING

small). If the loop period is very sensitive to resetaction, it is a sign that there is excessive valve

dead band. For sticky valves, you can make theoscillation significantly faster by using more rateand gain action. This will get the controller out-put through the dead band more quickly.

If the period of an upset is near the naturalperiod of the loop, which is two to four timesthe dead time, then the loop will amplify thedisturbance, and the oscillation will be worsewhen the loop is in automatic. If the period ismuch less than the natural period it is uncon-trollable noise. For a loop to have a chance of attenuating the upset, the period of the upset

must be more than twice as large as the naturalperiod of the loop.

Note that on Figures 20 and 21 “reset too hi” means the reset action is too high, which meansthe reset time is too small.

Rule 32 – If the oscillationperiod for the loop in automaticdrastically increases for lessaggressive controller tuning, thevalve has excessive dead band. It

takes longer for the controller output to work through the dead band if the PID action isslower due to less gain, reset, and rate action.



TROUBLESHOOTING 93

F i g u r e 2 0 — D

i a g n o s t i c

s f o r L o o p s i n M a n

u a l

o s c

. l e s s

f o r t h

i s l o o p

i n m

a n u a l

l i q u i d

p r e s s u r e o r f l o w

l o o p s

o s c . g o

n e

f o r t h i s l o o p

i n m a n u a l

o s c .

p e r i o d

< 4 s e c

o s c . g o n e

f o r o t h e r l o o p

i n m

a n u a l

o s c . l e s s i n

o t h e r l o o p s

∆ P V z e r o

f o r ∆ A O s

= 1 %

∆ P V j u m p s

f o r ∆ A O s

= 1 %

g a i n t o o h i

r e s e t t o o l o

r a t e t o o h i

v a l v e s t i c k s

v a l v e s l i p s

g a i n t o o h i

f i l t e r t o o l o

r a t e t o o h i

E M I , s e n s o r

n o i s e , w a v e s ,

o r r e s o n a n c e

o t h e r l o o p h a s

t u n i n g o r v a l v e

p r o b l e m s

o n - o f f

a c t i o n s ,

t r a p s , r e g u l a t o r s ,

b u r p a

n d f l a s h

g a i n t o o h i

r e s e t t o o l o

r a t e t o o h i

g a i n t o o l o

r e s e t t o o h i

r a t e t o

o l o

t r u e

t r u e

f a l s e

t r u e

t r u e

t r u e

t r u e

t r u e

t r u e

f a l s e f a l s e

f a l s e

f a l s e

f a l s

e

f a l s e

f a l s e

L a m b d a T u n i n g

M o s t u p s e t s

s t a r t o u t

a s a p r e s s u r e c h a n g e

T a k e o u t t h e r e s e t !



94 TROUBLESHOOTING

F i g u r e

2 1 — D

i a g n o s t i c s

f o r L o o p s i n A u t o m a t i c

w a n d e r s

o r t r a c k s

a n o t h e r

l o o p

o s c p e r i o d

m u c h l e s s t h a n

r e s e t t i m e

p e r i o d i c u p

s e t s

P V f a l t e r s

o r s t a i r s t e p s

t o s

e t p t

P V

o v e r s h o o t s

s e t

p t

l i q u i d

p r e s s u r e o r f l o w

l o o p s

o s c p e r i o d

< 4 s e c

o n - o f f a c t i o n s ,

t r a p s , r e g u l a t o r s ,

b u r p a n d f l a s h

s e n s o r n o i s e ,

p r e s s u r e w a v e s ,

o r r e s o n a n c e

v a l v e s t i c k s

v a l v e t o o s m a l l

- o n f l a t p a r t o f

i n s t a l l e d c h a r a c

g a i n t o o h i

r

e s e t t o o l o

r a t e t o o h i

g a i n t o o l o

r e s e t t o o h i

r a t e t o o l o

f r e e p a s s

t o h a p p y h o u r

g a i n t o o h i

r e s e t t o o l o

r a t e t o o h i

g a i n t o o

l o

r e s e t t o o h i

r a t e t o o

l o

t r u e

t r u e

f a l s e

t r u e

t r u e

t r u e

t r u e

t r u e

t r u e

f a l s e

f a l s e

f a l s e

f a l s e

f a l s e f a l s e

f a l s e

o s c p e r i o d

i n c r e a s e s i f g a i n

d e c r e a s e s

L a m b d a T u n i n g

T a k e o u t t h

e r e s e t !

