AG09_PID Deadband Implementation.pdf

APPLICATIONGUIDELINE#9PID Deadband Implementation

TAI #9: PID Deadband Implementation Page 1 of 13

R.2.3Printing:08/06/2012Controlstrategiesdepictedinthisdocumentarepublicdomain.However,allexplanationsandtextareconsideredproprietarytoTEGEnergyGroup,Inc.andmaynotbedistributedwithoutthewrittenconsentofTEGEnergyGroup,Inc.

Abstract

A PID deadband function can be useful in process controls to improve tuning characteristics and eliminate

unnecessary output adjustments when the process is near setpoint. Unfortunately, digital implementation of a PID

deadband can lead to erratic and destabilizing results. It is therefore necessary to understand the behavior of this

feature and the type of problems that can result from its use. The purpose of this document is to explain the

deadband feature embedded in a PID controller and to discuss important considerations in its implementation.

Deadband General Description

A deadband is defined as a region around the setpoint where the error is modified before PID gains are applied.

The deadband feature in a PID controller reduces the error value between the process variable (PV) and the

setpoint (SP) when it is located within the deadband region. This feature introduces the possibility of multiple

tuning strategies – a more aggressive approach when the error between the setpoint and the process variable is

large, and a less aggressive approach when the error is small. One of the major benefits of the deadband feature is

to prevent the final drive element from ‘hunting’ around the setpoint by forcing a steady state output when the

process is within the deadband.

When the error value between the process variable and the setpoint is located outside of the deadband region,

the PID gains are applied to the raw error signal. When the error is located within the deadband region, a

deadband gain is applied to the error before the PID gains are applied. The deadband error gain can be adjusted to

range from 0 to 1, effectively reducing the error value to the PID controller. It should be noted that the derivative

component of PID control is disabled while operating within the deadband.

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If the error is in the deadband,

Error to PID controller = raw error x deadband error gain

Else,

Error to PID controller = raw error

PV

SP

∆ Deadband

gain

P

I

-

+

RawError

AdjustedError

0 < DB gain < 1

PV

SP

∆ -

+

P

I

D

RawError

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Example

Figure 1 shows an example of a deadband application with the following parameters

Deadband limits = -10% and 10%

Deadband Error Gain = 0

Figure 1

Whenever the process variable is located outside the deadband (blue) the PID controller behaves normally.

However, when it is located within the deadband (red), the deadband error gain is applied to the actual error. In

this example, the deadband gain is set at zero, which effectively eliminates the error while the PV is within the

deadband region. In the plot, the PV begins outside of the deadband and the PID controller reacts normally

according to its tuning parameters of proportional gain, integral time, and derivative rate. When the PV enters the

deadband, the error between the PV and the SP is multiplied by the deadband gain of zero. This causes the output

to remain constant while the PV is located in the deadband. Once the PV leaves the deadband, the PID controller

resumes normal response to the raw error.

0

10

20

30

40

50

60

70

80

90

100

Percent (%

)

Normal Deadband Action

Process Variable

Deadband Limit

Set Point

Output

Blue region: Outside of deadbandError = 60 - 40 = 20%

Red region: Inside of deadbandActual error = 60 - 55 = 5%Effective error = 5 x 0 = 0%

Out of deadband, normal output response

Enters deadband, output holds

Output resumes reacting to changes

Reenters deadband, output holds

Leaves deadband, output decreases to react to increased error

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Deadband Transitions

When the process variable enters or exits the deadband, several changes in the PID controller must occur. Before

entering the deadband, the output of the PID controller is composed of proportional, integral, and derivative

components (Figure 2a). The transition into the deadband region will cause the error perceived by the controller to

be considerably reduced since the actual error is now being multiplied by the deadband gain, which in this

example is zero. Such a reduction in the effective error value will cause an abrupt, immediate reduction in the

proportional response of the PID controller (Figure 2b). In order to compensate for this abrupt change, and to

smooth transitions, the PID controller does not output the response of Figure 2b, but instead performs a hold and

track operation. During this transition cycle, the output of the PID controller is held at its previous value. The

integral term is then recalculated to reflect the total output of the PID controller (Figure 2c). After this transition

cycle, the PID controller continues to act normally according to the effective error, which is now modified by the

deadband gain. Since this operation is performed by a digital processor, the PID controller requires two scan cycles

to correctly perform the hold and track steps displayed below.1 Large process jumps and rapid transitions into and

out of the deadband can cause problems with this procedure. These problems will be discussed in the sections to

follow.

