control performance

8/13/2019 Control Performance

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8-1

CHAPTER 8

Control Performance 1

Once a control system has been designed and commissioned (started), it is necessary to monitor

it to assure continued performance. There are many reasons for changes in the performance of

control systems such as degradation in heat transfer areas due to fouling, mechanical problems

with valves and sensors, catalyst activations, and as we have mentioned several times in previous

chapters, nonlinearities. A couple of questions about installed working systems are, (a) how do I

know when my control system has problems? and (b) how can I achieve operational excellence

for my process control system?

Many metrics are available for this monitoring and for deciding if a control system is

performing to satisfaction. Sometimes we refer to them as Key Performing Index metrics, orKPI. We start with some of the traditional metrics and then move towards some of the most

recent ones in used now.

8-1 Traditional Evaluation Metrics

Chapters 3 to 5 mentioned that the great majority of open-loop systems respond to step changes

in forcing function as overdamped systems (monotonic, or non-oscillatory, response). However,

when a controller is installed and set in automatic (closed-loop) the response is commonly that of

an underdamped system (oscillatory response). For example, Fig. 8-1.1 may represent the

response of a closed-loop system to a unity step change in set point; Chapter 6 also showed some

of these types of response. Figure 8-1.2 shows a typical underdamped response. Chapter 2

presented and discussed this response, and for convenience of the reader we repeat the

presentation in the following paragraphs; the terms mentioned are metrics that have been

traditionally used in the performance evaluation of control systems.


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8-2

0 5 10 15 200

0.2

0.4

0.6

0.8

1

1.2

1.4

Time

Response,

y

.Underdamped

Overdamped

Critically damped

Figure 8-1.1 Possible responses to a set point Figure 8-1.2 Second-order underdampedchange response to step input

Per iod of Oscil lation; Decay Ratio; Rise Time; Settli ng Time; Overshoot

The specification of the desired value of the metric depends on the process and on what the

engineer thinks the control system should provide. A common value for the Decay Ratio is that

of and it is probably due to Ziegler Nichols tuning method (Chapter 6).

Another popular performance specification is the Integral Criteria; there are four of these

specifications. The Integral of the Absolute Error (IAE) provides an indication of the total erroras the integral is the area under the curve between the response and the set point, Fig. 8-1.3;

absolute value is used so that negative and positive dont cancel each other.

T

o

dtteIAE )(0 10 20 30 40 50 60 70 80

90

90.5

91

91.5

92

92.5

93

93.5

94

IAE (area under the

curve)

Time

Response

T

o

dtteISE2)(

T

o

dttetITAE )(

Figure 8-1.3 Integral of absolute value of the error (IAE) T

o

dttetITSE2)(

T

B

C

A

Rt

St

)(tY

Settling time

limits

t


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8-3

8-2 Key Metrics for an Installed Control System

The metrics presented in Section 8-1 have been traditionally used to evaluate the performance of

control systems. We now focus on the following five simple metrics and one troubleshooting

metric that we feel provide the necessary information. They are by no means inclusive but are

some of the ones we have used and feel confident.

% Time in Normal Mode - indicates if the loop is in the correct mode (auto, cascade) Average %ABS Error - indicates if the loop is controlling at set point Valve Travel, %/hrindicates if the valves are working too hard % Loops Oscillatingindicates if the loop is oscillating % Time Output is Saturatedindicates if there is an equipment sizing problem

Oscillation Periodthis is used as a troubleshooting aid

These metrics will advise/alert the operating personnel when work is required, what loops to

work on or who to call and when to call them. Knowing these metrics and acting to correct them

will stop wasting money and start saving money.

Next we discuss each metric and present the result of an audit that was performed at a

plant (for obvious reasons we do not divulge the name of the plant or any other information that

may be sensitive). An audit is a concentrated effort to analyze and tune loops at a site; fifty five

loops were considered. During the first visit, 26 loops were analyzed and tuned. During the

second visit, 29 loops were analyzed and tuned. In between visits, valves may have been worked

on that needed work, and control strategies may have been changed as recommended, with the

overall goal of improving the control system. The control system software used at the plant

provided an easy way to calculate the metrics.

During a normal operation (non-audit) the metrics are still active, and if a loop becomes

outside the specification, the control system will alert the operating personnel indicating which

loop has the problem.

8-2.1 % Time in Normal Mode The normal modeof a straight feedback controller is automatic, for the master controller of a

cascade system is automatic and for the slave controller is remote set (or cascade). These are the

modes required for complete benefit of automatic process control. If a controller is not in the

normal mode no action (or the wrong action) will be taken when a deviation of set point occurs.


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8-4

Figure 8-2.1 shows the % average time for all the loops in the plant including the result of

actions taken once the loops not in normal mode were identified.

0

10

20

30

40

50

60

70

80

90

100

Jan Feb Mar April May June July Aug Sept Oct Nov Dec

% Time in Normal Mode

26 loopsFirst visit 29 loops

Second visit

Figure 8-2.1 Average time in normal mode for all loops in the plant

At the start of the work, about 65% of the loops were in normal mode. After analyzing and

identifying the reasons the average rose to over 70% after the first visit and to about 95% after

the second visit.

8-2.2 Average %ABS ErrorFigure 8-2.2 shows the average % absolute error of all 55 loops; each error is calculated in %TO

(transmitter output).


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8-5

0

5

10

15

20

25

30

35


Average % ABS Error

29 loops

Second visit

26 loops

First visit

Figure 8-2.2 % Absolute Error

At the start of the work the average % absolute error was about 30%, dropped to 25% after the

first visit, dropped further as work was continued after the first visit, and dropped to 12% after

the second visit. As work then progressed on repairing valves and implementing the

recommended changes to the control strategy, the end result was about 8%. Figure 8-2.3 shows

a sample of loops; it shows how the control system provides the information and the ease of

identifying the necessary loops requiring work.

