In Honeywell TDC systems, you specify the tuning coefficients for a PID controller as controller gain, reset time and derivative time. In Foxboro IA systems, you tune by adjusting proportional band, reset rate and derivative time. In ABB Bailey systems, you use proportional gain, reset gain and derivative gain. And these are only some of the variations. Manufacturers do not even rely on the same coefficients in all product lines -- for instance, Honeywell UDC uses proportional band, reset rate and derivative time. Usually vendors opt for the same coefficients in successive models, but changes still occasionally occur.
There is always more than one way to skin a cat. This especially true for digital technology; flexibility is its greatest asset but, at times, becomes a liability. The different PID tuning coefficients used by the various manufacturers are only one manifestation of this.We had some of this prior to the era of digital controls; now we have even more.
Such variations are a mere nuisance to those skilled in the art but, to others, they can be confusing. From the perspective of practical applications, these alternatives contribute nothing. If you can get a loop to work using one of the implementations, you can get the loop to work using any of the others.
Operating companies have the option of purchasing their controls from one supplier, and thus possibly can avoid this confusion. Some have done so, but not all. Firms providing engineering services do not have this option.
In theory, standardizing on a "preferred supplier" means that everyone in the company would always be working with the same set of tuning coefficients. Unfortunately, this practice comes into conflict with other practices. For example, one way to shorten design and construction cycles is to purchase packaged equipment for water treatment, air compressors, boilers, etc. The manufacturer of the packaged unit supplies everything, including the controls. The purchaser can demand that certain controls be provided, but usually doesn't. The reason is simple, as one bluntly noted a few years ago: "You will be amazed at our flexiblity when we see the price."
The manufacturer of the packaged equipment has experience with certain models and can supply these at a reasonable cost. Providing any other controls significantly increases the price and possibly delays delivery. Therefore, the purchaser accepts one of the models with which the manufacturer of the packaged equipment is already familiar. Will these controls use the same tuning coefficients as the purchaser's preferred supplier? Given the variability within the industry, probably not. Consequently, personnel at the operating company are almost certain to encounter different sets of tuning coefficients.
Five common combinations
PB = proportional band, % of the PV span;
KC= controller gain, %/%; and
KP = proportional gain, %/%
Reset or integral mode:
TI= reset time, minutes;
RI= reset rate, repeats/minute; and
KI= reset gain, (%/%)/minute
KD= derivative time, (%/%)-minutes
The potential number of permutations is 18. But, in practice, only the five combinations shown in Table 1 are encountered.
The fifth combination is only available in digital controls. For reasons that we will examine subsequently, that combination is not practical for conventional (pneumatic or electronic) controllers.
The simple equations in Table 2 detail the relationships among the various coefficients. It is important to note that the proportional mode coeffcients KC and KP have the same numerical values but quite different influence within the control equation:
KC affects the overall sensitivity of the controller. From this perspective, it seems that the most appropriate term for KC would be "controller gain."
KP affects the sensitivity of only the proportional term. From this perspective, it seems that the most appropriate term for KP would be "proportional gain."
But, in practice, one has to be very careful with the terminology, as KC is commonly referred to as the proportional gain.
Two other permutations deserve mention:
1. With any set of the coefficients in Table 1, the units for time may be seconds instead of minutes. Fortunately, the implementations apply the same units for time to all modes. That is, if the reset time is in seconds (or reset rate is repeats/second), the derivative time will be in seconds.
2. Occasionally, the proportional band is expressed in the engineering units of the PV. Consider a temperature controller for which the measured input is via a thermocouple or RTD connected directly to the controller (that is, no external transmitter imposes a span on the measured input). What is the input span? Potentially it is the measurement range of the thermocouple or RTD. However, for most applications, this would be unreasonably large. The problem can be avoided by tuning using a proportional band in engineering units -- that is, the proportional band would be specified in either Degrees C or Degrees F.
One set of tuning coefficients offers no real advantage over another, although some people may think otherwise. If there were a distinct advantage for one set, then everybody would be doing it that way!
Making a choice
A manufacturer generally adopts in its latest model the same set of tuning coefficients used in its previous model. But why were these tuning coefficients originally chosen? Given the "right-sizing" of the past few years, the staffers who made that decision have long since left the company.