Armando b corripio ph d p e , michael newell turning of industrial control systems, third edition international society of automation (2015)

Tuning of Industrial Control Systems
Third Edition
By
Armando B. Corripio, Ph.D., P.E.
Chemical Engineering
Louisiana State University
and
Michael Newell
Automation Designer
Polaris Engineering


Notice
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Additionally, neither the author nor the publisher has investigated or considered the effect of
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The reader is responsible for reviewing any possible patents that may affect any particular use of
the information presented.
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product must be followed at all times, even if in conflict with the information in this publication.

Copyright © 2015 International Society of Automation (ISA)
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ISBN: 978-0-87664-034-0
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Preface to the
Third Edition

This third edition of Tuning of Industrial Control Systems has been significantly
simplified from the second edition with the goal of having the discussion
more in line with modern control systems and with language that is less academic and more in tune with the vocabulary of the technicians who do the
actual tuning of control systems in industry. For example, we have eliminated
any references to first- and second-order models since these terms are highly
mathematical and may discourage some from appreciating the usefulness of
the models. We have also eliminated the distinction between series and parallel PID controllers since most modern installations use the series version and
there is not much difference between the tuning of the two versions.
We have reduced the tuning strategies to just one; the quarter-decay-ratio
(QDR) formulas slightly modified by the Internal Model Control (IMC) rules
for certain process characteristics. All the tuning strategies are intended for
responses to disturbances with a discussion on how to modify these responses
to avoid sudden excessive changes of the controller output on set point
changes when such changes are undesirable.

Chapter 10 is new and deals with the auto-tuning feature that has become
standard on current process control systems. We have successfully used the
auto-tuning feature in our tuning work on oil refineries as a reference to guide
our selection of the final tuning parameters for the controllers.
We have kept the previous edition’s discussions on the problems of process
nonlinearities and reset windup, and how to compensate for them. All of the
tuning strategies are demonstrated with computer simulation examples.

ix


Contents

Preface to the Third Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ix
1 – Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1-1. The Goal of Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-2. Feedback Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-3. Other Control Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-4. Organization of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
3
7
8
8
8
8

2 – The Feedback Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2-1. The PID Control Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-2. Stability of the Feedback Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-3. PID Controller Tuning by the Ultimate Gain and Period Method . . . . .
2-4. The Need for Alternatives to Ultimate Gain Tuning . . . . . . . . . . . . . . . .
2-5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12
19
21
29
29
30
30

3 – Open-loop Characterization of Process Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 33
3-1. Open-loop Testing—Why and How . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-2. Process Parameters from the Open-loop Test . . . . . . . . . . . . . . . . . . . . . .
3-3. Physical Significance of the Time Constant . . . . . . . . . . . . . . . . . . . . . . . .
3-4. Physical Significance of Dead Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-5. Effect of Process Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34
36

41
46
50
53
54
54

v


vi

Tuning of Industrial Control Systems, Third Edition

4 – How to Tune Feedback Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4-1. Tuning from Open-loop Test Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4-2. Practical Controller Tuning Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4-3. Reset Windup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4-4. Processes with Inverse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4-5. Effect of Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4-6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5 – Mode Selection and Tuning of Common Feedback Loops . . . . . . . . . . . . . . . . . . 77
5-1. Deciding on the Control Objective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5-2. Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5-3. Level and Pressure Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5-4. Temperature Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5-5. Analyzer Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5-6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6 – Tuning Sampled-Data Control Loops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6-1. The Discrete PID Control Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6-2. Tuning Sampled-data Feedback Controllers . . . . . . . . . . . . . . . . . . . . . . 103
6-3. Selection of the Sampling Frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6-4. Compensation for Dead Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6-5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7 – Tuning Cascade Control Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
7-1. When to Apply Cascade Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7-2. Selection of Controller Modes for Cascade Control . . . . . . . . . . . . . . . . 125
7-3. Tuning of Cascade Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7-4. Reset Windup in Cascade Control Systems . . . . . . . . . . . . . . . . . . . . . . . 136
7-5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
8 – Feedforward and Ratio Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8-1. Why Feedforward Control? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
8-2. Design of Linear Feedforward Controllers. . . . . . . . . . . . . . . . . . . . . . . . 149


