Prior to digital controls, proportional band was almost universal. However, there were a few exceptions, such as Taylor, which used sensitivity (another word for gain) as the tuning coefficient for the proportional mode.
With the introduction of digital controls, suppliers of process control systems generally continued to use the same sets as used in their conventional (pneumatic or electronic analog) product line. A few, for example, Honeywell TDC, chose to change the proportional-mode tuning coefficient from the proportional band PB to the controller gain KC. A smattering of others, such as ABB Bailey, made the jump to individual gains for each mode.
The manufacturers of programmable logic controllers (PLCs) generally did not have a conventional product line to emulate. To those without a process background, formulations using the individual gains (KP, KI, KD) are usually the easiest to understand and implement. For example, the Modicon Quantum PLC uses KP, KI and KD as its tuning coefficients. Often, the major obstacle to those in the process world simply is understanding what is written in the PLC manuals -- automotive engineers seem to have a strange way of looking at PID.
However, the major difference between distributed control system (DCS) and PLC implementations is not the basic PID control equation, but, instead, what comes along with it. Most DCS implementations provide numerous options (such as proportional based on E versus proportional based on PV) and features for tracking or initialization (such as output tracking, integral tracking, external reset, etc.). Most PLCs expect the user to meet such requirements by providing the appropriate ladder logic in conjunction with their PID.
Why KC over PB? That's a hard question to answer. First, understand that the choice has no effect whatsoever on the internals of the controller. Conventional controllers illustrate this best. The controller sensitivity is set via a knob connected to a variable resistance within the controller. A calibration is currently provided in terms of proportional band, with tick marks for 20%, 50%, 100%, etc. What must be done to convert to gain? Just re-label the tick marks. That is, change 20% to 5%/%, 50% to 2%/%, 100% to 1%/%, etc. The internals of the controller don't change at all. The choice of KC vs. PB reduces to an issue of knob calibration. The same can be said for digital systems.
A minor technical issue
Derivative: Set TD or KD to zero.
Reset: Set RI or KI to zero. But what about TI? Lengthening (increasing) TI decreases the influence of the reset mode. But how do you get this influence to be zero? Not nearly zero, but exactly zero. You must have a gimmick. There are two possibilities:
1. Understand that TI = 0 means no reset action at all. This is somewhat of a discontinuity. Shortening (reducing) TI actually increases the influence of the reset mode. A value of zero for TI would make this influence infinitely large, which makes no sense. Therefore, the gimmick of using TI = 0 to mean no reset action at all is a viable option.
2. Specify an arbitrarily large value of TI to be the upper limit on the reset time. Any value greater than this value means no reset at all.
The former is more commonly encountered. For example, Honeywell does this within its TDC product line.
Proportional: Set KP to zero. However, KC, which is the overall controller sensitivity, cannot be set to zero unless this is given some special interpretation within the controller (analogous to understanding that TI= 0 means no reset action at all, not infinite reset). The alternative is to provide a special control equation for integral-only control, as Honeywell does for its TDC product line.
The above are the only technical issues that pertain to the choice of one set of tuning coefficients over another. In practice, these are very minor points. We largely use PI, but occasionally opt for PID. Rarely do we utilize controllers with no reset and, even more rarely, integral-only controllers.
So, treat with some skepticism claims that using a certain set makes the controller easier to tune. Most arguments for one set over another are subjective. People often prefer the set of tuning coefficients with which they are most familiar. Such preferences are perfectly acceptable but, remember, different people will have different preferences. Regardless, from a technical perspective, the following statement can be made:
If you can successfully tune a controller using one set of the coefficients in Table 1, the controller can be tuned to give the same performance with any of the other sets in Table 1.
The reason is very simple: the underlying control equation is the same.
PID control equation forms
In conventional (pneumatic or electronic analog) controllers, the PID control equation is computed in a "series" manner . This approach is also an option in digital controllers. The best way to express the control equation is via the following two-step computation sequence (we will use set 1 of the tuning coefficients in Table 1):
1. Apply derivative to the control error E to obtain a projected control error . The equation is: