From published literature, there is a wide range of pitfalls
into which control engineers frequently
stumble.^{1–3} As these pitfalls were documented,
more were discovered. In this article, we will focus on a very
specific area of control design. The following rules
investigate how substantial deterioration in process
performance is possible in proportional, integral and
differential (PID) control systems.
Rule 1. Use the ‘derivativeonerror’
algorithm.
The PID algorithm in its conventional analog form is usually
written as:
Despite this or, more often, its equivalent in Laplace form,
being used in most distributive control systems (DCSs)
vendors’ documentation it strictly applies only to analog
control. A close digital equivalent is:
The problem with this algorithm is that when the setpoint
(SP) is changed, assuming the process was previously
at steady state, the derivative action causes an immediate step
change in output, given as:
This is followed, at the next scan interval, by the same
change in the opposite direction. Known as the “derivative
spike,” it can readily move the manipulated variable
(MV) full scale. T_{d} might
typically have a value of around 1 minute, and ts will
be about 1 second. Even with quite a modest value for
K_{c}, ∆M can exceed 100%.
Fortunately, most DCS vendors have modified the algorithm
to:

Known as the “derivativeonPV”
algorithm, the derivative action no longer responds to changes
in SP. However, the response to changes in process
variable (PV), caused by process disturbances (or
“load” changes), is unaffected. Some DCS vendors have
retained the derivativeonerror version as an
option—unfortunately, often as the default version. A
poorly trained engineer might think that, since it bears the
closest resemblance to the conventional analog version, it
should be the one to apply. This seriously limits the use of
derivative action in those situations where it would be
particularly beneficial (See Rule 7).
Rule 2. Use the ‘proportionalonerror’
algorithm.
Using this algorithm is almost entirely to blame for hiding
opportunities to substantially improve the performance of
controllers responding to process disturbances. The alternative
“proportionalonPV” offered as an option in
most DCS is described as:
At first glance, this might appear to have a serious
disadvantage. When the SP is changed, the more
conventional proportionalonerror algorithm generates a
“proportional kick” equal to
K_{c}∆SP—doing much to ensure that
the SP is approached rapidly. The proportionalonPV
version does not do this, relying entirely on the much slower
integral action. Many engineers reject this algorithm solely
because of this perceived problem. However, they overlook the
fact that the controller can be retuned to compensate for the
loss of the proportional kick. As shown in Fig. 1, with
effective tuning, its response to SP changes would be
virtually indistinguishable, by the process operator, from that
of the algorithm it replaces.

Fig.
1. Response to a SP change. 
Its benefit becomes clear when the performance of the two
algorithms, both tuned for SP changes, is compared for
load changes. With the same tuning, provided the SP
remains constant, the two algorithms perform identically. The
much faster tuning necessary to make the
proportionalonPV algorithm perform well for
SP changes causes it to respond much faster to load
changes. Fig. 2 shows that both the duration of the disturbance
and the maximum deviation from SP are typically
halved. Were the PV to be related to product
composition, the volume of offspec production would be reduced
by more than 75%.