(a) Not in deadband (b) Enters deadband, deadband gain

applied to error, loss of proportional

contribution to output

(c) Integral resets to

compensate

Figure 2

Considerations – Process Variable Jump

Transitions into or out of the deadband put the PID controller in a special hold and track state while the integral

term is recalculated. One side effect of this transition state is that the first PV move out of the deadband does not

provoke a proportional output response, as would normally occur. Upon a transition out of the deadband, the PID

controller maintains its output at the previous value. By keeping the output constant during the transition cycle,

the PID controller effectively ignores the proportional change of this first step and only reacts to the subsequent

proportional changes in the error. Normally, when process variable movement is relatively smooth, a small

1 For more information on scan cycles and considerations when using digital circuits, see Application Guideline #8.

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transition out of the deadband does not warrant a significant proportional response; however, with a large jump in

the PV, the lack of a proportional response to that initial jump leads to an undesired lag in the response of the PID

controller output. Figure 3a shows the effects with a deadband implemented, while Figure 3b does not have a

deadband. With the deadband, the process variable (red) initially resides within the deadband and the output

(green) remains constant. When the process variable jumps to 70%, the output stays at its previous value while the

integral term is reset. From there on, the output gradually decreases, mostly due to the integral response of the

PID controller. The lack of proportional response to the PV jump significantly delays the reaction of the output

compared to the result without a deadband.

(a) Reverse-acting PID controller with deadband (b) Reverse-acting PID controller without deadband

Figure 3

0

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40

50

60

70

80

Percent (%

)

Time0

10

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40

50

60

70

80

Percent (%

)

Time

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Figure 4: Reverse-acting PID controller

The Noise Problem

If the process variable is close to the deadband limit, a jump in the PV due to a noisy signal can cause multiple

transitions into and out of the deadband in a short time period. Figure 4 shows an example of this situation. The

process variable starts near 40% and enters the deadband region as it approaches setpoint. Noise then causes the

process variable to exit and reenter the deadband multiple times until it finally remains in the deadband for good.

During these rapid successive transitions into and out of the deadband, the output performs three large,

destabilizing upward jumps.

This noise-induced problem comes from the relationship between scan rate of the PID controller and noise

frequency. With little noise, the scan rate is usually fast enough to complete the hold and track calculation before

the PV crosses the deadband limit again. However, with high-frequency noise, it becomes possible for the PV to

enter the deadband during one scan cycle, and jump out the next. The process variable is therefore not able to

establish itself in the deadband zone, which interferes with the hold and track operation. The inability of the PID

controller to complete this operation by the second crossing of the deadband limit leads to an undesired output

jump. To avoid this jump, the following condition must be met

scanrate 2 noisefrequency

Figure 5 meets this condition. The PV begins in the deadband region, and then exits. Since the PV stays outside of

the deadband for two scan cycles before reentering, the output does not jump as it did in Figure 4. The track and

hold function is given enough time to execute, and it performs a seamless transition.

10

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40

50

60

Percent (%

)

Time

Deadband with Noise

Set Point

Process VariableOutput

Deadband Limit

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Figure 5

Figure 6 illustrates how the hold and track operation performed during transitions into and out of the deadband

can cause large output jumps. In the first scan cycle (Figure 6a) the process variable is located outside the

deadband and the PID controller operates normally. When the process variable first enters the deadband (Figure

6b) the PID controller reacts by maintaining the output and resetting the integral portion to compensate for the

loss of proportional contribution. After that (Figure 6c), the process variable leaves the deadband. Since the PV

was not fully established within the deadband, the PID controller fails to re-perform the hold and track operation

as it had done in the previous step. Instead, it acts normally on the new error, which is much larger than the zero

error it had while in the deadband. This sudden proportional increase is added to the output, causing a significant

jump.

