August 2017

Process Control and Instrumentation

The lost art of proportional band, and the accidental art of performance monitoring

Most control engineers know that proportional band and controller gain are largely interchangeable terms—both terms refer to the proportional setting of a proportional-integral-derivative (PID) controller and are commonly used by control system manufacturers.

Kern, A., APC Performance LLC

Most control engineers know that proportional band and controller gain are largely interchangeable terms—both terms refer to the proportional setting of a proportional-integral-derivative (PID) controller and are commonly used by control system manufacturers. Proportional band and controller gain are inversely related by Eq. 1, such that a gain of 1.0 is equivalent to a proportional band of 100%, and larger gain values equate to smaller proportional band values.

Gain = 100%/PB, where PB = Proportional band, %      (1)

However, most control engineers are less aware that industry has morphed in past decades from mainly using a proportional band perspective on loop tuning to predominantly using a gain perspective. The difference can be important, even crucial, to achieve reliable loop tuning and control performance.

Gain perspective is based on the premise that optimum controller gain depends on process gain, so that tuning becomes a matter of conducting a process step test and setting controller gain based on the observed process gain by applying rules of thumb, such as Ziegler-Nichols.

Conversely, proportional band perspective is based on considering the control loop in its larger process and operational context, and posing the question: How much controller error should drive the control valve to be fully open or fully closed? This is an important and often illuminating question to pose when tuning any control loop, and often provides a more reliable tuning answer, regardless of process gain.

It is especially important to consider the proportional band question on critical loops and loops where process gain changes dynamically (as most do). In an industry that continues to view most tuning with healthy skepticism, the proportional band perspective provides a practical way to quickly gauge appropriate and reliable tuning of any loop.

Why the change of heart?

In historical process control practice—before computers—the proportional band perspective was the method of choice, because process gain was not well-known and proportional-only controllers were the main tools of industry for many decades. Framing the tuning question in terms of output response to percentage of error was an obvious and sensible way to arrive at a reliable proportional band setting. Actual process gain was of only incidental interest, however hard that might be to imagine today.

Beginning in the 1980s, control system computers, computer-based loop tuning tools and model-based multivariable control drove a shift from the proportional band mindset to a gain-oriented mindset. These tools provided methods of collecting, analyzing and visualizing process data that had previously been impossible. With these tools, process gain, rather than proportional band, became the most prominent underlying concept.

By the same token, computers added very little to the proportional band approach to loop tuning, which, however crucial and seemingly intuitive, is essentially a process knowledge question that does not readily lend itself to computerized analysis. This approach has further fueled its fall into obscurity in an increasingly computerized and gain-oriented space.

Presently, competency with computer-based tools and a solid grasp of gains are considered synonymous with process control competency, best practices and achieving success in both single-loop and multivariable control practice. However, an important, often crucial and overriding concept—the proportional band perspective—has been lost in translation by industry.

From commonplace to critical

Two examples, one a commonplace level control and the other a critical reaction-rate control, illustrate how the proportional band perspective can be essential to ensuring reliable control loop performance, not only as an expedient for tuning of non-critical loops, but also as an essential check on critical control loop tuning.

Level control loops are ubiquitous in industry and are well-trodden ground in process control literature. Nonlinear tank geometry, such as a round horizontal drum, is often put forth in discussions as a common complicating factor. Performance objectives often include “optimally” smoothing out flow surges. Underlying most examples, however, are assumptions about the magnitude of flow inlet or outlet disturbances that are arbitrary and unjustified for most real processes, thereby undermining the practical value of the entire exercise.

FIG. 1. Level controls are the second most numerous in the process industries (after flow). This simple distillation column includes several level control loops.
FIG. 1. Level controls are the second most numerous in the process industries (after flow). This simple distillation column includes several level control loops.

Conversely, the proportional band approach solves the level control puzzle by posing the simple question: When should the control valve become fully open? One sensible answer is when the level reaches 100%, which, assuming starting conditions of 50%, translates to a proportional band of 100%, or a gain of 1. Another good answer is when the level reaches 75%, which translates to a gain of 2. It should be noted that integral action will provide additional control action. While these answers are inherently conservative, they provide a reliable picture of how the controller and valve will respond in the event of a worst-case situation. In site loop tuning surveys, a level controller gain outside the range of 1–2 is flagged for review, and the integral term should reflect average vessel residence time.

Level control serves as a useful example because it is familiar to many people, but it would be a mistake to construe from it that the proportional band approach has value only as an expedient for non-critical loops (FIG. 1). To the contrary, one of the oil refining industry’s most critical loops—an exothermic hydrocracking reactor temperature control, a loop that hydroprocessing and advanced control experts alike have said (to the author) cannot be tuned due to the non-linearly dynamically changing gain of an exothermic runaway reaction—has been simply and reliably solved by applying the proportional band method.