Fig.
2. Response to a load change. 
Of course, it would be possible to achieve the same
improvement by applying the tuning developed for the
proportionalonPV algorithm to the
proportionalonerror version. However, it would then cause a
major process upset whenever the SP is changed. This
perhaps explains why the algorithm is not fully appreciated.
Many engineers select the more conventional
proportionalonerror algorithm and tune it for SP
changes. Its response to load changes will then appear
reasonable but will disguise the fact that the response can be
substantially improved.
Rule 3. Use the interactive algorithm.
There is an alternative derivation of the PID controller. It
starts with a conventional PI controller, but adds the
derivative action by replacing the E term with a
“projected error” defined as:
This results in a slightly different algorithm:
Comparison with the socalled “ideal” form
described earlier shows that the integral and derivative
actions are unchanged but the proportional action depends not
only on K_{c} but also now on
T_{i} and T_{d} —thus
earning the algorithm its “interactive” name. Some
DCS use this version, either as the only choice or as an
option. It exists primarily because it closely matches the
action of pneumatic analog controllers and their early
electronic replacements.
Using it these days presents no problem provided the tuning
method chosen is specifically designed for the changed
algorithm. Indeed, provided that in the ideal algorithm
T_{d} is less than 0.25
T_{i}, it is possible to calculate equivalent
tuning for the interactive version so that the performance of
the two algorithms is identical. And if the derivative is not
used, then both algorithms are the same in any case.
The problem arises because DCS vendors rarely retain the
algorithm in its pure form. It is common to include a
“derivative filter” (usually given the nomenclature
as a or a) or a “derivative gain limit”
(which is the reciprocal of a). This value may be
fixed within the system or configurable by the engineer. It
usually makes impossible adapting a tuning method designed for
the ideal algorithm for use with the interactive form.
Rule 4. Apply ZieglerNichols tuning.
Amazingly, ZieglerNichols is still by far the most
popularly taught tuning method. It was developed 70 years
ago.^{4} Few appreciate that it assumes the now rare
interactive version of the PID algorithm. Even fewer know that
it was developed for load changes and so, if applied to the
normal proportionalonerror algorithm, will result in far too
an aggressive response to a change in SP. And, even if
these issues are resolved, its main objective is to deliver the
“quarter decay ratio,” where the height of the second
PV overshoot is one quarter of the height of the
first. Few now accept that any amount of second
overshoot is the sign of a welltuned controller. The more
cynical control engineer might think inclusion of the method in
papers and textbooks is to establish a benchmark by which even
a poorly performing alternative would look good.
Another commonly reproduced method is that developed by
CohenCoon.^{5} It too uses the quarter decay ratio and
was developed using analog control almost certainly equivalent
to the interactive algorithm. If anything, its performance is
somewhat inferior to ZieglerNichols.
Rule 5. Ignore the MV.
Effective controller tuning is often a compromise between a
fast return to SP and avoiding excessive changes to
the MV. Many tuning methods use a penalty function,
such as the integral over time of absolute error (ITAE), as a
measure of control performance:

Minimizing such functions results in the fastest possible
return to SP but, if the deadtimetolag ratio is
small, this will result in excessive adjustments to the
MV. As the deadtimetolag ratio approaches zero, such
methods recommend a controller gain approaching infinity. One
such method is that developed by Smith, Murrill and
others.^{6,7} Defining the MV overshoot as the
percentage by which the peak change in MV exceeds the
necessary steadystate change, we can supplement this type of
tuning criterion by minimizing the penalty function subject to
a limit on MV overshoot. Typically, a 15% limit
results in what most would accept as a welltuned controller.
However, the limit may be increased if large changes in
MV do no harm and similarly reduced if the aim is to
minimize MV movement. Indeed the latter, in the case
of surge vessel level control, is the overriding consideration,
and large deviations from level SP should be the
norm.
One of the few published methods that permits the engineer
to specify the compromise between fast return to SP
and MV movement is internal model control (IMC)
tuning. Several companies have adopted this method as standard.
However, it does have a number of disadvantages. The method is
derived using “direct synthesis,” which develops a
control algorithm that will respond to an SP change
according to a defined trajectory. This is usually specified as
an approach to SP with a userspecified lag of l. The
resulting tuning equations vary greatly. For example, it can be
applied to both selfregulating and integrating processes,
using either the ideal or interactive algorithm. The synthesis
usually includes terms that are not part of the PID algorithm
and, so, some approximation is necessary or the terms simply
ignored. Different developers reach different conclusions. But
a common example for the ideal PID algorithm applied to a
selfregulating process is:

While the method permits the user to decide how aggressive
the control should be, the value of l has to be determined by
the trialanderror method. While some texts provide some
guidance, there is no predictable relationship between its
value and MV overshoot. Under a different set of
process dynamics, the relationship changes. It is possible to
develop formulae for the best choice of l. For example,
choosing a value given by 0.31u + 0.88t will give an
MV overshoot of 15%, but only for the
proportionalonerror form of the ideal controller applied to a
selfregulating process. We would need to develop such formulae
not only for different controllers and for integrating
processes but also for different MV overshoot limits.
While perhaps possible, the most damning limitation of this
tuning method is that no one has yet published the formulae for
the preferred algorithm—where both proportional and
derivative actions are based on PV rather than
error.
Rule 6. Ignore the scan interval.
The industry has now begun replacing first generation DCSs
with their more modern counterparts. Engineers have been
surprised to find in some cases that this has apparently
increased the level of measurement noise. This can arise
because of the faster scanning that may be available in the new
system. Fig. 3 shows how the total valve travel generated by a
PID controller varies as scan interval changes. The curve
starts at a ts/t ratio of 1/120—equivalent to a controller
with a scan interval of 1 second on a process with a lag of 2
minutes. Defining the total valve travel under these conditions
as 100%, we can see that, for a PID controller, reducing the
scan interval from 2 seconds to 1 would increase valve travel
by a factor of 4.

