PID spotlight, part 3: How to select one of four process responses

 

PID controlled process identification insights

• The method and rules used to tune a PID controller depend on the process type; self-limiting, integrating or exponential.
• A process is self-limiting if it has a negative internal feedback. Automatic control may be optional.
• A process is integrating if it has no internal feedback. Automatic control is mandatory.
• A process has an exponential response if it has a positive feedback. Automatic control is mandatory.

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An infinite variety of process responses exist, so it would seem impossible to use an algorithm with just three tuning parameters to control all possible process responses. Unfortunately, this is true. However, a proportional-integral-derivative (PID) controller can handle the vast majority of the processes in most applications.

How a PID controller is tuned depends on the type of process response; each type of process requires different tuning rules and procedures. Correctly identifying and classifying process responses is required to take the most effective approach to tuning the PID controller.

Definitions: Four process responses; number and types of internal feedbacks

Process responses fall into four general categories:

1. Self-limiting

2. Integrating

3. Exponential

4. Complex.

Each type of response is categorized based on the number and types of internal feedbacks it has. The first three have, respectively, a negative internal feedback, no internal feedback, and a positive internal feedback. All three of these can usually be controlled with a PID controller. The complex category includes any process that has multiple internal feedbacks. It may or may not be possible to control a complex process with a PID controller.

Following is a discussion of each of the first three process response types, including any relevant subcategories. It’s necessary to identify each process response because the procedure used to tune a PID controller differs for each type.

Self-limiting process response

A self-limiting process response (Figure 1) is one which, like the name says, eventually lines out at a new steady-state after the controller output is changed. This behavior is found in any process that has an internal negative feedback. Examples would include flow (pressure drop increases with flow) and most temperatures (heat loss increases with rising temperature). There are many more self-limiting processes. Within the world of self-limiting responses there are three subcategories:

• Lag dominant

• “Moderate”

• Deadtime dominant.

Lag dominant process response

First some definitions before discussing dominant process response:

• Deadtime (D_t): Time before the process starts to respond to a change in the controller output.

• Lag (T₁): The time for the process to get to 63.2% of the final (steady state) response.

When characterizing process responses, most will have multiple lags, however, for simplicity, generally all the lags are lumped together into one lag; the process is treated as first order plus deadtime (FOPDT).

The Figure 2 process response is a lag dominant response, which is defined as a response where the lag time is more than four times the deadtime:

T₁ > 4 * D_t

These definitions are according to Greg McMillan, Tuning and Control Loop Performance, 4^th Edition.

Deadtime dominant process response

This is a deadtime dominant response (Figure 3), defined as a response where the lag is less than ¼^th the deadtime:

T₁ < D_t / 4

‘Moderate’ self-limiting process response

A “moderate” self-limiting process is by definition neither lag dominant or deadtime dominant; that is:

D_t / 4 < T₁ < 4 * D_t

It’s helpful to take a quick peek ahead, to understand that:

• Moderate self-limiting processes can benefit from the use of derivative action in the PID controller. Controller gain will be roughly the inverse of the process gain.

• Lag-dominant processes can allow for a large controller gain, often several multiples of the inverse of the process gain. Derivative action is not recommended as it is usually detrimental to controller response.

• Deadtime dominant processes require the controller gain to be less than the inverse of the process gain. Derivative action is not recommended as it is always detrimental to controller response.

Integrating process response

An integrating response is characteristic of mass or energy balance processes. If what’s going out doesn’t match what’s going in the vessel level will fill, or empty, until it overflows or runs dry. Physically there is no internal negative feedback that will provide stability. This means that an integrating process cannot be left uncontrolled. Automatic control of a self-limiting process can be considered “optional.” Automatic control of an integrating process is mandatory.

Figure 5 shows an integrator response (level) to changes in the output flow. When the output flow is increased the level falls continuously until the output flow is lowered. The level then rises continuously until the output flow is raised to its initial value (to match the input flow). The process shown does not have deadtime or any process lags, however these may be present and must be accounted for during controller tuning.

Finally, lag dominant self-regulating processes that are sufficiently slow may be treated as a “near integrator.” Use the tuning process for an integrator to tune near integrators, which allows a greatly reduced time spent tuning (because there’s no need to wait for a slow process to come to steady state).

Exponential process response

Processes that exhibit exponential response have a positive internal feedback process. The process we normally associate a positive internal feedback with is an exothermic reaction. As temperature climbs heat generation increases, which leads to higher temperatures, which leads to more heat generation, and so on. Failure to positively control these processes will result in an unpleasant outcome, putting people and/or property at risk. Automatic control of an exponential process is mandatory.

Figure 6 shows the inherent danger of positive feedback. The cooling to the (imaginary) exothermic reaction is reduced 1% from the 3-to5-minute mark, after which it is restored to its original value. Initially the rate of climb is very small and may be missed by an operator. But eventually the positive feedback causes the reaction to run away exponentially.

Complex process response

I’m not going to show a process response for a complex process because the shape of the response could be almost anything. It may be possible to control a complex process with a PID controller (and tune the controller) if its response roughly acts like any of the other types of processes.

Complex process responses occur when the overall process has internal mass or energy recycles. Distillation towers, feed/product heat exchange networks and reactant recycle streams will create complex process responses in temperature, pressure, level and composition controls.

If a complex process cannot be controlled by an ordinary PID controller it often can be controlled through the use of advanced PID features and/or the addition of feedforward or decouplers to manage interaction between parts of the process.

Summary: To tune PID, pick the process, identify the type

The methodology used to tune a PID controller depends on the type of process the PID is controlling. Before you can pick the tuning methodology, you must be able to identify the type of process. Processes are categorized into four types.

Self-limiting processes are by far the most common. These processes, when disturbed, will settle at a new steady-state value because they have internal negative feedback, which provides stability. Flows and most temperatures are examples of self-limiting processes. Automatic control of these processes may be optional.

Integrating processes are the second most common. These processes will, when disturbed, trend in a new direction until they meet a constraint. There is no internal feedback to moderate the response. Levels are the most common example. Automatic control of these processes is mandatory.

Exponential processes are unusual. These processes, when disturbed, will due to positive internal feedback proceed with increasing velocity (exponentially) toward a constraint. Exothermic reactors are the most common example. Automatic control of these processes is mandatory.

Complex processes occur in processes that have internal recycles, either mass or energy. If these processes act sufficiently like any of the above, they can be controlled using a PID controller (and can be tuned as if they are one of the above types). If not, then control may require more sophisticated techniques.

Ed Bullerdiek is a retired control engineer with 37 years of process control experience in petroleum refining and oil production. Edited by Mark T. Hoske, content manager, Control Engineering, CFE Media and Technology, mhoske@cfemedia.com.

KEYWORDS: Proportional-integral-derivative, PID tutorial

CONSIDER THIS

First things first with PID: What’s the process and process type?

REFERENCE

Gregory K. McMillan, Tuning and Control Loop Performance, Fourth Edition, Momentum Press LLC, 2015.

ONLINE

Aug. 1 RCEP webcast: How to automate series: The mechanics of loop tuning

More on PID and advanced process control from Control Engineering.

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