2. Compute the proportional-integral equation with each term based on the projected control error . The equation is:

Combining these two equations gives a PID equation with all terms based on the control error E:

 

To some, the term (T_D / T_I) E in this form of the PID equation is a cause for concern. The extent to which it truly leads to problems is debatable. But let's not get into this. It has no relevance to the choice for the tuning coefficients.

However, the following observation is relevant. The use of K_P, K_I and K_D as the set of tuning coefficients makes no sense for this form of the PID control equation. The way the computations are performed is just not consistent with individual gains for each mode. This is why conventional controllers do not provide individual gains for each mode. Furthermore, the hardware implementation of the control equation dictated that KC is the overall controller sensitivity, that is, it is applied to all terms.

With digital controls, an alternative approach to implementing the PID control equation is as follows:

1. Apply derivative to the control error E to obtain a projected control error . The equation is:

 

2. Compute the proportional-integral equation with the proportional term based on the projected control error and the integral term based on the current control error E. The equation would be written as follows:

 

 Combining these two equations gives a PID equation with all terms based on the control error E:

In this form of the control equation, individual gains for each mode certainly make sense. The equation would be written as follows:

 

It is appropriate to call this form "parallel," because the individual modes can be computed in parallel and then summed to give the controller output.

In the above equations, modes were expressed in terms of the control error E. Most digital implementations can base the derivative mode on either the control error E or the measured variable PV. Many can do the same for the proportional mode. However,the choice will have no impact on the units used for the tuning coefficients, so no further discussion is relevant.

Future directions

The current situation possibly will continue into the future. Are there any realistic alternatives?

What about developing a standard to specify the set of tuning coefficients to use? This would lead to a first-class catfight, which may have some entertainment value but otherwise is unlikely to produce results. Furthermore, this is just not the way the computer industry works. There, standards do not drive the technology, they follow it. The marketplace is allowed to determine the winner among competing technologies. When a clear winner emerges, then a standard can follow.

Indeed, the computer industry is very adept at effectively thwarting standards efforts. Just look at fieldbus. Standards committees within the ISA have put a lot of effort into fieldbus. However, look what we now have. There is a document we call a standard [2]. But is it really a single standard -- or five standards written into one? We could have a standard for tuning coefficients, but with all options in Table 1 written into it. The only benefactor would be the ISA, which at least could make money selling copies of it.

Realistically, there is only one glimmer of hope. Computers are supposed to be user-friendly. Why do we let a computer tell us what set of tuning coefficients we have to use? In this context, user-friendly means that we tell the controls what set of tuning coefficients we want to use, along with the units for time (minutes or seconds). Perhaps this was too much to expect of the early digital-control products. However, given the power of today's microprocessors, even single-loop controllers could provide this capability.

Cecil L. Smith, PhD, PE, is a consultant based in Baton Rouge, La., who focuses exclusively on industrial automation of both batch and continuous processes. He also teaches continuing education courses on various aspects of process control.