Fig.
3. Effect of scan interval on noise
passed to an actuator. 
All DCS include the ability to filter a measurement and most
use the first order exponential type. The digital version of
this filter is often defined as:
Changing the scan interval of a controller in a system in which
the engineer defines P directly will result in a
different filter lag. Even the most modern of controller tuning
methods still assumes analog control. While this is of little
concern when the scan interval is small compared to the process
dynamics, it can cause problems otherwise. For example,
compressorsurge protection systems are applied to a process
where the deadtime is effectively close to zero and the lag
only a few seconds. Tuning such controllers without taking
account of scan interval will drastically affect performance.
It goes some way to explain why package vendors (usually
mistakenly) insist that compressor controls can only be
implemented in special purpose control systems that have a much
shorter scan interval.
Rule 7. Avoid using derivative action.
Depending on the textbook a control engineer might read, if
the process has a large deadtime, the derivative action is
either beneficial or becomes less effective. In fact, it offers
an advantage on processes with either little or a large
deadtime—depending on the disturbance source. Fig. 4 shows
the impact on ITAE of removing deadtime from a welltuned
controller, and retuning the PI controller as well as
possible. It shows that for SP changes, removing
derivative action causes controller performance to deteriorate
more on processes that have a larger deadtimetolag ratio. For
load changes, the opposite is true. But, for both cases, the
effect of removing it is always adverse, and, in any case, most
controllers have to deal with both disturbance types.

Fig.
4. Impact in ITAE of removing derivative
action. 
In practice, the derivative action is only used by a minority
of controllers. There are several reasons for this. First, it
has a reputation for causing problems if there is measurement
noise. Certainly, it will grossly amplify noise, but modern
DCSs do offer a wide range of filtering techniques that can
readily reduce noise to a point where derivative action is
viable. Second, it adds another tuning parameter. Adding
derivative action requires the proportional and integral tuning
to be readjusted. Fig. 5 shows that the addition of derivative
action is beneficial because it permits a larger controller
gain. If the engineer has already spent hours tuning a PI
controller by the trialanderror method, there will be an
understandable reluctance to abandon this tuning and start
afresh with a threedimensional search.

Fig.
5. Impact on Kp of inclusion of
derivative action. 
Rule 8. Use filters to improve PV trending.
Most control engineers use filters to make the PV
trend look good. Gone are the days when we have to concern
ourselves with the amount of ink used in drawing such trends. A
better criterion is to examine the movement
of the final actuator, usually a control valve. This will
depend not only on the amplitude of the measurement noise but
also on the controller tuning. If the impact on valve movement
is acceptable, then the filter serves no purpose and will
reduce the controllability of the process. Its presence means
that tuning has to be relaxed to maintain stability.
Conversely, we must remember that, if a filter is removed, then
the benefit will not be apparent until the controller is
retuned to accommodate the change in apparent process
dynamics.
Filtering can be beneficial if it permits greater use of
derivative action. Since derivative action responds to the rate
of change error, the small fluctuations in signal occurring at
a high frequency are greatly amplified. Many DCSs now offer the
facility to selectively filter only the measurement passed to
derivative action. This permits derivative to be used without
changing the dynamics seen by the proportional and integral
actions.
Rule 9. Tune by trialanderror methods.
Over 200 tuning methods have been published.^{8} All
of them have at least one flaw. It is not surprising that
control engineers have generally adopted the trialanderror
method as the main tuning method. It requires no knowledge of
the process dynamics and little understanding of the control
algorithm being applied. But its main disadvantage is that it
is extremely timeconsuming. Trials conducted on a simulated
process with dynamics of a few minutes showed that engineers
would spend around 30 minutes finding the best tuning. Quite a
modest investment one might think until one realizes that the
simulation was running much faster than real time and each test
was exactly reproducible. On the equivalent real process such
an exercise would easily have filled a working week. In
practice, no engineer can commit this time to a single
controller and will stop trying to improve its performance once
it is stable and looks “about right.” The result is
that the process operator will likely be unimpressed by its
performance during the next process upset and will switch the
controller to manual.
Developers of tuning methods have attempted to develop a set
of tuning formulae that can be applied to any situation. In
reality, such an approach is unlikely ever to be successful.
There are two fundamentally different processes:
selfregulating and integrating. There are two fundamentally
different PID algorithms: ideal and interactive. Some versions
of the algorithm include a derivative filter that cannot be
changed by the user. Proportional action can be based on error
or PV, as can derivative action. These options are not
mutually exclusive; just considering those listed so far gives
32 possible combinations. If we add to this the requirement to
specify the aggressiveness of the control, allow for different
scan intervals and to take account of vendorspecific
modifications to the algorithm, then the number of sets of
tuning formulae grows to an impractical level.
Figs. 6–8 show comparisons between the commonly
published tuning methods and userdefined optimum tuning. For
the comparisons to be fair, the controller was assumed to be
analog and subject to a SP change. The results were
obtained by using a tuning constant optimizer freely
available.^{9} In this case, the optimum tuning was
specified as minimum ITAE subject to a 15% MV
overshoot limit. So, unlike many methods, the optimized
controller gain does not approach infinity as u/t approaches
zero. The IMC method appears to estimate the controller gain
well, but only because the choice of l has been optimized for
this particular case. Note: The method developed by Smith,
Murrill and others is only applicable to values of u/t less
than 1. Outside of this range, it can generate negative tuning
constants. But, most importantly, optimization permits tuning
to be derived also for the preferred
proportionalonPV algorithm. The much higher gains
derived for this controller will substantially reduce the
impact of process disturbances.