M o s t u p s e t s s t a r t o u t

a s a p r e s s u r e

c h a n g e



TROUBLESHOOTING 95

The oscillation can be made much faster andtighter by using higher gain and rate action.

Figure 22 is a spectrum analysis for a level,which shows that the predominant frequency is0.08 cycles per minute. By analyzing the power spectrum of process variables in the applicationdepicted in the figure, Walsh Automation wasable to find the source of a cycle with a twelve-minute period in a series of distillation columns.It was an oscillation in the feed, which wascaused by level switches on a feed tank thatturned pumps on and off. This power spectrumanalysis tool can quickly point to common peri-odic oscillations that noise and upsets would

make it difficult to spot in trend recordings.

Rule 33 – A power spectrum ana-lyzer can rapidly point you to theculprit by indicating which loopsexperience significant peaks in

the power at the same frequency.The first step is to enter the data for loops inautomatic into the power spectrum analyzer.The data gathering must be done quicklyenough to prevent aliasing. For chemical pro-cesses, it is sufficient to use data from a historianwith no compression and an update time of 1second. For sheets (webs), you may need to storethe data using a device with an exceptionally fast



96 TROUBLESHOOTING

F i g u r e 2 2 — P o w e r S p e c t r u m A n a l y s i s ( S o u r c

e : C o u r t e s y o f W a l s h A u t o m a t i o n , T o

r o n t o )



TROUBLESHOOTING 97

scan time (50 milliseconds or less) that is directlyconnected to the analog input terminals.

5.2 Great Expectations and PracticalLimitations

When all is said and done, a loop will at bestonly pass on variability from its PV to its output.Variability in the output of one loop can greatlydisturb another loop. Loops will actuallyincrease the variability of the PV if there is asticky valve, overly aggressive tuning settings, or upsets that have a period close to the naturalperiod of the loop (two to four times the loopdead time). Most periodic upsets are caused by

on-off actions and oscillating loops (which areoften associated with level switches or level con-trollers that have too much gain or reset action).You can avoid a lot of headaches and wastedeffort by first resolving valve problems and peri-odic upsets.

The most troublesome practice is using resetaction correctly. It is not widely understood thatthe reset time as a factor of the loop period var-ies by an order of magnitude depending uponthe degree of dead-time dominance and self-reg-ulation. For example, for a process that tends toramp or run away, the reset time should be larger than ten times the loop period. For a self-regulat-



98 TROUBLESHOOTING

ing process with a small dead-time-to-time-con-stant ratio, the reset time should be between 0.5

and 1.0 times the loop period. For pure dead-time processes, the reset time can be one quarter (¼) of the dead time. Since the natural period istwice the dead time for a dead-time-dominantloop, the reset time ends up being about one-eighth (1/8) of the loop period. If a dead-timecompensator is added to this loop, the reset timecan be set to be about one quarter of the uncom-pensated dead time. If the dead time is underes-timated by 10 percent, the reset time can be aslow as one eightieth (1/80) of the loop periodfor a dead-time compensator.

To make it even more interesting, the rule of thumb to set the reset time greater than tentimes the loop period for integrating and run-away processes is designed to essentially elimi-nate the possibility of oscillations due to resetaction. There is a gain window for such non self-

regulating processes. If the gain is below the lowlimit or above the high limit, there is a loss of control. The closer the controller is to the lowgain limit, the more sensitive it is to reset action.Proportional action makes the response moreself-regulating and thus, more tolerant of resetaction. Some consultants recommend propor-tional-only controllers for level loops and pro-portional plus derivative controllers for



TROUBLESHOOTING 99

exothermic reactor temperature loops to protectagainst instability caused by reset. In practice,

some reset is useful to eliminate offset and facili-tate startup. For level loops, it has been foundthat to prevent oscillations, the product of thecontroller gain and reset time must be greater than 4 times the fastest time for the level toramp full scale. While the actual minimumproduct of gain and reset that triggers oscilla-tions will change depending upon the amountof loop dead time and valve dead band, the rela-tionship is useful to determine how to simulta-neously adjust the gain and reset for level loops.If the loop response is smooth and the control-ler gain is doubled, the reset time can be halved

and still keep the product of the two adjust-ments the same. It is critical to note that theopposite is true (the reset time must be doubled)if the loop is approaching the upper gain limit. If you are confused, don’t feel alone. It is safe tosay that 99% of users who don’t carry this guide

don’t even have a clue that this strange twist of the rule on tuning reset even exists.

