Basic Regulatory Control

Sidebars: Introducing a new Control Engineering article series Nominal conditions operating costs

A generic flow-through reactor, common to most industries, can serve as a performance reference for advanced control technologies. Looking at how the reactor operates can illustrate which control methods are best.

Figure 1 is a diagram of a reactor and its nominal operating conditions. The product from this reactor is a heated mixture of two ingredients, A and B. To meet quality specifications, the product must reach at least 120 °F and be 75% A at all times (see ‘Controlled variables’ sidebar).

Temperature and flow transmitters directly measure the process streams. Their readings can be considered instantaneous compared to the response of the exchanger itself.

Controlled variables

Tag
Range
Nominal values

Product composition
AC1000
0 – 100% A
80% A

Product temperature
TC1000
0 – 300 °F
125 °F

Product flow rate
FC1000
0 – 200 gpm
100 gpm

Flow control loop for manipulated variables

Flow rate of ingredient A
FCA
0 – 150 gpm
80 gpm @ 50 °F

Flow rate of ingredient B
FCB
0 – 100 gpm
20 gpm @ 175 °F

Flow rate of steam
FCSTEAM
0 – 30,000 lb/hr
20,000 lb/hr

But measuring the percent of ingredient A in the product requires an analyzer. Analyzers are delicate and expensive instruments, typically remotely mounted in protective sheds. A slipstream from the product provides a sample to this analyzer. Its flow delay combines with the analyzer sampling interval and analysis time to add a significant delay in measuring product composition. (See ‘Flow control loop’ sidebar.)

Disturbance variables also affect control loop performance. These are variables that can’t be controlled or manipulated. Sometimes they can be measured, providing an opportunity for feedforward control. When this is not possible, their variation is only recognized by their affect on the controlled variables.

For this process, the disturbance variables are the temperatures of ingredients A and B. Changes in these temperatures will, after a delay, change product temperature unless they are immediately compensated by advanced control.

The economics of the reactor are also important. The values for the process streams are: product value=$1.25 per gallon; cost of ingredient A=$0.40 per gallon; cost of ingredient B=$0.10 per gallon; and cost of steam=$ 4.50 per 1,000 lb.

The economic return for this reactor is the difference between the value of the product and the costs for ingredients and steam. This difference depends on the production rate and the composition of the product. Both will be affected by the performance of the control technologies.

Characteristics, control

Because every process differs, how can this simple process represent the broad range of processes that exist in industrial plants? Though physically unique, the behavior of every process under automatic control depends on a set of generic characteristics that describe its response to input changes and its approach to steady state. Key characteristics are:

Dead time —the time between a change in the control signal and the beginning of the process variable response;

Lag time —the time constant of the process variable response, once it begins; and

Steady state gain —the ratio of the size of process variable change to the size of control signal change.

The reactor and its nominal operating conditions are used as the process example in this article.

Figure 2 shows the responses of the reactor’s controlled variables to changes in the manipulated flows. These responses reveal the process characteristics.

1. Both ingredient flows affect product composition, rate, and temperature. Steam flow only affects product temperature because it does not change either the ratio or the amount of the two ingredients.

2. Increasing ingredient B flow causes the temperature to drop, and then rise. This inverse response is an indication of different dynamics for two effects. The temperature drops first because of the increased rate and then rises as the hotter ingredient reaches the outlet.

3. Composition response to changes in either ingredient flow is virtually pure dead time. Total time is about two minutes; lag delay is negligible because the mixed ingredients travel through the reactor as essentially plug flow with little back mixing until their analysis. The ratio of dead time delay to lag time constant is large.

4. The composition is much more sensitive to changes in the flow of ingredient B than it is to the same change in ingredient A.

5. Because liquids are incompressible, flow changes at the outlet of the reactor precisely follow flow changes of the ingredient flows and reach steady state very quickly. The only lag in this almost immediate response comes from lags in the ingredient flow control loops. Both dead time delay and time constant lag are small.

6. Steam flow affects product temperature with a moderate dead time and a much longer first order lag, so the ratio of dead time delay to time constant lag is also small.

The relationship between these characteristic process parameters and the difficulty of control has been the focus of countless technical articles and textbooks, described by mathematics and practical experience. Key understandings include:

Dead time delay is the process characteristic that makes control difficult. During this delay, a controller sees no response to its control action. A feedback controller has to be detuned so that it will not overreact during this delay and thereby overcorrect for an error condition. But too much detuning can cause sluggish control.

Controlling processes dominated by capacity lags is much easier. A large lag makes a process variable change more slowly and filters noise from the measurement signal. However, many small lags can combine and look like dead time.

Process gains dictate how tightly the controller can be tuned. High gain processes require low gain controllers, and vice versa. Variable gains in the process or valve characteristics can be a problem for any controller, since loop stability is variable. Controllers have to be tuned for stability when the process gain is highest. Then, at other times, the controller can be too sluggish. Adaptive tuning can address this problem.

Measuring performance

Process characteristics are revealed in the responses of the reactor’s controlled variables to changes in the manipulated flows.

Many different indexes have been proposed to quantify the performance of a process controller. Most are some mathematical function of the size and duration of any error between the setpoint and measurement of a controller.

Although there are reasons to consider other indices, this series will use the integral of the error squared (ISE) as a performance index. Squaring the error prevents positive and negative errors from canceling each other as a measurement swings around its setpoint. Squaring the error punishes large errors more than smaller ones. In any case, using the same index for each technology will provide a valid relative basis for comparing control performance.

Effect of changes in production rate and product composition setpoint on basic regulatory controls’ response is illustrated.