Fig.
6. Determination of process gain. 

Fig.
7. Determination of integral time. 

Fig.
8. Determination of derivative time. 
Rule 10. Don’t train engineers in basic control.
The most effective way of reducing process profitability is
to ensure that the control engineers are kept completely
unaware of what can be achieved by minor changes to PID
control. Those that have studied control theory at university
will have been subjected to daunting mathematics, much of which
is irrelevant to the process industry. Almost certainly little
will have been covered on the alternative forms of the PID
algorithm, let alone which one to use and how to properly tune
it.
While it is common practice to send staff on vendor supplied
courses in DCS programming and multivariable predictive control
(MPC), it is rare to consider also training in basic control
techniques. Industry seems to expect engineers to somehow
acquire this expertise without outside assistance. This ensures
that the techniques described above, many of which have been
available for over 30 years, are still not properly appreciated
and that plants continue to operate away from maximum
profitability. HP
NOMENCLATURE
E Controller error
E_{n} Current error
E_{n1} Previous error
K_{c} Controller gain
K_{p} Process gain
M Controller output
MV Manipulated variable
PV Process variable
SP Setpoint
t Time
T_{d} Derivative action time
T_{i} Integral action time
ts Controller scan interval
X_{n} Current filter input
Y_{n} Current filter output
Y_{n1} Previous filter output
u Process deadtime
t Process lag
t_{f} Filter lag
LITERATURE
CITED
^{1} King, M. J., “How to lose money with
advanced controls,” Hydrocarbon Processing, June 1992,
pp. 47–50.
^{2} King, M. J., “How to lose money with basic
controls,” Hydrocarbon Processing, October
2003, pp. 51–54.
^{3} King, M. J., “How to lose money with
inferential properties,” Hydrocarbon Processing, October
2004, pp 47–52.
^{4} Ziegler, J. G. and N. B. Nichol,“ Optimum
settings for automatic controllers,” Transactions of the
ASME, 64, pp. 759–768, 1942.
^{5} Cohen, G. H. and G. A. Coon, “Theoretical
considerations of retarded control,” Transactions of the
ASME, 75, pp. 827–834, 1953.
^{6} Smith, C. L., Digital Computer Process
Control, Intext Educational Publishers, p. 147,
1972.
^{7} Lopez, A. M., J. A. Miller, C. L. Smith and P. W.
Murrill, “Tuning controllers with errorintegral
criteria,” Instrumentation Technology, 14, pp. 57–62,
1967.
^{8} O’Dwyer, A., “A summary of PI and PID
controller tuning rules for processes with time delay,”
IFAC Digital Control: Past, Present and Future of PID
Control, Terrassa, Spain, 2000.
^{9} http://www.whitehouseconsulting.com/tune.htm.
BIBLIOGRAPHY
King, M., Process Control: A Practical Approach,
published by Wiley, ISBN 9780470975879.
The author 


Myke King
is the author of Process Control: A Practical
Approach. He is the director of Whitehouse
Consulting. Previously, he was a founding member of KBC
Process Automation, and prior to that he was employed by
Exxon. He is responsible for consultancy services
assisting clients with improvements to basic controls and
with the development and execution of advanced control projects. He has 35 years of
experience in such projects, working with many of
the world’s leading oil and petrochemical companies. Mr.
King holds an MS degree in chemical engineering from
Cambridge University and is a Fellow of the Institute of
Chemical Engineers. 