Contents

vii

8-3. Tuning of Linear Feedforward Controllers . . . . . . . . . . . . . . . . . . . . . . .
8-4. Nonlinear Feedforward Compensation . . . . . . . . . . . . . . . . . . . . . . . . . .
8-5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

152
158
165
166
166

9 – Multivariable Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
9-1. What is Loop Interaction?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-2. Pairing of Controlled and Manipulated Variables . . . . . . . . . . . . . . . . .
9-3. Design and Tuning of Decouplers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-4. Tuning of Multivariable Control Systems . . . . . . . . . . . . . . . . . . . . . . . .
9-5. Model Reference Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

170
174
186
193
196
198
199
199

10 – The Auto-tuner Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
10-1. Operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10-2. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10-3. Features and Settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10-4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

202
205
209
212
213

Appendix A – Suggested Reading and Study Materials . . . . . . . . . . . . . . . . . . . . . . 215
Appendix B – Answers to Study Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233


1
Introduction

Automation is essential for the operation of chemical, petrochemical, and
refining processes. It is required to maintain process variables within safe
operating limits while maintaining product purity and optimum operating
conditions. Because all processes are different in their speed of response and
sensitivity to control adjustments and disturbances, the parameters of the
automatic controllers must be adjusted to match the process characteristics.
This procedure is known as tuning. The purpose of this book is to provide
you, the reader, with an understanding of the most commonly used and successful tuning techniques for the various control strategies used in industry.
This first chapter presents a general discussion of the goal of tuning, a description of feedback control—the most common strategy—and a brief introduction to other common control strategies.

Learning Objectives — When you have completed this chapter, you should be
able to

A. Define the main goal of tuning a control system.
B.

Understand the feedback control strategy.

C. Identify the various components of a feedback control loop.

1


2

Tuning of Industrial Control Systems, Third Edition

1-1. The Goal of Tuning
The goal of tuning is to produce a smoothly operating process. One common
misconception is that every process variable should be brought to its desired
value as quickly as possible and closely maintained at that value. When a controller is “tightly” tuned to maintain close control of a process variable, it must
make large, fast changes in its output, which usually causes disturbances to
other variables in the process. As the controllers of these other variables take
action they, in turn, cause further disturbances that affect other variables.
Before long the entire process is in a state of continuous change, which is
undesirable and may be unsafe in some occasions. The situation worsens
when the controllers cause oscillatory process responses, because then the
process variables will be continuously changing.
The following heuristics (“rules of thumb”) may prove helpful to those just
starting in the tuning of processes:
• The variability of the controller output should not be excessive; however, keeping the output variability low must be balanced against the
precision with which the process variable is to be controlled.
• Some variables do not have to be maintained at their desired values.

The most common example of this is liquid levels, which usually only
need to be kept within a safe range.
• The controller cannot move the process variable faster than the process
can respond, so the controller speed must be matched to the speed of
response of the process. Some processes respond in a matter of minutes, while others may take close to an hour or longer to respond. Not
many processes respond in a matter of seconds.
One more item to keep in mind is that there is no such thing as fine-tuning a
controller, particularly a feedback controller. In most cases the tuning parameters need only be adjusted to one, or at most, two significant digits. There are
two reasons for this. One is that feedback controllers are not that sensitive to
variations in the third digit of their tuning parameters. The other is that the
characteristics of most processes—that is, speed of response and sensitivity to
changes in controller output—vary with operating conditions, sometimes
slightly and other times not so slightly. This means that the controller tuning


Introduction

3

parameters are usually compromises selected to work in the range of operating conditions, and so their values are not precise.
Understanding this simplifies the task of tuning because it reduces the number of values of the tuning parameters to be tried. For example, it is a lot easier
to decide between gain values of 1.0 or 1.5 than to try to find out whether the
gain should be 1.276. In practice, all three of these values will work about the
same.
Armed with these heuristics and basic concepts, we are now ready to look at
the feedback control strategy.

