300 process control

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Chevron Corporation 300-1 June 1989

300 Process Control

Abstract

This section is an introductory reference to process control. It discusses control

theory, control modes and problems and includes guidelines for typical process

control situations. This section also discusses controller tuning and control mode

selection.

Contents Page

310 Introduction 300-2

320 Control Loops 300-2

321 Open Loop Control

322 Closed Loop Control

330 Control Modes 300-5

331 Proportional Control

332 Integral Control

333 Proportional-Plus-Integral Control

334 Derivative Control

340 Advanced Control 300-14

341 Cascade Control

342 Feed-forward Control

350 Controller Tuning 300-18

351 Quarter Decay Method

352 Ultimate Sensitivity Method

353 Process Reaction Curve Method

360 References 300-23


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300 Process Control Instrumentation and Control Manual

June 1989 300-2 Chevron Corporation

310 Introduction

Process control is fundamental to most industrial processes. Although control tech-

nology has evolved greatly in arriving at todays microprocessor and digital imple-

mentations, all control methods rely on the same basic structure, called a control

loop. Control loops have six basic constituents, as follows:

Controlled variable. The condition that is being controlled

Setpoint. The value at which a controlled variable must be maintained

Manipulated variable.A condition (variable) that can be changed to cause the

controlled variable to change

Controller. A device that keeps the controlled variable at the setpoint

Final control element. The device adjusted by the controller(s) to change the

manipulated variable

Disturbances. Process conditions that tend to change the value of the

controlled variable

320 Control Loops

Control loops can be either manual orautomatic. A manual control loop requires a

human being to observe the value of the controlled variable. If this variable is not at

the setpoint, the human observer adjusts a manipulated variable(see

Figure 300-1).

An automatic control loop employs a controller to keep the controlled variable at

the setpoint. In Figure 300-2, the controller receives a signal from a transmitter (the

circled X) representing the condition of the controlled variable, and sends an outputsignal to a valve regulating the manipulated variable.

In a refinery furnace, a controller monitors the outlet temperature (controlled vari-

able). If the outlet temperature is not at the desired value (setpoint), the controller

Fig. 300-1 Manual Control Fig. 300-2 Automatic Control


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Instrumentation and Control Manual 300 Process Control


changes the fuel flow (manipulated variable) by changing the position of the fuel

valve (final control element). Automatic control may be open loop (feed forward)

or closed loop (feedback).

321 Open Loop Control

In open loop control, the controller adjusts the final control element without

measuring the process. An example of open loop control is a cycle timer that oper-

ates a drain valve, as in the simple gas-liquid separation process shown in

Figure 300-3. At predetermined intervals, the timer causes the drain valve to open

even if there is nothing to drain.

A more common example of open loop control would be an automatic lawn sprin-

kler system. Here a clock timer opens a water valve for several minutes each day. It

would not check to see if the lawn needed water and would even turn on the sprin-klers in the rain. Open loop control like these examples is not widely used. Open

loop control operating in a feed forward mode is frequently used along with closed

loop control. Feed forward control is discussed in Section 342.

322 Closed Loop Control

Closed loop control, also known as feedback control, is the most widely used type

of automatic control. If feedback control were used in Figure 300-3, the controller

would open the drain valve only when the liquid level rose above the controller

setpoint and would continue to adjust the valve as needed to keep the liquid drained

from the vessel.The gas separation process in Figure 300-4has a feedback (closed loop) level

control system in which the controller LC receives a signal from the level trans-

mitter LT. The controller compares this measurement with the setpoint and adjusts

the outlet valve as necessary. The difference between the controller measurement

and controller setpoint is the error signal. When the error is not zero, the level

controller opens or closes the outlet valve to return the level to the setpoint.

Fig. 300-3 Open Loop Control


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On/Off Control

On/off control is the simplest mode of automatic control. It has only two outputs

on(100%) or off(0%)and only responds to the sign of the errorpositive or

negative; i.e., whether it is above or below the setpoint.