Calculating this index will show the response of the strategies to various upsets. While the process is at steady state, the index is reset to 0. Applying an upset causes errors. Integrating the squared error continues until the control technology returns the reactor to steady state at setpoint. The final value of the integrated squared error for each controlled variable is the measure of how well the control technology performed.

Regulatory control

The simplest and most common approach to control, by far, is basic regulatory control (see Figure 1). The performance of a properly assigned and well-tuned basic regulatory control strategy provides a benchmark for comparing the performance of more advanced control technologies.

This basic regulatory control strategy includes three cascade control loops. A controller for each product variable drives its manipulated variable through the setpoint of a flow controller. These primary controllers were tuned by a self-tuning algorithm to avoid weak performance from poor manual tuning.

Because both ingredient flows affect all the controlled variables—composition, flow, and temperature, this multi-variable process is also interactive. However, this creates problems for assigning the control loops and controlling the process.

One question dominates the application of basic regulatory controls to a multi-variable interacting process. How should the control loops be assigned? A simple set of concepts guides the assignment of these loops.

1. Since steam flow only affects temperature, the product temperature controller must be assigned to manipulate steam flow. If either of the other two controllers manipulated steam flow, the temperature controller would not have a variable to manipulate that affected its measurement.

2. Since the product is 80% A, the bulk of the product comes from this ingredient stream. The product flow controller should manipulate the flow of ingredient A to have the strongest impact on total flow.

3. Similarly, ingredient B provides only 20% of the final stream. The product composition controller should manipulate the flow of ingredient B to have the most precise effect on final composition.

But no matter how the control loops are assigned, the effects of interaction will still create problems for these controllers. Because of the interaction in the process, the individual controllers upset each other:

When AC1000 manipulates the flow of ingredient B to control composition, it upsets total flow and product temperature; or

When FC1000 manipulates the flow of ingredient A to control production rate, it upsets composition and product temperature.

Each controller seeks to return its own measurement to its setpoint. As they do, the controllers trade reciprocal upsets back and forth until the oscillations all die out. Each controller has to be somewhat de-tuned to allow for the effects of interaction. Proper single loop assignment can only minimize this problem.

Before quantifying the performance of these basic regulatory controls, it is important to differentiate between the roles of the three primary controlled variables.

1. Product quality variables . These determine the value of a process stream in terms of its properties. For the reactor, they are the product temperature and composition. Typically, setpoints for these variables change only to produce multiple products or one product with varying quality specifications. These controllers correct for upsets that drive product quality away from setpoint.

2. Process throughput variables . These determine the value of a process stream in terms of its volume. For the reactor, it is the product flow rate. Typically, setpoints for these variables often change in response to varying product demand and operating conditions elsewhere in the plant. These controllers deliver production rate changes.

3. Material inventory variables . These are associated with equipment that provides buffers between various operations and units in a plant. Typical examples are levels in storage vessels and pressures in tanks and headers. These setpoints are usually chosen to protect process equipment, rarely change, and have little economic impact on normal operations.

Very often, production rate changes create load upsets for product quality controllers. For example, changing the setpoint for reactor product flow upsets product composition and temperature.

The response of basic regulatory controls to a change in production rate and to a change in product composition setpoint is shown in Figure 3. The performance index values (averaged for positive and negative changes) for this control approach are shown in Table 1.

Economics and quality

Figure 3 shows that product temperature drops to 123 °F on a rate increase and the composition drops to 77% A on rate decrease. This is the reason for the nominal setpoints—to maintain quality specifications during transients. But this cushion is expensive. Nominal conditions require the flows of steam and the more expensive ingredient to be continuously higher than necessary. To operate precisely at specifications requires 5 gpm less of ingredient A and 5 gpm more of ingredient B, and a steam flow of 15,497 lb/hr. (See ‘Nominal conditions’ sidebar.)

While basic regulatory control provides adequate control performance, its economic performance is poor. The real question is, what is the benefit from better control, and will the benefit justify the expense?

The next article will cover advanced feedforward and decoupling control.

References

1. Shinskey, F.G., ‘Process Control Systems,’ McGraw-Hill Publishing, New York, 1988

Table 1. Performance index values

Change production rate

Change product composition

Control Technology
Comp. ISE
Temp. ISE
Total ISE
Comp. ISE
Temp. ISE
Total ISE

Basic regulatory Control
.53
.28
.81
1.79
0.55
2.34

Author Information

Lew Gordon is a principal application engineer at Invensys;

Introducing a new Control Engineering article series

This issue of Control Engineering begins a series of articles that presents the principles and compares the performance of several different control technologies against the same problem—control of a flow-through reactor. Basic and advanced regulatory control, rule based control, and model predictive control will all be applied. They will not all perform equally well. These performance differences will demonstrate how process characteristics ultimately dictate the most cost-effective solution for a control problem.

Techniques for economic optimization and proving control system performance round out the content of the series, which will conclude with a control technology selection guide and guidelines for achieving technical and economic success in a control project.

Nominal conditions operating costs

To compute the extra materials cost of operating at nominal conditions:

5 ($0.40 – $0.10) x 60 min/hr x 24 hr/day x 350 days/yr = $756,000/yr

The extra energy cost is:

$4.50 (20,000 lb – 15,497 lb) x 24 hr/day x 350 days/yr = $170,213/yr

The total cost of using only basic control is an ongoing loss of $926,213 per year at the nominal production rate.

And, to brush up on barcode versus RFID, take a look at an article from Control Engineering ’s sister publication, EDN, “Reading between the lines: RFIDs confront the venerable bar code.”

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