1-2. Feedback Control
Feedback control is the basic strategy for the control of industrial processes. It
consists of measuring the process variable to be controlled (the controlled

variable), comparing the measurement with its desired value or set point, and
taking action based on the difference between them to reduce or eliminate the
difference—that is, to bring the controlled variable to its desired value. The
action taken results in the adjustment of a process flow, such as the steam flow
to a heater, which has a direct effect on the controlled variable, such as the
outlet process temperature. The three instrumentation components required
for feedback control are:
• A sensor/transmitter to measure the process variable and send its
value to the controller (Measurement)
• A controller to compare the value of the process variable to its desired
value, determine the required control action and send it to the final
control element (Decision)
• A final control element, usually a control valve or variable speed drive,
to vary the manipulated process flow (Action).
A fourth element of the loop is the process itself, through which the manipulated flow affects the controlled variable. The controlled variable is also
known as the process variable (PV), its desired value is the set point (SP), and the
signal from the controller to the final control element is the controller output
(OP).


4

Tuning of Industrial Control Systems, Third Edition

It is important to realize that a feedback controller does not use a model of the
process to compute its output. It takes action by trial and error. Tuning the
controller is the procedure of adjusting the controller parameters to ensure
that the controller output converges quickly to its correct value.
In order to better understand the concept of feedback control, consider as an
example the process heater sketched in Figure 1-1. The process fluid flows

inside the tubes of the heater and is heated by steam condensing on the outside of the tubes. The objective is to control the outlet temperature T of the
process fluid in the presence of variations in process fluid flow (throughput or
load) F and in its inlet temperature Ti. This is accomplished by manipulating
or adjusting the steam flow to the heater Fs and with it the rate at which heat is
transferred into the process fluid, thus affecting its outlet temperature.

Figure 1-1. Feedback Temperature Control of a Process Heater

SP

Steam
OP

TC

Fs

PV

F
Ti

TT

Process
fluid

T

Steam

trap

Condensate


Introduction

5

In this example, the outlet temperature T is the (controlled) process variable
PV, the steam flow Fs is the manipulated variable, and changes in the process
flow F and inlet temperature Ti are the disturbances that cause the temperature to deviate from its desired value or set point SP. The job of the feedback
controller is to bring the temperature back to the set point by adjusting the
steam flow whenever variations in the process flow or inlet temperature cause
the outlet temperature to deviate.
In Figure 1-1 the sensor transmitter is shown as a circle with the letters TT in it
and the feedback controller is a circle with the letters TC in it. This follows the
standard ISA instrumentation notation1 in which the first letter denotes the
variable being measured or controlled, in this case “T” for temperature, and
the second letter is “T” for the transmitter and “C” for the controller. The control valve is represented by the symbol shown on the steam line to the heater.
Its purpose is to adjust the flow of steam (Fs) in response the controller output
signal (OP).
The transmitter and the control valve are located in the field while the controller is located in a central control room. Today, the signals between the transmitter and the controller and between the controller and the control valve are
typically digital signals transmitted through a fieldbus or by wireless transmission. The control function is carried out by a computer or distributed control
system (DCS) that receives the transmitter signal and transmits the controller
output to the control valve. The control valve is usually pneumatically operated, requiring that the controller output be converted to an air pressure signal. This is done by a current-to-pressure (I/P) transducer.
This book uses the instrumentation symbols recommended by the ISA-5.11984 standard for conceptual diagrams, that is, diagrams that convey the basic
control concept without regard to the specific implementation hardware. In
these diagrams the signals are represented as percent of range. To facilitate
understanding we will deviate slightly from the standard ISA notation for signals and show the signals as arrows to indicate the direction in which the signals travel, as shown in Figure 1-1.