Because of an effect known as constant cycling, on/off control is not generally suit-

able for continuous automatic feedback control. If the control valve in Figure 300-4

were to remain completely open when the level is above setpoint, and completely

closed when the level drops below setpoint, a constant cycling of valve position and

level would result (see Figure 300-5). As with open loop control, the varying level

resulting from constant cycling may be acceptable in some noncritical level applica-

tions.

Differential Gap Control

Differential gap control is a refinement of on/off control. Instead of changing

output from on(100%) to off(0%) at a single setpoint, differential gap action

changes output at high and low limits called boundaries. As long as the measure-

ment remains between the boundaries, the controller holds the last output. This

Fig. 300-4 Closed Loop Control

Fig. 300-5 On/Off Control


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extends the period and limits the amplitude of the controlled variable oscillations

(see Figure 300-6). On many controllers the size and position of the differential gap

is adjustable, permitting fine-tuning.

Differential gap control is suitable for some continuous automatic feedback control

loops. It slows the rapid cycling of on/off control, reducing wear on the final

control element while maintaining much of the simplicity of on/off control. A

typical application of differential gap control is the operation of a dump valve or

pump to keep a vessel level within an acceptable range.

330 Control Modes

Controllers can be adjusted to function correctly in many different applications.Each controller usually has three adjustment modes:

Proportional. Controller output changes by an amount related to the size of

the error

Integral. Controller output changes by an amount related to the size and dura-

tion of the error

Derivative. Controller output changes by an amount related to the rate of

measurement change

With pneumatic controllers and early electronic controllers, each mode added to a

controller made it more expensive. Most electronic controllers available today are

equipped with all three modes at no additional cost. The unneeded modes can be

turned off.

Most control applications use proportional-plus-integral control. Proportional-plus-

integral-plus-derivative is sometimes used for temperature control with delays

(deadtime) of several minutes. Proportional-only control is sometimes used in

noncritical services such as draining vessels.

Fig. 300-6 Differential Gap Control


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Note that the proportional and integral actions depend on the error (defined as

setpoint measurement), but the derivative action only depends on the measurement.

Controllers are constructed this way so there will be no large change in controller

output when the operator enters a new setpoint for the controller.

331 Proportional Control

(Controller output can go directly to a valve or to the setpoint of another controller.

In the following discussions, it is assumed that controllers send their output directly

to a valve.)

Figure 300-7shows the relationship between valve position and error that is charac-

teristic of proportional control: The valve position changes in exact proportion to

the amount of error, not to its rate or duration. The response is almost instanta-

neous, and the valve returns to its initial value when the error returns to zero.

Control Algorithm

The linear relationship between the setpoint deviation (error) and the valve position

(controller output) for proportional action can be expressed as follows:

O = KcE

(Eq. 300-1)

where:

O = Controller output

Kc = Controller Gain = Output / ErrorE = Error = (Setpoint - Measurement)

This equation is called the control algorithm. The gain, Kc, is also called the

controller sensitivity. It represents the proportionality constant between the control

valve position and controller error.

Fig. 300-7 Proportional Control Response


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Proportional Band

Another way of characterizing a proportional controller is to describe its propor-

tional band. The proportional band is the percent change in value of the controlled

variable necessary to cause full travel of the final control element. The proportional

band, PB, is related to its gain as follows:

Kc= 100/PB

(Eq. 300-2)

Both proportional band and gain are expressions of proportionality. Manufacturers

may call their adjustments gain, sensitivity, or proportional band. Figure 300-8

shows the relationship between valve opening and proportional bands of different

percentages. High percentage proportional bands (wide bands) have a less sensitive

response than low percentage proportional bands (narrow bands).

Bias

Bias is the amount of output from a proportional controller when the error is zero.

Equation 300-1implies that when the error is zero, controller output is zero. The

valve is either fully open or fully closed and provides no throttling action. Adding a

bias provides this throttling action. Equation 300-1then becomes:

O = KcE + B

(Eq. 300-3)

where:

B = Bias (percent of full output)

Typically, manufacturers set the bias at 50%. To prevent a process bump, the oper-

ator is sometimes allowed to adjust the bias before putting the controller in auto-

matic. Figure 300-9shows controller output versus error at different proportional

bands with a 50% bias. At zero error, the controller output is 50% of full range for

any proportional band.

