PID Control in the Industry
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PID Control in Practice. For an investigation of the PID’s operation in real life, let’s consider a
wastewater treatment system that is a very slow chemical process where, as is widely known, the
cleaning of an average wastewater quantity lasts several hours and generally responds slowly to the
action of the controller. If there is a sudden error (e.g., change of set point), the PID controller’s
reaction will be determined mainly by the differentiation term in Equation 9.1. This will cause
the controller to start an explosive corrective action when the error will change value from zero.
The proportional term will then affect the control signal in order to maintain the output of the
controller until the error reaches zero.
Meanwhile, the integration term will also begin to contribute to the output of the controller
as the error accumulates over time. After a period of time, the integration term will prevail on the
output signal, because the error will slowly diminish in the sewage treatment process. Even after
clearing the error, the controller will continue to produce one output based on past errors that have
accumulated in the controller’s integrator. Then, the process variable will surpass the desired value,
creating an error with an opposite sign from the previous one. If the integration gain (I) does not
have a large value, the next error will be smaller than the initial one, and the integration term will
begin to diminish as negative errors will be added to the previously positive term. This operation
can be repeated a few times until the current error and the accumulated error are eliminated.
Meanwhile, the differentiation term will continue to add its portion in the output of the control-
ler, based on the derivative of the varying error signal. The proportional term will also contribute
positively or negatively to the output signal of the controller, depending on the error.
In the case that a fast process responds quickly to the action of a PID controller, the integration
term will not have a significant contribution to the output of the controller because the errors will
have a very short duration. On the other hand, the differentiation term will tend to get large values
because of rapid changes in the error and absence of long delays.
It is clear, from the above detailed description of the behavior of a PID controller that the effect
of each term in Equation 9.1 on the value of the output of the controller depends on the behavior-
response of the controlled process. For the sewage treatment process, a large value of the differen-
tiation gain D could be desired in order to accelerate the action of the controller. An equally large
value of the D gain for a quick process could cause an unwanted fluctuation of the output of the
controller, as any change in the error will be amplified by the action of the differentiation term. In
conclusion, the optimal choice of the three gains P, I, and D for a specific application is the essence
of PID controller tuning.
PID Controller Tuning Techniques. There are three principal
techniques to configure the
parameters of a PID controller that are going to be mentioned briefly without expanding from a
theoretical analysis. Therefore, the reader should refer to the corresponding theory of automatic
control systems for a detailed description of the first two of them, since the third technique is
based on engineering experience.
The first technique is based on a mathematical model of the process that associates the value
of the process variable PV (t) with the rate of its variation and a number of previous values of the
output of the controller, for example the equation,
PV t
K CO t d
T d
dt
PV t
( )
(
)
( )
= ⋅
− −
(9.3)
Equation 9.3 refers to a process with a gain K, a time constant T, and a dead time d. The gain
K of the process represents the size of the controller’s action on the process variable. A large value
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Introduction to Industrial Automation
of K means that the process converts the small controller actions in major changes of the process
variable, while the time constant T represents the time delay of the process. For the sewage treat-
ment process, the time constant T will have a large value. The dead time d refers to another kind
of delay that is found in all processes when the sensor used for measuring the controlled variable
is located at a distance from the actuator that implements the action of the controller. The time
required for the actuator’s action to affect the process is the dead time. During this time interval,
the process variable does not react to the action of the actuator. Only after the dead time, the pro-
cess variable starts to react substantially and then it begins the measurement of the time delay T.
The second technique, known as the Ziegler-Nichols method (which first appeared in 1942)
is the most popular because of its simplicity and applicability in any process that can be modeled
in the form of Equation 9.3. The technique consists of three tuning rules for the PID controller,
which convert the parameters of Equation 9.3 into values for the gains P, I, and D of the controller
and are expressed by the equations,
P
T
Kd
I
T
Kd
D
T
K
=
=
1 2
0 6
0 6
2
.
,
.
,
.
,
(9.4)
The Ziegler-Nichols method also proposed a practical method for the experimental estimation
of the values of the parameters K, T, and d of a process.
The third technique is empirical and based on the iterative procedure “trial and error” by try-
ing out a set of three values for the constants of the PID controller and observing the behavior of
the error. Depending on the behavior of the corresponding error, the gains of the PID controller
can be further tuned by their direct increase or reduction. Experienced control engineers know
very well according to the controlled process and after some test steps, how much is required to
increase or reduce any constant of the PID controller in order to improve its behavior.
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