Figure 1-2 is a block diagram of the feedback control loop for the process
heater. It graphically shows the loop around which signals travel: a change in
outlet temperature T causes a proportional change in the signal PV to the controller; the summer (circle), a part of the controller, calculates the error E or


6

Tuning of Industrial Control Systems, Third Edition

deviation of the process variable from the set point SP and acts on this error
by changing the signal OP to the control valve; the control valve position
changes, causing a change in steam flow Fs to the heater; this in turn causes a
change in the outlet temperature T which then starts a new cycle of changes
around the loop.

Figure 1-2. Block Diagram of the Temperature Control Loop of the Process
Heater

Ti

F
-

SP

E

+

Controller

T

Fs +

OP+

+

Control Valve

+

Heater

-

PV

Sensor
Transmitter

+

The signs in Figure 1-2 represent the action of the various input signals on the
output signal; that is, a positive sign means that an increase in input causes an
increase in output—direct action—while a negative sign means that an increase
in input causes a decrease in output—or reverse action. For example, the negative sign by the process flow into the heater means that an increase in flow
results in a decrease in outlet temperature. Notice that by following the signals around the loop, there is a net reverse action in the loop. This property is
known as negative feedback and is a required characteristic of a feedback loop

for the loop to be stable. In this example it means that an increase in heater
outlet temperature results in a decrease in controller output, which in turn
closes the control valve and reduces the steam flow. This results in a decrease
in outlet temperature, as desired.
To ensure this self-regulating effect the controller must act in the correct direction when the process variable changes. In this example the controller action is
reverse, that is, an increase in process variable results in a decrease in control-


Introduction

7

ler output. Other processes may require direct action, for example when a tank
level controller adjusts the flow out of the tank. In this case, an increase in liquid level in the tank requires that the exit control valve open to increase the
flow out of the tank and decrease the level. Consequently, the action (direct or
reverse) of the feedback controller is its most important characteristic.

1-3. Other Control Strategies
Although feedback control is by far the most common automatic control strategy, there are other strategies that have been known to enhance control performance in terms of improving loop stability, preventing initial deviation of
the process variable, and allowing tighter control. This section will briefly
introduce these strategies; their details and tuning procedures will be presented in later chapters.
• Cascade Control. This strategy consists of cascading feedback controllers
in a hierarchy with each controller adjusting the set point of the controller below it in the hierarchy, the controller at the top of hierarchy, or
primary, controls the primary process variable while the output of the
controller at the bottom of the hierarchy adjusts the final control element. The controllers below the master controller, called secondaries,
control variables that have an effect on the primary controlled variable.
The basic premise is that the secondary feedback loops improve the stability of the primary controller by speeding up the overall response of
the process.
• Feedforward and Ratio Control. This strategy consists of measuring the
disturbances that affect the controlled variable and adjusting the final

control element to prevent deviation from the desired value of the controlled variable. In general the scheme requires a model of the process
to determine the control adjustment in the final control element. Feedback control is combined with the feedforward controller to correct for
errors in the process model. Ratio control is the simplest form of feedforward control in which the manipulated flow is ratioed to the flow
which constitutes the disturbance.
• Decoupling. This strategy consists of installing decouplers between the
output signals of two or more feedback controllers to reduce the effect
of interaction between the controllers. The interaction occurs through


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Tuning of Industrial Control Systems, Third Edition

the process when each controller output affects the process variables
controlled by the other controllers.

1-4. Organization of the Book
The details of the PID (Proportional-Integral-Derivative) controller are presented in Chapter 2, and tuning methods for feedback controllers are presented in Chapters 2, 3, and 4. How to select the controller modes for various
types of control loops is the subject of Chapter 5. Chapter 6 presents the tuning of loops in which the process variable must be sampled, such as compositions measured by gas chromatographs and similar analyzers. Tuning of
cascade control systems is discussed in Chapter 7, design and tuning of feedforward and ratio controllers in Chapter 8, and design and tuning of decouplers in Chapter 9. Finally Chapter 10 presents the auto-tuning algorithms
available in current computer control systems.