(a) (b) (c)

Figure 6

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20

30

40

50

60

70

Percent (%

)

Time

Smooth Deadband Transition

Set Point

Process Variable

Output

Deadband Limit

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Observable results

The effects of the previously described overcompensation are illustrated in Figure 7. The four possible scenarios

and their corresponding output reactions are depicted. The process variable is in red, the output in green, and the

deadband is the dashed black line. As shown, the output is steady during the first PV jump into or out of the

deadband. The problem of the output jump occurs when the PV returns to its original region at the next scan cycle.

This output jump depends on the direction of the PV change. The graphs in the left column show upward spikes in

the PV, causing the output to increase. The graphs in the right column show downward spikes in the PV, causing

the output to decrease.

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Various Process Variable Jumps and Output Responses

Figure 7

A fast PID controller scan rate causes output jumps to compound upon one another as a result of high frequency

noise. Figure 4 is an example of this phenomenon, and is presented again below in Figure 8. The PID controller that

is used has the following tuning parameters

Deadband limits at -5% and 5%

Deadband error gain = 0

Proportional gain = 1

Time Time

Time Time

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Figure 8

In this example, the process variable approaches setpoint, but noise causes it to enter and exit the deadband

region several times before settling. Each time the PV exits the deadband, the output jumps. This output jump is

proportional to the difference between the error value within the deadband and the error value outside of the

deadband. It is also related to the proportional gain of the PID controller. Since the deadband gain is zero in this

example, the error in the deadband is also zero. Upon the first jump back out of the deadband, the PV obtains the

value of 43%, an error of 7% that causes an output jump of 7% due to the proportional gain of 1. If the

proportional gain were 2 instead, the output jump would be 7×2 = 14%.

With this knowledge, it is possible to make several generalizations about the behavior of these output jumps. As

previously stated, the magnitude of the output jump is directly related to the proportional gain. The size of the

deadband limit also affects the size of output jumps. A large deadband limit would result in a large difference

between the error inside and the error outside the deadband, which would cause large output jumps. In addition,

the deadband gain also has an effect. If the gain is closer to 1, the output jump is less prominent since the change

in error upon transitions is smaller.

Proposed solution

To avoid these potential output jumps associated with scan time, it is necessary to have the process variable hold

its value upon transitions into and out of the deadband zone. This establishes the PV either inside or outside the

deadband over two successive scan cycles, allowing time for the hold and track operation of the PID controller to

execute.

A transport delay of two scan cycles can be used to temporarily hold the process variable. A digital circuit that

detects when the PV crosses the deadband limit can also be implemented so that the transport delay on the PV is

only activated during transitions into and out of the deadband region. The solution depicted in Figure 9 ensures

two successive scan cycles upon transition across the deadband without unnecessarily delaying the PV signal.

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40

50

60

Percent (%

)

Time

Multiple PV jumps

Set Point

Process VariableOutput

Deadband Limit

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Figure 9: Transport delay logic circuit

∆

TransportDelay

H//L

H//L

OR

AND

NOT

AND

TY

N

TransportDelay

PVSP

PID

M/AStation

F(x)

-+

SP

PV

Final DriveElement

DeadbandLimit

DeadbandLimit

1 Scan Cycle

2 Scan Cycles

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Conclusion

Due to possible noise-induced output jumps caused by transitions into and out of the deadband region, caution

should be taken when using the deadband function. The deadband in a PID controller works well when the process

variable signal is clean, but can cause undesired output jumps when the signal is noisy and erratic. Using a

smoothing algorithm or a lag function can reduce noise, but will introduce undesired delays in the process without

ensuring protection from erratic jumps. The logic strategy proposed in this document is a possible solution to

prevent destabilizing output jumps from the deadband implementation. With this strategy, the deadband can be a

very powerful tool to reduce or eliminate valve adjustments when the process variable is close to set point.

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Appendix

Figure 10 depicts the entire logic circuit for a deadband simulation.

∆

PID

M/AStation

TransportDelay

LAG

A

A

∑

∆

TransportDelay

H//L

H//L

OR

AND

NOT

AND

TY

N

TransportDelay

PV

One Shot

NOT

OnDelay

TY

N

AI

SP

+ -

1 Scan Cycle

2 Scan Cycles

DeadbandLimit

DeadbandLimit

Noise Generator

Figure 10

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AG09_PID Deadband Implementation.pdf