FIG. 2. Hydrocracking reactor bed outlet temperature control is one of the most critical and challenging control loops in the industry.
FIG. 2. Hydrocracking reactor bed outlet temperature control is one of the most critical and challenging control loops in the industry.

In this example, as with level control, the proportional band method is easy to apply. The question is: At what point should a hydrogen quench valve become fully open? The answer is: When a temperature excursion reaches 20°F (ca. 10°C) above normal operating temperature. At that point, the reaction rate has roughly doubled, consuming the entire reserve quench capacity (normally ca. 100%). If the valve is not 100% open by the point of a 20°F excursion, then the critical quench capacity is being underutilized to bring the excursion under control, and the risk of a reactor depressurization event occurring—the final safety-system response to an uncontrolled runaway reaction, usually triggering at approximately 30°F–40°F—is rapidly escalating.

In the hydrocracker example, while process gain is unknown, the proportional band method still provides a practical method to arrive at an appropriate and reliable controller gain value (FIG. 2). Taking the proportional-band approach when loop tuning often cuts through the confusion, complexities and unknowns to reveal reliable, logical answers.

Reliability (not accuracy) is the key to successful tuning

This discussion sheds light (and doubt) on a basic assumption that has underpinned process control ever since Ziegler-Nichols: the assumption that optimal controller tuning is based on process response models and that the primary performance criteria is error minimization. Loops and multivariable controllers tuned on this basis can be said to be “accurately” tuned.

This assumption has served industry as the starting point for process control design, tuning and performance measurement for decades, but accumulated experience shows that it may be more of the exception than the rule. The persistent prevalence in industry of “retuning” and “remodeling” (i.e., “high-maintenance”)and research suggest that 20 yr of aggressive application of model-based methods throughout industry has barely budged the historical performance levels of single-loop and multivariable control.1,2

The lesson that industry can take from this is that reliability, not accuracy, is the goal of process control. Reliability can be defined as control-loop performance that is consistent, stable and responsive, without performance degradation or maintenance needs over time. Most people still find this a reasonable expectation, even though the advanced control community sometimes seems more committed to the idea that performance degradation and periodic maintenance are to be expected.

The proportional band method and rate-predictive control (RPC) represent two “new,” or rediscovered, process control solutions to emerge out of the unexpected and persistent difficulties of model-based/error-minimization methods to provide durable and reliable low-maintenance results.3 What these new solutions share is a way to specify “operational” performance criteria, independent of process gain and error-minimization criteria, indicating that reliable operational performance is not always synonymous with model-based, error-minimization methods.

One way to break the endless high-maintenance cycle of single-loop tuning and retuning, or of multivariable control modeling and remodeling, is to apply new rules and techniques for reliable operational performance, such as the proportional band or RPC methods.

Accidental art of performance monitoring

As mentioned in the proportional band discussion, operational methods are based on process knowledge and do not necessarily lend themselves to ready mathematical analysis for either tuning or performance measurement. Fortunately, successful tuning and reliable performance are already well-served by existing and more fundamental metrics, such as loops in manual and the number of alarms.

Where loops are in manual or alarm rates are high, or where multivariable controllers suffer from degradation or low utilization, they can be reconsidered from an operational perspective, rather than from a retuning or remodeling for error-minimization methodology. As industry has now seen, models are short-lived, and model-based criteria often conflict with operational priorities. These are the roots of the problem, which repetition does not address.

More advanced metrics—such as integral of error or coefficient of variation—lack objective baselines and usually simply identify normal healthy loops that happen to be high in these aspects. Performance monitoring is, in many ways, an accidental part of modern process control practice. Indeed, modern process control tools, such as loop tuning software and model-based control, were expected to put performance issues in the past by solving performance perfectly by virtue of model-based tuning and error-minimization theory. When this failed to materialize in practice, performance monitoring was born to increase understanding. Unfortunately, performance monitoring has repeated the same mistake—beginning from an error minimization basis—and is sending industry further down this rabbit hole.

Presently, based on the concept of operational performance, industry is in a position to learn its lessons and put performance monitoring in the past in favor of more fundamental metrics and a fuller understanding of process control performance criteria. HP


  1. Smuts, J., “Process Control for Practitioners,” Opticontrols Inc., 2012.
  2. Jubien, G. and J. McIlwain, “Successful APC: Design and maintain for long-term benefits,” ISA Expo, 2009.
  3. Kern, A., “The history, and possible future, of model-less multivariable control,” Hydrocarbon Processing, October 2016.

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