The following equation by Harold Wade showshow to eliminate oscillations near the low gainlimit for a level controller if the dead time andvalve dead band are negligible:

K C * TI > 4 * TL



100 TROUBLESHOOTING

TL = VS / ∆F

Where:

∆F = maximum difference between inletand outlet flows (gpm)

K C = controller gainTI = controller reset time (minutes/repeat)T

L= fastest level full scale ramp time

(minutes)VS = volume for level measurement span

(gals)

Finally, in order to tune the loop you need to be

able to see the response. If the update time is tooslow, the period of an oscillation and any timemeasurements will appear longer than actual. If 10% accuracy is desired, then the update timemust be less than one tenth of the dead time or time constant. The scan times of any devicesthat supply data should be twice as fast as the

trend update time to ensure sufficient over sam-pling. In order to get good accurate estimates of gains, the compression (value for exceptionreporting) should be smaller than the measure-ment or valve resolution. Otherwise the gainswill be in error to the degree that the compres-

sion approaches the step size.



TROUBLESHOOTING 101

Rule 34 – The update time of trend recordings should be less

than one tenth of the loop deadtime or time constant. The com-pression of data should be less than

one tenth of the step size and less than the mea-surement or valve resolution, whichever is larg-est.

If you understand and practice everything in thispocket guide, you might become the next CEOof your company. If this is not realistic, maybeyou will be given stock options for every loopthat is tuned. If this is a pipe dream, theimprovement in loop performance might lead to

a promotion. Well, maybe you will get a gift cer-tificate to Burger King.

Seriously, I wish you all the best of luck in tun-ing loops.



INDEX 103

Index

Aabrupt responses 19, 27accuracy

auto tuner 1measurement (see

measurementresolution)

tuning 1action

control 2–6direct 2–6fail-open 2–6gain 7, 14, 16, 22, 86, 87,

91, 92, 95on-off 89, 91, 97

process 2–6rate 8, 14, 37, 52, 85, 87,

91, 92, 95reset 7, 14, 16, 20, 22, 24,

51, 52, 75, 78, 79, 84,86, 87

reverse 3–6valve 2–6

actual valve position 57actuator 66, 71advanced control tuning 8,

16, 44algorithm

error-squared 20, 52PID 9, 47update time 95, 100, 101

aliasing signal 95analog output

function blocks 4, 12

PID 4, 12, 40, 51, 55, 57,60

analog to digital converter (A/D) 27, 29

analog to digital converter signal 63

analyzer cycle time 27

auto mode 6auto tuner

accuracy 1identification of dead

band 75integrator gain 40pretest 77

relay method 75, 76automatic mode 1, 6

Bback-calculate

function blocks 4, 7ball valve 66, 71batch control tuning 8, 16, 44

blending (see pipeline andstatic mixer)bump 43, 51, 53, 60butterfly valve 12, 36, 66, 71

Ccalibration 64calibration span 11, 27, 37

cas (cascade) mode 6cascade control 3, 8, 9, 16cascade control tuning 44, 48,

85–88



104 INDEX

characteristicvalve 12, 22, 31, 36, 37,

71, 73, 85

characterizationsignal 71, 73, 84

chatter 27, 28closed loop 6, 7, 44, 47, 48,

53, 58closed loop method tuning

51–57coating of sensor 63, 64, 75

column control tuning 14,19, 21, 22, 24, 36, 53, 82

column control valve 70compression 95, 100, 101compressor control tuning

37, 38compressor control valve 66,

70

concentration control tuning27, 29, 38, 75, 86

constrained multivariablepredictive controllers(CMPC) 28

controlbump 43, 51, 53, 60cascade 3, 6, 8, 9, 16, 19constrained multivariable

predictive controllers(CMPC) 28

disturbance (see alsoupset) 30, 78, 82, 85

error 7, 8, 11, 28feedback 2, 33, 78feedforward 52, 82–84, 86interaction 16, 20, 44, 52,