Fig. 300-8 Effect of Proportional Band


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Offset

A controllers error is the difference between its setpoint and measurement. In a

proportional-only controller, a change in setpoint or load introduces a permanent

error called offset(see Figure 300-10). It is impossible for a proportional-only

controller to return the measurement exactly to its setpoint, because proportional

output only changes in response to a change in the error, not to the errors duration.

Assume that a proportional-only controller controls the outlet temperature of a

furnace and that the temperature is at the setpoint. If the feed rate to the furnace

increases, more fuel will be needed. This disturbance represents a load change to

the furnace. To get more fuel, the fuel valve must be opened more. As is suggested

by Equation 300-3, the only way that the valve can be at some value other than its

starting point is for an error to exist. Thus, the proportional controller alone cannotreturn the outlet temperature to its setpoint. As mentioned, some controllers allow

the operator to adjust the bias until the value of E (the error, or offset) is zero.

Offset is determined by the proportional band value for the controller and the

change in valve position that occurs when a disturbance takes place:

E = PB (O) / 100(Eq. 300-4)

where:

E = Change in error

PB = Proportional band

O = Change in valve position

The proportional-only controller is the easiest continuous controller to tune. It

provides rapid response and is relatively stable. If offset can be tolerated (loose

control), proportional-only control can be used.

Fig. 300-9 Effects of Proportional Band with 50% Bias Fig. 300-10 Proportional Control Response to aLoad Change


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332 Integral Control

Integral (reset) action is the result of an integration of controller error with time.

With integral action, controller output is proportional to both the size and duration

of the error. As long as a deviation from setpoint exists, the controller continues to

drive its output in the direction that reduces the deviation. The rate of change of

controller output is proportional to the magnitude of the error. Figure 300-11illus-

trates the open loop response of integral action.

Integral action is normally used in conjunction with proportional action; it is rarely

used by itself. Integral action is quantified as the time (the reset time) required to

change controller output by an amount equal to the change caused by proportional

action. In other words, it is the time required to repeat the contribution of the

proportional action.

On some controllers, integral settings are in repeats, meaning repeats per minute;on others, settings are in minutes, meaning minutes per repeat. One setting is the

reciprocal of the other; decreasing the integral time increases the amount of integral

action.

Fig. 300-11 Integral Controller Response (Open Loop)


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Figure 300-13depicts proportional-plus-integral control for a closed loop. In

response to a step change in load (top graph), the controlled variable (middle graph)

falls below the setpoint. The integral action adjusts the bias from 50% initially to

about 75% after the load change and shifts the position of proportional band

(shaded area) on the scale. Notice that the percentage value of the proportional

band is not changed. The lower graph shows the output of the controller.

Wind-up

A basic problem with integral controllers is that integral action continues as long as

an error exists. Assume a proportional-plus-integral controller is used to maintain

the level in the gas-liquid separator vessel in Figure 300-4. If a valve is closed

upstream of the vessel, the level drops below the setpoint. The controller then

closes the control valve in the outlet line to maintain the level setpoint. With no

inlet flow, the control valve closes completely and the vessel level is still less than

the setpoint.

A pneumatic control valve will typically be fully closed at a controller output of 15

psig. Since the measured vessel level is less than the setpoint, the integral action of

the controller continues to increase the controller output to the air supply pressure

(typically 20-30 psig). The action of the integral controller trying to exceed the

normal range of the controller output is called wind-up.

If the upstream valve is opened and flow is restored, the vessel level will rise abovethe setpoint. The response of the controller to this high level will be delayed by the

wind-up. When the controller does respond, the output goes to the opposite limit. In

this case, the control valve will fully open and the vessel level will drop sharply.

The controller may oscillate through several cycles, stroking the control valve from

stop to stop on each cycle, before the oscillations cease and control is restored.

Fig. 300-13 Proportional-Plus-Integral Control Response (Closed Loop)


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Such oscillations overwork the control valve and, depending on the fluid and pres-

sures involved, can cause mechanical damage and seriously disrupt the process

downstream on the valve. An anti-wind-up feature may be included on controllers

that are frequently subject to this type of disturbance. This limits the controller

output range and thus prevents wind-up. When the process returns to normal, the

controller lag is eliminated and the oscillations are no worse than those in a propor-tional controller.