1-5. Summary
This first chapter has presented the goals of the tuning procedure and has
introduced the feedback control strategy. A brief description of other common
control strategies has also been presented.

References
1. ANSI/ISA-5.1-2009 - Instrumentation Symbols and Identification, International Society of Automation, Research Triangle Park, NC.

Review Questions
1-1. What is the main goal of controller tuning?
1-2. Which two process characteristics must be considered when tuning the
controller?
1-3. What are the three instrumentation components of a feedback control
loop?
1-4. What is the fourth element of the feedback loop?
1-5. What is the most important characteristic of a feedback control loop?


Introduction

9

1-6. A controller controls the temperature in an exothermic reactor by manipulating the flow of cooling water to the jacket around the reactor. What
should be the fail position of the cooling water control valve, open or
closed? What must be the action of the controller, direct or reverse?
1-7. A controller controls the level in a stirred tank reactor by manipulating
the flow of the reactants into the reactor. Recommend the fail position of
the reactants control valve, open or close, and the controller action, direct
or reverse.
1-8. A controller controls the composition of a caustic stream by manipulating the flow of the water that dilutes the concentrated caustic stream
entering a mixer. The control valve fails closed. What must be the controller action, direct or reverse?


2
The Feedback
Controller

The basic concept of feedback control was introduced in the preceding chapter. This chapter presents details of the feedback controller and one of the

methods proposed to tune it: the ultimate gain and period method.

Learning Objectives—When you have completed this chapter, you should be
able to:
A. Describe a Proportional-Integral-Derivative (PID) feedback controller.
B.

Know the functions of each of the three PID control modes.

C. Understand how each of the three PID control modes responds.
D. Define loop stability.
E.

Tune PID controllers by the ultimate gain and period method.

11


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Tuning of Industrial Control Systems, Third Edition

2-1. The PID Control Algorithm
The previous chapter showed that the purpose of the feedback controller is to
compute its output signal based on the difference between the controlled process variable and its desired value or set point. This section presents the three
basic modes used by the controller to compute its output signal.
The three basic modes of feedback control are proportional (P), integral (I)—also
called reset—and derivative (D)—also called rate. The controller can function
in a single mode or in a combination of either two modes or of all three,
although today most controllers function in either two or three modes. Either

way the device is known as a PID controller, based on the assumption that it
can function in all three modes. Each of these modes introduces an adjustable
or tuning parameter into the operation of the feedback controller.

Proportional Mode
The purpose of the proportional mode is to cause an instantaneous response
of the controller output to changes in the process variable. The adjustable
parameter for the proportional mode is the gain—proportional gain or controller gain—Kc. Figure 2-1 illustrates how the proportional mode responds to
the process variable PV assuming that the controller is reverse acting and that
the loop is open, that is, that the controller output does not affect the process
variable. The figure shows that:
• The controller output OP responds instantaneously to the process variable PV.
• The response is proportional to the gain Kc.
• The proportional mode does not eliminate the sustained deviation (offset) between the process variable PV and the set point SP.
If a controller only has proportional mode there will normally be an offset.
Since console operators prefer to see all the variables at their set points, not
many controllers are proportional only.


The Feedback Controller

13

Figure 2-1. Response of the Proportional Mode with the Loop Open

PV
SP

OP

Kc = 1.0
Kc = 2.0

time
Integral or Reset Mode
The purpose of the integral or reset mode is to eliminate the deviation
between the process variable and the set point. The controller does this by
moving its output with time at a rate proportional to the magnitude of the
deviation. Thus, as long as there is a deviation, the integral mode will keep
moving the output. The adjustable tuning parameter for the integral mode is
the integral time—or reset time—TI, which is inversely proportional to the
rate at which the controller output changes. Figure 2-2 illustrates how an integral reverse-acting controller responds to a sustained deviation between the
PV and the SP with the loop open. The figure shows that:
• The output does not change when the deviation is zero.
• The output changes continuously as long as there is a deviation.
• The response is not instantaneous; that is, the integral mode takes time
to act.
• The rate of change is slower the higher the integral time.


