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2017-09-01   Control Engineering

The venerable proportional-integral-derivative (PID) algorithm can solve a variety of feedback control problems, but not all.


By: Vance VanDoren, PhD, PE

Proportional-integral-derivative (PID) loops are by far the most common feedback control mechanism for industrial processes, as reflected in Control Engineering's editorial coverage. Its website includes almost 8,900 mentions of "PID" or "proportional-integral-derivative" compared to 7,600 mentions of all other control methods combined.

Why is that? First, PID loops are relatively easy to understand and implement. The effects of the proportional (P), integral (I), and derivative (D) components of the PID algorithm can be predicted intuitively, sometimes reducing the design process to "This should work, let's try it," followed by "That wasn't quite right, we need more (or less) proportional (or integral or derivative)," and eventually ending with, "Good enough."

When a process is already up and running, this kind of trial-and-error design can be much more convenient than the more academic alternatives that require taking the process offline for tests. And even when a more advanced control technique theoretically would provide improved performance, the extra effort and expense required may not be worth it.

Furthermore, industrial control engineers have spent more than 70 years examining, refining, and enhancing the PID technique and developing work-arounds for the shortcomings they've found (see "Fixing PID," Control Engineering, November 2012, May 2014, and December 2015).

As a result, PID has become the de facto standard-the one controls topic that non-specialists are likely to study if they're going to study feedback controls at all. Even specialists tend to prefer PID for simple applications because it can get the job done with less of the mathematical modeling and analysis associated with more advanced techniques.

The historical popularity of the PID algorithm has in turn motivated automation vendors to offer PID controllers as an off-the-shelf commodity. Other feedback control algorithms are available as commercial products, but none are so widely available as PID. 

Widely applicable too

PID's other big advantage is its ability to handle a wide range of control problems across the entire spectrum of process industries, provided: 

  • The controlled process is reasonably "well-behaved."
  • The controller's only mission is to force the process variable to match the setpoint "sooner or later."
  • The actuator responsible for executing the controller's corrective efforts has enough sway over the process to make the setpoint achievable.

In academic terms, "well-behaved" generally means the process is first or second order, minimum phase, linear, time-invariant, and either open-loop stable or integrating. In practical terms, that means the process consistently moves in the right direction if the controller continues to push it. And if the controller pushes harder, the process moves faster at a predictable rate (see Figure 1).

Fortunately for the process industries, many if not most processes requiring the control of temperature, pressure, level, and flow tend to be well-behaved. Still, there are a number of common feedback control problems where PID faces challenges, some of which can be overcome with suitable extensions to the basic algorithm, others, not so much. 

Harder problems for PID

Consider, for example, the process behavior depicted in Figure 2 where the process variable does not respond immediately to the controller's efforts. It's not just slow about moving in the direction the controller wants it to go, it doesn't move at all until long after the controller has started pushing.

If the delay, or deadtime, between the controller's efforts and the beginning of the process's response is not all that long, an unmodified PID controller can be used to regulate the process as long as the PID algorithm is configured to act slowly and patiently. But if the deadtime is particularly long or the application requires less waiting, a PID controller would have to be augmented with additional intelligence (see "Overcoming process deadtime with a Smith Predictor," Control Engineering, February 2015).

The process behavior depicted in Figure 3 is an even tougher case. Here, the process variable responds more dramatically to the controller's efforts when the process is running near 100% capacity. A much less aggressive control effort is required to take the process variable from 50% to 100% compared to the effort required to take it from 0% to 50%. In other applications, the reverse could be true.

A basic PID controller would have trouble regulating this process because its efforts would tend to be too aggressive when the process is running close to maximum capacity and too conservative at the other extreme. The classic solution to this problem—known as "gain scheduling"—doesn't require adding any additional intelligence to the PID algorithm, but it requires more than one controller, each active only when the process variable falls within a certain range.

Specifically, a conservative controller would be configured to take over as the process variable approaches 100%, and an aggressive controller would take over as the process variable approaches 0%. The process variable also could be divided into more than two ranges, each with its own PID controller configured to accommodate the process's behavior in each range (see "How gain scheduling works," Control Engineering, January 2011).

On the other hand, if a nonlinear process like this example happens to operate with its process variable constrained to just one narrow range, then a single, traditional PID controller should suffice. The other ranges where the process becomes either more sensitive to the controller's efforts or less wouldn't matter because the process would never go there. Fortunately, this is a fairly common situation in industrial applications where the object is to maintain the process variable at a fixed setpoint. 

Not suitable for PID

But as simple, popular, and versatile as PID loops may be, some feedback control problems call for alternative solutions. There are times when PID would be overkill. Consider, for example, an on/off heating element regulating the temperature within an oven. A PID loop would be necessary only if high precision were required. Otherwise, a thermostatic controller like the one in most homes should be able to maintain a more-or-less constant temperature by simply turning the heater on when the temperature drops too low or off when the temperature rises too high.

At the other extreme are control problems that require more intelligence than PID provides, such as constraint control where the controller must plan ahead to avoid driving either the control effort or the process variable outside of their acceptable ranges. Advanced planning also is required for multivariable control where the controller must coordinate the efforts of multiple actuators to control multiple process variables simultaneously (see "Exploring the basic concepts of multivariable control," Control Engineering, February 2017).

PID loops could be force-fit into either of these applications, but more advanced, custom-designed control techniques often are more cost-effective, at least initially. But all too often, the specialist who designs and implements them will move on to other projects, leaving non-specialists to maintain both the process and its controller. Thus, if something goes wrong later on there may not be sufficient in-house expertise to fix the problem. This situation often leads to the advanced controller being replaced by PID or disabled altogether in spite of the resulting performance degradation. And then there are control problems that would be difficult, if not impossible, to solve by any choice of control algorithm. Misplaced sensors, undersized actuators, broken connections, and so on must all be resolved before feedback control of any kind will work. 

Vance VanDoren, PhD, PE is a Control Engineering contributing content specialist. Reach him at controleng@msn.com. Edited by Jack Smith, content manager, CFE Media, Control Engineering, jsmith@cfemedia.com.

MORE ADVICE

Key Concepts 

  • The historical popularity of the PID algorithm has motivated automation vendors to offer PID controllers as an off-the-shelf commodity.
  • Fortunately for the process industries, many if not most processes requiring the control of temperature, pressure, level, and flow tend to be well-behaved.
  • There are times when PID would be overkill.

Consider this

Are the processes in your plant well-behaved, challenging, or difficult?

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