Integral Time

Integral time should be proportional to the time it takes for the process to respond

to control action. When the process responds quickly, the integral time can be

shorter. If the integral time is too short, the control valve reaches its limit before the

measurement has time to respond. When the measurement does respond, it will

overshoot the setpoint, causing the integral to drive the valve to its opposite limit.

The time lag built into the gradual response of integral action lengthens the period

of oscillation of a loop. For a loop with proportional-plus-integral control, the

period of oscillation after a load change is longer than for proportional alone.

For loops where the exact value of the controlled variable is not critical, the shorter

period of the proportional-only controller can be an advantage. For example, a

vessel may operate within a wide range of liquid level without adversely affecting

pressure or gas quality. Therefore, the system level does not have to be accurately

controlled, and proportional control is often sufficient.

334 Derivative Control

With derivative action (also called rate action), the controller output is proportional

to the rate of change of the error. This means the faster the change in level, the

faster the change in controller output and control valve settings. By the same token,if the level remains constant, even with a large error, the controller output would be

zero. This makes the use of derivative action by itself impractical.

Derivative action is normally combined with proportional action or proportional-

plus-integral action. Derivative action, being proportional to the rate of change of

the measured variable, introduces a lead (anticipation) element into the controller.

This increases the speed of response of the controller and compensates for the lags

introduced by proportional and integral actions. Figure 300-14illustrates derivative

action.

The output from a proportional-plus-derivative controller may be expressed as

follows:

(Eq. 300-6)

where:

O = controller output

O Kc En TD

Mn Mn 1

S-----------------------------

+=


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Derivative action, being sensitive to the rate of change of the measured variable,

cannot be used in processes that require fast response, or that have rapid fluctua-

tions or high noise levels. These conditions cause instability through large increases

in the derivative gain, and rapidly change direction (sign). Although derivative

action is difficult to tune because of its extreme sensitivity to measurement noise

and other high frequency disturbances, it does have some applications. Most impor-tantly, it is used with proportional and integral action in temperature processes that

have large time lags.

Derivative action can be very helpful in controlling processes that have significant

deadtime, but using it can be difficult. Sometimes adding derivative action can

make the control loop appear slow and inactive with some types of process distur-

bances. This sluggishness might lead one to increase the amount of derivative and

perhaps also increase the controller gain. However, these new tunings might make

the controller unstable when a different disturbance occurs in the plant.

340 Advanced Control

Because this section of theInstrumentation and Control Manualis meant to be

introductory in nature, we will define the term advanced control to be anything

more sophisticated than simple, single-loop feedback control. Advanced control

would therefore include cascade control, feed forward control, signal selector

control, adaptive gain control, self-tuning controllers, multivariable control, matrix

control, and many other techniques too numerous to mention.

We will only deal here with cascade. The reader is encouraged to consult the refer-

ences listed in Section 360for additional information. The Monitoring and Control

Systems Division in the Engineering Technology Department is also available for

consultation.

341 Cascade Control

Cascade control should also be considered when the primary control variable is

slow to react to disturbances. Like any feedback control loop, a cascade control

loop has a controlled variable, a setpoint and a controller. However, instead of

having a valve as its final control element, a cascade controller sends its output to

the setpoint of another controller, adjusting this setpoint to correct an error in the

controlled variable. This other controller is called the secondaryor slave

controller. The cascade controller is called the primary or master controller.

If disturbances in the process can be recognized and quickly corrected, the primary

control loop will not be affected. This suggests that the secondary control loop mustoperate faster than the primary loop. In fact, general guidelines suggest that the

secondary loop should respond at least five times faster than the primary loop.

Looking again at the example of the furnace, let us assume that the fuel system

provides fuel to several other furnaces as well. Over the course of hours, the pres-

sure in the system might well vary as the fuel demand in all of the furnaces

changes. A change in the fuel header pressure changes heat transfer in the furnace.


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Because heat transfer is a slow process, the outlet temperature controller cannot be

tuned well enough to eliminate the effect of changing fuel flow (see Figure 300-15).

