CHAPTER 8 An Introduction to Process Control EVA SORENSEN 8.1 INTRODUCTION All chemical plants need process control to ensure that they are operated safely and profitably, while at the same time satisfying product quality and environmental requirements. Furthermore, modern plants are be- coming more difficult to operate due to the trend towards complex and highly integrated processes. For such plants, it is difficult to prevent disturbances from propagating from one unit to other, interconnected, units. The subject of process control has therefore become increasingly important in recent years and it is vital for anyone working on a chemical plant to have an understanding of both the basic theory and practice of process control. This chapter will give a brief summary of basic control theory as applied in most chemical processing plants. It will start with a discussion of process dynamics and why an understanding of the dynamics, or the transient behaviour, of a process is essential in order to achieve satisfac- tory control. Standard feedback controllers will then be discussed and different strategies for tuning such controllers will be presented. A brief overview of more advanced control strategies, such as feed-forward control, cascade control, inferential control and adaptive control, and for which processes these may be suitable, will be given next. Finally, an introduction will be given to plant-wide control issues. In most process control courses for chemical engineers, the first part of the course normally deals with the development of dynamic process models from first principles (mass and energy balances), since these are used in the analysis of process dynamics and often also for controller tuning. In this chapter, however, the focus will be on process control and modelling will not be considered. Neither will the chapter consider 249
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CHAPTER 8
An Introduction to Process ControlEVA SORENSEN
8.1 INTRODUCTION
All chemical plants need process control to ensure that they are operated
safely and profitably, while at the same time satisfying product quality
and environmental requirements. Furthermore, modern plants are be-
coming more difficult to operate due to the trend towards complex and
highly integrated processes. For such plants, it is difficult to prevent
disturbances from propagating from one unit to other, interconnected,
units. The subject of process control has therefore become increasingly
important in recent years and it is vital for anyone working on a
chemical plant to have an understanding of both the basic theory and
practice of process control.
This chapter will give a brief summary of basic control theory as
applied in most chemical processing plants. It will start with a discussion
of process dynamics and why an understanding of the dynamics, or the
transient behaviour, of a process is essential in order to achieve satisfac-
tory control. Standard feedback controllers will then be discussed and
different strategies for tuning such controllers will be presented. A brief
overview of more advanced control strategies, such as feed-forward
control, cascade control, inferential control and adaptive control, and
for which processes these may be suitable, will be given next. Finally, an
introduction will be given to plant-wide control issues.
In most process control courses for chemical engineers, the first part of
the course normally deals with the development of dynamic process
models from first principles (mass and energy balances), since these are
used in the analysis of process dynamics and often also for controller
tuning. In this chapter, however, the focus will be on process control and
modelling will not be considered. Neither will the chapter consider
249
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frequency response techniques for process analysis and controller tun-
ing, as these are considered beyond the scope of this book. The emphasis
will therefore be on control concepts and the reader is referred to
standard control textbooks for more information.1–4 In addition, al-
though instrumentation is essential for control, it is a complete subject
area in itself and is therefore not considered here.
8.2 PROCESS DYNAMICS
The primary objective of process control is to maintain a process at the
desired operating conditions, safely and efficiently, while satisfying
environmental and product quality requirements. The subject of process
control is concerned with how to achieve these goals. Luyben3 gives the
following process control laws:
First law: The simplest control system that will do the job is the best.
Bigger is definitely not better in process control.
Second law: You must understand the process before you can control it.
Ignorance about the process fundamentals cannot be overcome by sophis-
ticated controllers.
The process control system should ensure that the process is maintained
at its specified operating conditions at all times. To be able to do this, we
must first understand the process dynamics as advised by Luyben in his
Second Law.3 The dynamics of a process tells us how the process behaves
as a result of the changes. Without an understanding of the dynamics, it
is not possible to design an appropriate control system for it.
In the following text, important aspects in the study of process
dynamics are outlined. An example of a dynamic process is given first.
Stability of a process is defined next, followed by a discussion of typical
uncontrolled, or open loop, responses.
8.2.1 Process Dynamics Example
As an example of a dynamic process, consider the process in Figure 1,
which is a tank into which an incompressible (constant density) liquid is
pumped at a variable feed rate Fi (m3 s�1). This inlet flow rate can vary
with time because of changes in operations upstream of the tank. The
height in the tank is h (m) and the outlet flow rate is F (m3 s�1). Liquid
leaves the tank at the base via a long horizontal pipe and discharges into
another tank. Both tanks are open to the atmosphere. Fi, h and F can all
vary with time and are therefore functions of time t.