53, 58, 62, 85, 87, 89,90

limit cycle 55material balance 21offset 12, 24, 86, 99

oscillations 16, 21–25, 34,48–55, 58, 70, 75, 78

overshoot 8, 14, 24, 25,91

performance 28, 33, 82,85, 101

residence time 35, 36resonance (loops) 89, 91

set point 8, 14, 16, 17, 18,20, 23

split-ranged 14stability 22, 24upset (see also

disturbance) 30, 52, 53,55, 60, 82, 85, 86, 89,91, 95, 97

variability 1, 2, 16, 19, 27,97

control action 2–6controlled variable 11, 37, 80conveyor control tuning 19,

24, 58crystallizer control tuning 14,

21current-to-pneumatic

transducer (I/P) 4cycle time analyzer 27

Ddead band

valve 2, 19, 20, 29, 33, 47,48, 51, 53, 55, 60, 64,71, 73



INDEX 105

dead timeof valve 47, 53, 55, 56, 58,

60, 71, 73

dead time or time delayresponse 30–34, 53–57,78, 79, 80, 82, 85, 87

dead time to time constantratio 16, 35

dead-time compensator tuning 78, 79, 80–82, 98

dead-time dominant

response 16, 19, 35, 52,58, 91, 98

delayfrom transportation 33,

78, 79derivative action (see rate)derivative mode 8, 10desuperheater control tuning

19, 36, 38, 58digital positioner 64, 71direct action 2–6direct digital control (DDC)

7distillation (see column

control)disturbance control (see also

upset) 30, 78, 82, 85drift sensor 63, 64dynamic classes

valve 66, 69

Eerror

control 8, 28error control 7, 8, 11, 28error-squared algorithm 20,

52

evaporator control tuning 14,21, 86

FfaceplatePID 14

fail-openvalve 4, 5, 6

falter or hesitate response 16,91

feedback control 2, 33, 78

feedforward control 52, 82–84, 86

fieldbus function blocks 4, 9,88

fieldbus mode 6, 7filter 8, 12, 19, 27, 51, 55, 60,

84, 85, 87flow (feed) ratio 36–40

flow control tuning 19, 38,52, 75, 79, 85

fluctuations or wavespressure 89, 90

function blocksanalog output 4, 12back-calculate 4, 7fieldbus 4, 9, 88

PID 4

Ggain action 7, 14, 16, 22, 86,

87, 91, 92, 95gain tuning 7–11, 19–24, 35,

47, 48, 51, 52, 55, 57, 60,61, 92, 99, 100

general-purpose methodtuning 44–48



106 INDEX

Hheat exchanger control

tuning 19, 36, 38historian

compression 95update time 95

Iidentification of dead band

75increase-to-close valve 3–6initialization manual (IMan)

mode 7integral action (see reset)integral mode 7, 10–11integrating response 47, 98integrator gain

for auto tuner 40integrator response 39, 40, 41interaction 85, 87interaction control 16, 20, 44,

52, 53, 58, 62, 89, 90inverse response 27, 52, 53,

61, 80, 82, 84

Llag

thermowell 29lag (see time constant)Lambda tuning 35, 37, 57,

58–62, 86, 87level control valve 63, 70, 71level switches 89, 95, 97level tuning 19, 20, 21, 24, 25,

29, 44, 51, 52limit cycle 55limits

output 51, 87, 88

set point range 87, 88set point velocity 8, 19,

52

local mode 6local override mode 6loop

closed 6, 7, 44, 47, 48, 53,58

master (also known asprimary) 8, 56

open 6, 47, 53, 58

primary (also known asmaster) 8, 56

secondary (also known asslave) 8, 48, 85–88

slave (also known assecondary) 8, 48, 85–88

troubleshooting 89–101

Mmaintenance

of valve 64, 71, 72manipulated variable 3, 9, 11,

22, 28, 31, 36, 39, 40manual (Man) mode 6master loop (also known as

primary) 8, 56, 85–88

material balance control 21measurement resolution 27,

28, 100, 101methods

tuning 1, 16mode

auto 6automatic 1, 6cascade (Cas) 6derivative 8, 10



INDEX 107

direct digital control(DDC) 7

fieldbus 6, 7

initialization manual(IMan) 7

integral 7, 10–11local (see auto) 6local override (LO) 6manual (Man) 6operational 6output tracking 6

proportional 7, 9–12remote (see cascade) 6remote cascade (RCas) 7remote output (ROut) 7remote set point (RSP) 6supervisory 7

model predictive control (seeconstrained multivariable

predictive control)

Nnoise signal 19, 20, 27, 30, 42,

44, 51, 55, 60, 63, 70nonlinearity response 1, 36,

47, 58, 84, 85

Ooffset control 12, 24, 86, 99on-off action 89, 91, 97open loop 6, 47, 53, 58open-loop gain response 34–