(For details on controller tuning, see Section 350.)

On the other hand, if the fuel flow remains steady while the pressure is changing,

the furnace temperature will be more constant. Fuel flow changes almost immedi-

ately when the control valve is moved. Therefore, the flow controller can be tuned

to eliminate most of the disturbances in fuel flow.

Such circumstances lend themselves to the use of cascade control: a fast process

(fuel flow), a slow process (furnace heat transfer), and a disturbance (fuel pressure)

that affects the fast loop. Figure 300-16shows the cascade control system for the

furnace.

Fig. 300-15 Feedback Control Performance

Fig. 300-16 Cascade Control


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Compare Figure 300-17to 300-15. With cascade control the outlet temperature is

much more steady. The fuel gas controller (secondary controller) has eliminated

almost all fuel pressure disturbance from the furnace.

342 Feed-forward Control

Feed-forward control measures a disturbance before it can affect the controlled vari-

able, and changes the manipulated variable to compensate for the disturbance. Of

course, for feed-forward control to work properly, the magnitude and timing of the

effect on the controlled variable must be known. The process might be worse off if

the manipulated variable is changed too much or too quickly.

In Figure 300-18, a gas-fired furnace process is equipped with a temperature

controller (TC), a feed-forward controller (FFC), and a summer, which adds the

two controller outputs together. The feed-forward controller, also called a flow frac-

tion controller, operates like a simple multiplier: The output of the FFC consists ofits input (from the flow transmitter FT) multiplied by a ratio entered by the operator.

Fig. 300-17 Cascade Control Performance

Fig. 300-18 Feed-forward Control


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Figure 300-19shows what might happen in a real furnace as the feed rate is

changed. In the top graph, the feed rate to the furnace is raised at time 1. By time 2,

the furnace outlet temperature begins to drop below setpoint. The fuel valve then

begins to open and raises the outlet temperature back to the setpoint by time 3. In

the bottom graph, the fuel valve has begun to open by time B, and by time C the

furnace temperature is back to the original setpoint. With feed-forward and feed-back control, the process has recovered from the feed rate disturbance much faster

than with feedback control alone. Note that the temperatures period of oscillation

is the same in both cases. This period is a dynamic characteristic of the furnace and

cannot be changed by the control system. However, the feed-forward controller has

been able to reduce the size of the temperature disturbance and has speeded up the

recovery.

Feed-forward control should not be used by itself, but always with feedback

control, because the rate and magnitude of the reaction of a process to a disturbance

is rarely consistent.

Fig. 300-19 Feedback/Feed-forward Control Performance


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350 Controller Tuning

Several methods are available to tune a controller to function in a specific loop. The

following discussion considers some of the methods commonly used. Several of the

references in Section 360, particularly Reference 5, should be useful when difficult

situations are encountered.

351 Quarter Decay Method

The quarter decay method is a closed loop controller tuning method. This means

that the controller remains in automatic while tuning adjustments are made.

The quarter decay method defines the ultimate limit for tight controller tuning.

Often, the tuning constants it produces are too tight (too sensitive) in processes that

have sticky valves and noisy measurements.

To prevent controllers from going unstable unexpectedly, tuning constants should

be set to values one-half as sensitive as those obtained with the quarter decay

method. After these less sensitive tunings are exposed to actual upsets and irregular-ities, and the operators gain confidence in the controller tuning, it may be appro-

priate to make the tunings more sensitive.

The general tuning sequence is as follows:

1. With the controller in automatic, adjust all tuning constants to their least sensi-

tive (least effective) setting. Proportional band should be at its highest value

(proportional gain should be at its lowest value). Integral time should be at its

highest value (most minutes per repeat or least repeats per minute). Derivative

time should be at its highest value.

2. Make a small step change in controller setpoint and record the controller

measurement until it settles out.

3. Change the setpoint back to its original value. Record the measurement as

before.

4. Increase the proportional gain (reduce the proportional band) in small steps

and repeat steps 1-3until the recording of the output resembles Figure 300-20,

curve B; that is, until the amplitude of the first positive excursion of curve B is

approximately four times that of the second (thus the name, quarter decay

method).