250 Chapter 8
Let us now consider the dynamics of this tank, starting with the steady
state conditions. By steady state we mean the conditions when nothing
changes with time. The value of a variable at steady state is normally
denoted by a subscript s. (Note that some control textbooks use a
different notation, for instance, by placing a bar over the variables.) At
steady state, the flow out of the tank, Fs, must equal the flow into the
tank, Fi,s, and the height of the liquid in the tank is constant, hs. At
steady state we therefore have the steady-state equation:
Fi;s ¼ Fs
The value of hs is that height which provides enough hydraulic pressure
head at the inlet of the pipe to overcome the frictional losses of liquid
flowing out and down the pipe. The higher the flow rate Fi,s, the higher
the height hs.
Now consider what would happen dynamically if the inlet flow rate Fi
changed. How will the height h and the outlet flow rate F vary with time?
Figure 2 is a sketch of the problem.
The problem is to determine which curves (1 or 2) represent the actual
paths that F and h will follow after a step change in Fi. The curves
marked ‘‘1’’ show gradual increases in h and F to their new steady-state
values. However, the paths could follow the curves marked ‘‘2’’, where
the liquid height rises above its final steady-state value. This is called
overshoot. Clearly, if the peak of the overshoot in h is above the top of
the tank, the tank would overflow. The steady-state calculations give no
information about what the dynamic response of the system will be.
Before a controller can be designed to control the tank height, the
designer must determine which of the curves (1 or 2) the tank height h
and the flow rate F are most likely to follow, i.e. what are the dynamics of
the process?
h
Fi
F
Figure 1 Gravity-flow tank
251An Introduction to Process Control
8.2.2 Stability
A process is said to be unstable if its output becomes larger and larger
(either positively or negatively) as time increases, as illustrated in Figure
3. Note that no real system really does this, as some constraint is usually
encountered, for example, the level in a tank may overflow, a valve on a
flow stream may completely shut or completely open or a safety valve
may blow.
Most processes are open loop stable, also called self-regulating, i.e.
stable without any controllers on the system. This means that after a
change in the system caused by either a disturbance or by a deliberate
change in a manipulated variable, the process will come to a new stable
operating condition, i.e. a new steady state. This is not necessarily the
1
2
1
2
h
F
Fi
time t
Figure 2 Dynamic responses of gravity-flow tank
Time t
Outp
ut
Unstable
Stable
Figure 3 Stability of a process
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desired operating condition, and in most cases it is not, but nevertheless,
the new operating condition is stable. If, however, the process does not
settle out to a new steady state, it is called non-self-regulating and will
require control in order to ensure that the system remains safe and
stable. In the tank example, as F is free to vary with the liquid level in the
tank, the process is self-regulating since if Fi increases, the level will rise
causing F to increase, thereby bringing the system to a new steady state
where F rises to the new value of Fi. If, however, there is a pump on the
outlet line, i.e. F remains constant whatever the conditions within the
tank, the system will be non-self-regulating as the tank would overflow if
Fi increased and F remained constant.
What makes controller design challenging is that all real processes
can be made closed loop unstable when a controller is implemented to
steer the process to specified operating conditions. In other words, a
process which is open loop stable and therefore will come to a new,
although not the desired, steady state after a disturbance may become
unstable when a controller is implemented to steer the process towards
the desired steady state. Stability is therefore of vital concern in all
control systems.
8.2.3 Typical Open Loop Responses
The term process response is used to describe the shape of the plot one
would obtain if one plotted the controlled variable as a function of time
after a disturbance or set point change. In the tank example, the
response would typically be given by tank height h as a function of
time and would be referred to as ‘‘the response in h’’. Almost all
chemical processes fall within a few standard response shapes, which
makes analysing them easier. These standard responses are illustrated in
Figure 4. The order of a process refers to the order of the differential
equations describing the system, and refers loosely to the number
of parts of the process in which material and energy can be contained.
Simple processes can often be assumed to be of first order, while
more complex processes are of second order or higher. In Figure 4, y
refers to the variable that is observed. For instance, in the tank example,
y is h.
Dead time is the length of time, td, after a disturbance occurs before
any change in the output is noticed and is illustrated for a first order
process in Figure 4(c). It occurs particularly when material or energy is
being transported some distance. Clearly it means that disturbance
detection is slow and control actions are made on the basis of old
measurements. Dead time is the most troublesome characteristic of a
253An Introduction to Process Control
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system to control and can cause otherwise stable systems to become
unstable when the control loop is closed.
The process gain, Kp, of the system is the value that the response will
go to at steady state after a unit step change in the input, i.e. it relates the
input to the output at steady state.
The time constant, tp, of a process is, for a first-order system, defined
as the time it takes for the response to reach 63.2% of the final response
value (see Figure 4(c)). Theoretically, the process never reaches the new
steady-state value, given by the process gain Kp, except at t - N,
although it reaches 99.3% of the final steady-state value when t ¼ 5tp.