42, 57, 60, 61operational mode 6oscillations 16, 21, 24, 25, 34,

48–55, 58, 70, 75, 78control and response 16

output limits 51, 87, 88

output tracking 6overshoot control 8, 14, 24,

25, 91

Ppatterns of response 82performance

control and tuning 28,33, 82, 85, 101

pH control tuning 27, 29, 31,36, 53

pH control valve 70, 78PID

analog output 4, 12, 51,55, 57, 60

faceplate 14function blocks 4scan time 11, 28, 29, 45,

46, 53, 63, 75, 85, 87,

97, 100PID algorithm 9, 47PID analog output 12, 40pipeline control tuning 19,

24, 27, 38, 58, 79positioner

digital 64, 71pneumatic 64, 70

smart (see digitalpositioner)

valve 4, 64–71power spectrum signal 95, 96pressure

fluctuations or waves 89,90

pressure control tuning 16,24, 35, 36, 37, 44, 48, 51,75, 86, 90

pressure control valve 66, 71



108 INDEX

pressure waves 89, 91pretest

auto tuner 77

primary loop (also known asmaster loop) 8

primary loop (also known asmaster) 56, 85–88

process action 2–6process variable 2, 3, 8, 9, 11,

14, 16, 19, 27, 31, 36, 39,51, 57, 58, 60, 78, 80

proportional action (see gain)proportional band tuning 9,

11, 20proportional mode 7, 9–12pulp and paper control

tuning 20pump control tuning 37, 38

Q quarter-amplitude response

21, 22

Rramp rate 39, 40, 41, 53, 54,

55, 97, 99, 100rate

tuning 8, 10, 11, 25–27,47, 58

rate action 8, 14, 27, 37, 52,85, 87, 91, 92, 95

rate time to dead time ratio52

ratiodead time to time

constant 16, 35, 98flow (feed) 36–40rate time to dead time 52

reset time to oscillationperiod 24, 48, 52

signal-to-noise 63

reactor control tuning 14, 16,21, 22, 44, 48, 51, 86, 99

relay methodauto tuner 75, 76

remote cascade mode 7remote mode (see cascade) 6remote output (ROut) mode

7

remote set point (RSP) 6reset action 7, 14, 16, 20, 22,

24, 51, 52, 75, 78, 79, 84,86, 87

reset time to oscillationperiod ratio 24, 48, 52

reset tuning 10, 11, 14, 22–35,47

residence time control 35, 36resistance temperature

detectors 63resolution

measurement 27, 28, 100,101

valve 27, 28, 29, 64resolution valve 71response

abrupt 19, 27analyzers 27chatter 28dead time or time delay

53–57, 78, 79, 80, 82,85, 87

dead-time dominant 16,18, 19, 35, 52, 58, 91,98

falter or hesitate 16, 91



INDEX 109

integrating 47, 98integrator 39, 40, 41inverse 27, 52, 53, 61, 80,

82, 84nonlinearity 1, 36, 47, 58,

84, 85open-loop gain 57, 60, 61oscillations 70patterns 82quarter-amplitude 21, 22runaway 47, 48, 98

self-regulating 40sensor 63set point 44, 48, 51, 52,

55, 60smooth 19, 20, 35, 78, 86staircase 25, 91steady-state gain 80time constant 8, 16, 20,

27, 36, 40, 79, 80, 85,87

time constants (TC) 57time to steady state 58–

62, 66, 67, 68, 69trajectory 14, 29

reversalof signal 3–6

rotary valve 66, 70, 71runaway response 47, 48, 98

responserunaway 22

Sscan time 28, 29, 45, 46, 53

PID 11, 63, 75, 85, 87, 97,100

secondary (also known asslave) 85–88

secondary loop (also knownas slave) 8, 48, 85–88

self-regulating response 40

sensitivity of valve (see valveresolution)

sensitivity to measurement(see measurementresolution)

sensor coating 63, 64, 75drift 63, 64

response 63sequence control tuning 19,

44set point control 8, 14, 16, 17,

18, 20, 23set point range

limits 87, 88set point response 44, 48, 51,

52, 55, 60set point velocity 8, 19set point velocity limits 52settings for tuning 43, 45, 51,