5. Measure the period of oscillation. Set the reset and derivative:

TR= P/1.5 minutes

(Eq. 300-7)

TD= P/6 minutes

(Eq. 300-8)


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352 Ultimate Sensitivity Method

The ultimate sensitivity method ( Figure 300-24) is also a closed loop test. Adjust

the integral time and/or the derivative time to their minimum values. Then narrow

the proportional band (increase gain) in small steps, each time changing the

setpoint as described in Section 351, until the controller measurement just begins to

cycle continuously. This proportional band setting is called the ultimate propor-

tional band, denoted PBu. The period of oscillation at the ultimate proportional

band is called the ultimate period, measured in minutes and denoted Pu. The

amplitude of the oscillations in Figure 300-24has been exaggerated for clarity.

The ultimate proportional band, PBu, and the ultimate period, Pu, are then used to

calculate tuning constants as shown in Figure 300-25. These constants give the

quarter damping response already discussed.

Note that Figures 300-25and 300-26show two sets of equations for a proportional-

plus-integral-plus-derivative controller. The set identified as Commercial should

be used for controllers encountered in industry. The set identified as Ideal is

based on an ideal control algorithm equation commonly used in universities. They

are included here for completeness.

353 Process Reaction Curve Method

This is an open loop tuning method. The controller remains in manual while

response tests are made. The tuning method measures two parameters to describe

the response characteristic of the process: process deadtimeand process time

constant.

The deadtime is the delay between a change in valve position and the resulting

change in the controlled variable. The process time constant is the time required for

the controlled variable to reach approximately 60% of its final value.

Fig. 300-23 Proportional-Plus-Derivative Controller Response


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To perform this test, change the controller valve position by a small amount and

record the controlled variable. The deadtime, TD, and time constant, TC, are

measured and their values used to calculate the controller tuning constants.

Figure 300-26shows how the measurements are made and used.

Fig. 300-24 Ultimate Sensitivity Method

Fig. 300-25 Ultimate Sensitivity Method Tuning ConstantsProportional Band

(%)Reset Time(minutes)

Derivative Time(minutes)

Proportional Controller 0.5 PBu

Proportional + Integral Controller 0.45 PBu Pu/ 1.2

Proportional + Integral + Derivative

Controller

Ideal

0.6 PBu Pu/ 2.0 Pu/ 8.0

Proportional + Integral + Derivative

Controller

Commercial

0.3 PBu Pu/ 4.0 Pu/ 4.0

Notes PBu = Ultimate Proportional Band, %

Pu = Ultimate Period, minutes


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Note that the process reaction curve method cannot be used to integrate processessuch as level control; when a valve controlling a level is changed the level

continues to change until the vessel overflows or empties. Level controllers can be

tuned using the ultimate sensitivity method or more advanced methods discussed in

Reference 5.

Figure 300-27gives typical ranges of controller tuning constants for various

processes. Use these values with caution; your process might not be typical. The

Fig. 300-26 Open Loop Reaction Curve Method Tuning Constants


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exact values must be determined by one of the above methods. For future reference,

always record the control loop ID number (e.g., FRC-123), the date, and the tuning

constant when you have finished tuning a control loop.

360 References

1. Fundamentals of Process Control Theory.Instrument Society of America,

1981.

2. Process Control Systems.McGraw-Hill, 1979.

3. Process Instruments and Controls Handbook. McGraw-Hill, 1974.

4. Controllers & Control Theory.Production Facility Bookware Series, Interna-

tional Human Resources Development Corp., 1987.

5. Tuning and Control Loop Performance.Instrument Society of America, 1983.

Fig. 300-27 Tuning Constants for Typical Process

LOOP TYPEPROPORTIONAL

BAND %RESET TIME(MINUTES)

DERIVATIVE TIME(MINUTES)

Flow 100 - 500 0.02 - 0.1 none

Liquid Pressure 100 - 500 0.02 - 0.1 none

Gas Pressure 1- 50 0.1 - 0.5 none

Level 1- 50 0.05 - 0.25 none

Temperature 10 - 100 1 - 10 0.5 - 20

300 process control

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