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Tuning of Industrial Control Systems, Third Edition

Figure 2-2. Response of the Integral Mode to a Step Change in PV with the Loop
Open

PV
SP

Kc = 1.0
OP

TI = 6
TI = 12
time

The step in output shown in the figure is the instantaneous response of the
proportional mode. It takes the integral mode a period of time equal to TI to
duplicate the instantaneous response of the proportional mode.
The integral mode thus forces the process variable to the set point at the
expense of slower action than the proportional mode. This slow action introduces some instability into the response of the loop.

Derivative or Rate Mode
The purpose of the derivative or rate mode is to anticipate the movement of
the process variable by taking action proportional to its rate of change. Just as
the slow response of the integral mode decreases the stability of the control
loop, the advance response of the derivative mode increases the stability. The
adjustable tuning parameter of the derivative mode is the derivative or rate
time TD. Figure 2-3 illustrates the response of the derivative mode to a ramp


The Feedback Controller

15

change in process variable, assuming a direct acting controller and an open
loop. The figure shows that:
• The derivative mode action is zero when the process variable remains
constant.

• The derivative response is proportional to the rate of change of the process variable.
• The derivative response is proportional to the derivative time TD.
• The derivative mode does not eliminate the sustained deviation
between the process variable and its set point.

Figure 2-3. Response of the Derivative Mode to a Ramp in the PV with the Loop
Open

PV
SP

OP

TD = 6.0
TD = 3.0

0
time


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Tuning of Industrial Control Systems, Third Edition

To better illustrate the anticipation action of the derivative mode, the response
to a ramp in the process variable is shown in Figure 2-4 for a direct-acting controller having both proportional mode (with a gain of 1.0) and derivative
mode. The initial step in the output is caused by the derivative mode and the
continuous change is caused by the proportional mode. As a result, the output
leads the process variable by a period of time equal to the derivative time.
Notice that this does not mean the controller can predict the future, since the

output cannot change until the process variable starts changing.

Figure 2-4. Response of a Proportional-Derivative (PD) Controller to a Ramp in PV
with the Loop Open

Kc = 1.0

OP

10

PV

TD = 10
SP
time

Although the derivative mode increases the stability of the control loop, it has
two undesirable characteristics. One is that if the transmitter signal (PV) is
noisy, the derivative can amplify noise. To limit this amplification as the frequency of the noise increases, practical controllers have a built-in filter on the
derivative mode that limits the amplification factor. The other undesirable
characteristic is that the derivative mode can cause sudden changes in controller output with sudden changes in the process variable. This is usually not a
problem because very seldom will the process variable change suddenly in
practice. To prevent sudden changes in set point from causing sudden
changes in output, all practical controllers have the derivative mode work
only on the process variable, not on the deviation from the set point.


The Feedback Controller

17

PID Tuning Parameters
The three adjustable tuning parameters of the PID controller are the proportional gain Kc, the integral time TI, and the derivative time TD. The time
parameters are specified in minutes for most controllers, although some
brands may require them in seconds. Although modern control systems display the process variable in engineering units (°F, lb/hr, barrels/day, psi,
etc.), the proportional gain is dimensionless, because it is defined as the
change in percent controller output per percent change in the process variable’s transmitter output (i.e., the fraction, in percent, that the process variable
value is of the calibrated range of the transmitter).
Figure 2-5 illustrates this concept for a temperature controller. The left scale
shows the process variable PV both in engineering units, °F, and percent of
transmitter output. The transmitter is calibrated to measure the temperature
in the range of 50°F (0% of the range) to 250°F (100% of the range). The set
point SP is assumed to be in the middle of the range, 150°F or 50%.
Figure 2-5. Process Variable in Engineering Units (ºF) and Percent of Range.
Illustration of Controller Proportional Band

T, °F
250

150

50

PV, %

OP, %

100

100

80

80

60

60

SP

Kc = 5.0 (20% PB)

40

40

20

20

0

0


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Tuning of Industrial Control Systems, Third Edition

Figure 2-5 also illustrates the concept of the controller proportional band (PB)
defined as the fraction of the transmitter output range that causes a 100%
change in the controller output OP. For the assumed gain of 5.0 the proportional band is 20%. In some older controllers the gain was specified as the proportional band, but that is no longer the practice.