The difference between dead time and time constant must be empha-
sised; dead time is the time it takes before anything at all happens, while
time constant is a measure of how slowly or quickly a response settles to
its new steady-state value once the change has started. A slow process
that has a large time constant does not necessarily have any dead time.
Time constants in chemical engineering processes can range from less
than a second to a couple of hours, or even days for biochemical
applications.
τp
t
y
(a)
y
t
∆y
(c)
t
y
t
y
(b)
(d)
td
63.2%
Kp
Figure 4 Typical open-loop unit step responses. (a) First order, (b) Second (or higher)order, (c) first order with dead time and (d) non-self-regulating process
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8.3 FEEDBACK CONTROL SYSTEMS
Most plant control systems are very simple and are normally standard
feedback controllers, either P-, PI- or PID controllers. These will be
described in more detail in this section, together with two techniques
that can be used to tune these controllers. First, however, we need to
define the control objective, i.e. what do we want the controller to do,
and define what we mean by feedback control.
8.3.1 Disturbance Rejection and Set Point Tracking
The operation of a process may deviate from its desired operating
conditions for two different reasons:
Disturbances. These are changes in flow rates, compositions, tempera-
tures, levels or pressures in the process which we can not control because
they are either given by the feed conditions (assumed controlled by an
upstream unit), ambient conditions, such as the weather, or utilities,
such as steam or cooling water.
Set point changes. These are deliberate changes in the operating condi-
tions, such as a change in polymer grade for a polymerisation reactor,
change in distillate composition for a distillation column, etc.
The control objective is different in the two cases. In disturbance rejec-
tion, the control objective is to reject the disturbance as quickly as
possibly, i.e. to bring the process back to the original steady state by
counteracting the effect of the disturbance (see Figure 5(a)). As an
example, consider a person in a shower who wants to maintain the water
temperature at a constant value. To achieve this, the person may have to
turn the cold water tap up to increase the flow rate of the cold water if
there is a sudden increase in temperature as a result of someone else in
the house using cold water, i.e. to fill a kettle in the kitchen. (This is an
example of a disturbance caused by a shared utility, here the cold water.)
t
Outp
ut
Outp
ut
t=0
(a)
t t=0
(b)
Old set point
New set point
Figure 5 Process responses: (a) disturbance rejection and (b) set point tracking
255An Introduction to Process Control
In set point tracking, the set point for the controller is changed and the
control objective is to bring the process to the new set point as quickly as
possible (see Figure 5(b)). For a person in the shower who wants to
reduce the temperature at the end of the shower time, this means turning
the hot water tap down to reduce the flow rate of hot water, thereby
bringing the temperature down to the new desired level.
8.3.2 Feedback Control Loop
A feedback control loop is generally illustrated as shown in Figure 6.
The Process refers to the chemical or physical process (the tank in the
example earlier). The Measuring Device is used to measure the value of
the variable that is to be controlled (the level indicator in the tank
example or a thermometer in a shower). The Control Element (usually a
flow control valve or the setting on a heater or cooler) changes the value
of the manipulated variable. The manipulated variable is the variable
used to change the controlled variable (in the tank example, the output
flow rate is the manipulated variable used to change the level in the tank,
which is the controlled variable).
The input to the Feedback Controller (P-, PI-, PID- or PD-controller,
discussed later) is the difference (also called error) between the set point
and the measured variable; hence the minus sign in the control loop. The
controller has its name from the fact that the comparison between the
controlled variable and the set point is fed back to the controller. The
Feedback Controller determines the change required in the manipulated
variable to bring the error back to zero, i.e. the controlled variable to its
set point value, and sends a signal to the control element that executes
this change. The effect of this change on the process, together with the
effect of any disturbances, is then measured and compared to the set
point and the loop started again.
Feedback control systems can be either analogue, where the controller
is a mechanical device, or digital, where the controller is a computer or
disturbance manipulated
variable
controlled
variable
setpoint Control
element
measured variable
Feedback
ControllerProcess
Measuring
device
Figure 6 Feedback control loop
256 Chapter 8
microprocessor. A digital control system will have additional elements
in the control loop to convert the various signals from analogue to
digital or vice versa.1–11
How often the control loop is executed is determined by the sampling
interval, which is how often the measurement is taken. A critical pressure
on an exothermic reactor may be sampled several times per second,
while the level of a buffer tank may only be sampled a few times an hour.
The sampling time must be chosen with care to ensure that possible
changes in the process are detected early enough for the controller to
take appropriate action. However, sampling too often is undesirable as
it may upset the process and because a large number of data points
would have to be sampled and stored.