53shaft of valve 66, 68, 71, 73sheet (web) control tuning 19,

20, 24, 58shortcut tuning 75signal

aliasing 95analog to digital

converter (A/D) 27, 29,63

current-to-pneumatictransducer (I/P) 4

filter 8, 12, 19, 27, 51, 55,60, 84, 85, 87



110 INDEX

noise 19, 20, 27, 30, 42,44, 51, 55, 60, 63, 70

power spectrum 95, 96

signal characterization 71, 73,84

signal reversal 3–6signal-to-noise ratio 63size

step 43, 53, 58, 66, 69, 90,100, 101

slave loop (also known as

secondary) 8, 48, 70, 85–88

sliding stem (globe) valve 71smart positioner (see digital

positioner)smart transmitter 63, 64smooth response 19, 20, 35,

78, 86

responsesmooth 27

spancalibration 11, 27, 37

span time 69specification

valve 66spinning (fibers) control

tuning 19split range valve 70split-ranged control 14stability 22, 24staircase response 25, 91startup control tuning 16static mixer control tuning

19, 36, 38steady-state gains 30–42, 80steam traps 89, 91

step size 43, 53, 58, 66, 69, 90,100, 101

stick-slip valve 31, 64, 92, 97

stroking time (see valveresponse time)

supervisory control tuning 7supervisory mode 7

Ttemperature control tuning

14, 24, 27, 28, 29, 35, 38,

48, 52temperature control valve 70,

71temperature detectors 63thermowell lag 29time constant response 8, 16,

20, 27, 30–37, 40, 57, 79,80, 85, 87

time delay (see dead time)time to steady state response

58–62trajectory of response 14, 29transmitter

smart 63, 64transportation delay 33, 78,

79

trend recordingcompression 95, 101update time 95, 101

troubleshooting loop 89–101tuning

accuracy 1advanced control 8, 16,

44batch control 8, 16, 44cascade control 44, 48,

85–88



INDEX 111

closed loop method 51–57

column control 14, 19,

21, 22, 24, 36, 53, 82compressor control 37,

38concentration control 27,

29, 38, 75, 86conveyor control 19, 24,

58crystallizer control 14, 21

dead-time compensator 78, 79, 80–82, 98

desuperheater 36desuperheater control 19,

38, 58evaporator control 14, 21,

86flow control 19, 38, 52,

75, 79, 85gain 35, 47, 48, 51, 52, 55,

57, 60, 61, 92, 99, 100general-purpose method

44–48heat exchanger control

19, 36, 38Lambda 35, 37, 57, 58–

62, 86, 87level 19, 20, 21, 24, 25,

29, 44, 51, 52pH control 27, 29, 31, 36,

53pipeline control 19, 24,

27, 38, 58, 79pressure control 16, 24,

35, 36, 37, 44, 48, 51,75, 86, 90

proportional band 9, 11,20

pulp and paper control 20

pump control 37, 38rate 8, 10, 11, 47, 58reactor control 14, 16, 21,

22, 44, 48, 51, 86, 99reset 10, 11, 14, 22–35, 47sequence control 19, 44settings 43, 45, 51, 53sheet (web) control 19,

20, 24, 58shortcut 75slave loop 8, 48, 70, 85–

88spinning (fibers) control

19startup control 16static mixer control 19,

36, 38supervisory control 7temperature control 14,

24, 27, 28, 29, 35, 38,48, 52

web control 19, 24, 58window of allowable

gains 22, 47Ziegler-Nichols 21, 48

tuning methods 1, 16, 47–62

Uupdate time of algorithm 95,

100, 101upset control (see also

disturbance) 52, 53, 55,60, 82, 85, 86, 89, 91, 95,97



Vvalve

actual position 57actuator 66, 71ball 66, 71butterfly 12, 36, 66, 71column control 70compressor control 66,

70dead band 2, 19, 20, 29,

33, 47, 53, 60, 64, 71,73

dead time 47, 53, 55, 56,58, 60

deadband 48, 51, 55dynamic classes 66, 69fail-open 4, 5, 6level control 63, 70, 71

maintenance 64, 71, 72pH control 70, 78positioner 64–71pressure control 66, 71resolution 27, 29, 71response time 66, 67, 68,

69rotary 66, 70, 71

valve specification 66variability 1, 2, 16, 19, 27, 97variable

controlled 11, 37, 80manipulated 3, 9, 11, 22,

28, 31, 36, 39, 40process 2, 3, 8, 9, 11, 14,

16, 19, 27, 31, 36, 39,51, 57, 58, 60, 78, 80

variable speed drive (VSD) 3,36

Wwaves

pressure 89, 91web control tuning 19, 24, 58window of allowable gains

tuning 22, 47, 99, 100

ZZiegler-Nicholstuning 21, 48

pid control - good tunning - a pocket guide

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