Industrial Feedback Controllers
At the time when feedback controllers were individual off-the-shelf instruments about 75% of the controllers used in industry were proportional-integral (PI) or two-mode controllers and the balance were proportional-integralderivative (PID) or three-mode controllers. Today control calculations are performed by digital control computers and distributed control systems so that
all controllers contain all three modes, and to reduce them to two modes one
simply sets the derivative time TD to zero. As we will see in Chapter 5, there
are some control loops in which a single mode would be preferred, either proportional or integral, but in most systems it is not possible to specify a singlemode controller.
The feedback controllers are displayed for the operators in the control console
and provide the following features:
• Process variable display
• Set point display
• Controller output display
• Set point adjustment
• Manual output adjustment
• Auto/Manual switch
• Remote/local set point switch (cascade systems only)
With these the operator can observe the current value of all the variables associated with the control loop, adjust the set point, and if necessary switch the
controller to Manual and adjust the controller output. In cascade control systems the operator can switch the slave controller to “local set point” and
adjust its set point. The controllers are programmed so that the switching
from Manual to Auto and from local to remote set point is bump-less; that is,


The Feedback Controller

19

the controller output does not change, and, optionally, the set point is set to

the current value of the process variable when the switch is performed.
When the console is properly authorized under password protection, the
instrument person or engineer can access the following features:
• Proportional gain, integral time, and derivative time adjustments
• Direct/reverse action switch
Having introduced the feedback controller in this section, the next section
presents the concept of loop stability, that is, the effect of the controller on the
process response.

2-2. Stability of the Feedback Loop
One of the characteristics of feedback control loops is that they may become
unstable. The loop is said to be unstable when a small change in a disturbance
variable or the set point causes the system to deviate widely from its normal
operating point. The two possible causes of instability are that the controller
has the incorrect action (direct when it should be reverse or vice versa) or that
it is tuned too tightly—that is, the gain is too high, the integral time is too
short, the derivative time is too long, or a combination of these. Another possible cause is that the process is inherently unstable, but this is rare.
When the controller has the incorrect action, instability is manifested by the
controller output “running away” to either its upper or its lower limit. For
example, if the temperature controller on the process heater of Figure 1-1 were
set so that an increasing temperature increases its output, a small increase in
temperature would result in an opening of the steam valve, which in turn
would increase the temperature some more and the cycle would continue
until the controller output was at its maximum with the steam valve fully
open. On the other hand, a small decrease in temperature would result in a
closing of the steam valve, which would further reduce the temperature, and
the cycle would continue until the controller output was at its minimum point
with the steam valve fully closed. Thus, the stability of the temperature control loop of Figure 1-1 requires that the controller decrease its output when the
process variable increases. As we have seen, this is known as reverse action.

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Tuning of Industrial Control Systems, Third Edition

When the controller is tuned too tightly, instability is recognized by observing
that the signals in the loop oscillate, and that the amplitude of the oscillations
increases with time, as seen in Figure 2-6. The cause of this instability is that
the tightly tuned controller over-corrects for the error and, because of the
delays and lags around the loop, the over-corrections are not detected by the
controller until sometime later, causing a larger error in the opposite direction
and further overcorrection. If this process is allowed to continue the controller
output will end up oscillating between its upper and lower limits.

Figure 2-6. Response of an Unstable Feedback Control Loop

As pointed out earlier, the oscillatory type of instability is caused by the controller having too high a gain, too short an integral time, or too long a derivative time, or a combination of these. This leads into the simplest method for
characterizing the process for the purpose of tuning the controller, that of
determining the ultimate gain and period of oscillation of the loop.