8.3.3 P, PI and PID Controllers
The most commonly used controller in the process industries is the
three term or PID controller. This controller is a feedback controller
and adjusts the manipulated variable in proportion to the change in
its output signal, c, from its steady state value (bias), cs, on the basis
of a measurement of the error in the controlled variable, e, which is
given by
eðtÞ ¼ yspðtÞ � yðtÞ ð1Þ
where e is the error signal, ySP(t) is the set point and y(t) is the meas-
ured value of the controlled variable, e.g. the height of the liquid in the
tank example. The change required in the control signal c is obtained
from the error (calculated numerically in a digital controller or obtained
by a mechanism inside an analogue controller) by the following rela-
tionship:
c ¼ cs þ Kc eþ1
tI
Z
t
0
e dtþ tD
de
dt
0
@
1
A ð2Þ
where P is the Proportional, I is the Integral (Reset) and D is the
Derivative (Preact).
The relationship involves three terms and three adjustable parameters,
the controller gain, Kc, the integral time, tI, and the derivative time, tD(hence the name). Finding the right values of these parameters for the
best possible control action is called tuning. There are several techniques
available for controller tuning as will be discussed later.
257An Introduction to Process Control
8.3.3.1 Proportional Action. Control action is proportional to the size
of the error, and Equation 2 becomes:
c� cs ¼ Kc e
That is, the change required in the manipulated variable is proportional
to the error in the controlled variable. Some control literature refer to
the proportional band which is defined as 100/Kc. Some offset is associ-
ated with this control action, as will be shown later.
8.3.3.2 Integral Action. Control action is proportional to the sum, or
integral, of all previous errors. This controller eliminates offset. Some
control textbooks refer to the reset rate, which is defined as 1/tI.
8.3.3.3 Derivative Action. Control action is proportional to the rate
of change of the error and so anticipates what the error will be in the
immediate future.
8.3.3.4 Composite Control Action. Composite control actions are also
possible, i.e. P, PI or PD, as well as PID. The most common is PI as P
alone will have an offset and the derivative action in PID or PD can
introduce unnecessary instability in the response.
8.3.4 Closed Loop Responses
When a controller is implemented on a process, the response after either
a disturbance or a set point change is called the closed loop response as
the control loop in Figure 6 is now closed (recall that open loop means
without controller). Figure 7 shows typical closed loop responses of a
first-order process to a unit step change in the input. Figure 7(a) and (b)
show how Proportional control introduces some offset from the final
desired steady state for both set point tracking and disturbance rejection
after a change at t ¼ 0. The size of the offset depends on the gain of the
process Kp and on the proportional gain of the controller Kc and is, for a
first-order process, given by:
Offset ¼1
1þ KpKc
The offset decreases as Kc becomes larger and should theoretically go
towards zero for infinitely large controller gains. However, using very
large controller gains should generally be avoided as it may lead to
unstable control if any deadtime, however small, is present in the system.
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Figure 7(c) shows that Integral action removes offset but at the
expense of introducing some oscillation. The level of oscillation depends
on the control parameters. Systems with significant amounts of dead-
time will always result in some oscillation in the closed loop response.
Figure 7(d) shows how incorrect controller tuning may lead to an
unstable response whereby the changes made in the manipulated vari-
able by the controller are too large, causing the measured variable to
fluctuate more and more (for the example with a person in the shower, if
the person makes a large change in cold water flow rate to compensate
for the loss of cold water when the kettle is being filled in the kitchen, the
water temperature may become too low. The person may then compen-
sate with a large decrease in cold water flow rate causing the water to
become too hot, etc.).
8.3.5 Controller Tuning
How do we choose the values of the controller parameters Kc, tI and tD?
They must be chosen to ensure that the response of the controlled
variable remains stable and returns to its steady-state value (disturbance
rejection), or moves to a new desired value (set point tracking), quickly.
However, the action of the controller tends to introduce oscillations.
t
Outp
ut
t=0
(b)
Old set point
New set point
Offset
t
Outp
ut
Outp
ut
Outp
ut
t=0
(a)
Offset
t t=0
(c)
t t=0
(d)
Figure 7 Closed loop responses of first-order process. (a) P only (set point tracking), (b)P only (disturbance rejection), (c) stable PI or PID (disturbance rejection) and(d) unstable PI or PID (disturbance rejection).
259An Introduction to Process Control
How quickly the controller responds and with how little oscillation,
depends on the application. The following are some of the available
tuning methods, of which we will consider the last two in detail (see
textbooks1–11 for numerous other methods):
(i) trial and error (not recommended);
(ii) theoretical methods (frequency response methods, see text