30.96 30.6 25.11 18.32 17.17 11.95 8.972 7.118 6.389 6.652 7.722 7.756

Tagname Jan Fe b Mar April May June July Aug Sept Oct Nov Dec

FIC-2000 53.9 52.3 26.7 8.6 7.3 8.3 8.4 8.9 8.2 7.7 10.1 9.9

TIC-2303 5.6 5.7 5.4 4.8 4.7 4.5 3.2 3.1 2.7 2.7 3.2 3.0

LIC-2303 14.3 15.4 13.9 13.6 11.9 13.0 14.9 2.3 2.3 2.3 2.8 2.4

LIC-2402 16.7 15.4 11.9 5.8 4.6 5.6 5.3 6.0 5.2 5.8 6.0 6.1

TIC-3405 9.5 9.2 5.7 3.5 1.7 1.8 2.0 1.7 1.7 2.6 2.1 1.9

TIC-2404 6.2 6.2 5.8 5.3 4.9 5.1 1.9 1.9 1.8 1.7 2.0 2.1

FIC-2413 37.6 36.2 25.7 23.0 6.0 5.5 6.8 6.3 5.8 5.2 7.3 7.1

FIC-2613 53.9 49.5 27.6 17.0 9.0 9.8 10.3 10.4 8.9 10.2 10.7 10.9

TIC-3131 52.5 52.0 29.8 19.8 19.8 19.0 22.6 21.9 18.8 18.1 22.3 24.0

LIC-6201 30.8 30.5 30.3 29.0 28.9 12.0 5.2 3.9 4.1 4.8 5.3 5.1

TIC-12302 49.5 46.8 48.1 41.1 41.3 26.6 18.9 10.7 8.2 7.7 8.6 9.6

Average % ABS Error

Figure 8-2.3 Average % Absolute Error of individual loops


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8-6

8-2.3 Average Valve Travel

Figure 8-2.4 shows the progression in reduction of valve travel. At the start, the average travel

for the 55 loops was about 1150 %/hr. At the end of the work, this number was less than 200

%/hr, or a five-fold reduction.

0

200

400

600

800

1000

1200

1400


Valve Travel %/Hr

Second visit

First visit

Figure 8-2.4 Average monthly valve travel

8-2.4 % Loops OscillatingFigure 8-2.5 shows the % of loops oscillating. In some cases oscillation may go up slightly after

tuning due to valve problems. The number goes down as control strategies are implemented and

valves repaired or replaced. It is necessary to point out that in some processes oscillations may

not disappear due to operating procedures such as start/stop machinery, purging of lines and

other equipment, etc.


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0

5

10

15

20

25

30

35


% Oscillation

Second visit

First visit

Figure 8-2.5 % Loops Oscillating

8-2.5 % Time Controller Output is Saturated

In this context saturation refers to the controller output reaching one of its limits, either 0% or

100%. If the controller output is at its limit, or even including less than 5% or more than 95%,

the process is essentially out of control. Under a major or extreme disturbance the controller

may have to drive its output to one of its limits to compensate for the deviation. However, if the

% of time the output is saturated is significant (up to the operating people define what is

significant) it is an indication of a problem. Certainly the controller itself may have stopped

working but, if this is not the case, the one thing we can say is that the action taken by the

controller (increasing or decreasing its output) is not affecting the controlled variable and this is

why the controller keeps moving. The reason may be due to an upset operation, new operating

conditions that may require new equipment sizing, or a mechanical problem with the final

control element (common) or with the sensor, transmitter or the unit operation itself, etc.

8-2.6 Period of Oscillation

Figure 8-2.6 shows a number of loops that share a period of about 223 seconds. During the audit

the operating personnel claimed the analysis had to be incorrect because the loops were located

all through the plant and not anywhere near one another. But, they are all related to steam flow.

Thus there is a loop somewhere that is oscillating and these loops are seeing the oscillation as a

disturbance. In this case the period of oscillation provided a troubleshooting aid.


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8-8

TAG NAME DESCRIPTION

OSCILLATION

PERIOD SEC

21PC3775 50#F STEAM EXPORT 222.6

21PC2727 135 TO 50 LB STEAM 222.621PC2799 50 LB STM HEADER 222.6

21LC2517 DEAERATOR 222.7

21FC1399 STM TO X FRAC REBOILER 222.7

21FC2395 50 STM TO RERUN REBOILER 222.7

21FC1379 X4 REBOILER STEAM 222.7

21FC387 X3 REBOILER STEAM 222.7

21PC3720 X7 BURNER INJ 135# STEAM 222.8

21FC2185 STM TO GAS STABILIZER REBOILER 222.8

Figure 8-2.5 Period of Oscillation

8-3 Nonlinearities (revisited, once more)

In previous chapters we have presented and discussed the meaning and effect of process

nonlinearities. This is an important process characteristic and very much related to the topic of

this chapter; thus, a couple real examples are justified.

Example 8-3.1

Consider the heat exchanger shown in Fig. 8-3.1 where a process fluid is cooled using cooling

water. The process fluid flow varies often between 400 and 600 gpm. The temperaturecontroller was tuned at the 600 gpm level.

TV

TT

TIC

Cooling

Water

FI

Process

Fluid

Figure 8-3.1 Nonlinear process


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8-9

Figure 8-3.2 shows the controlled responses to a disturbance and to a set point change from 900F

to 92 0F and back to 90 0F. Both responses are stable and show small deviation from set point.Set point

changed from 90

to 92 F

0

10

20

30

40

50

60

70

80

50

60

70

80

90

100

110

0 500 1000 1500 2000 2500 3000 3500

ControllerOutputP

Va

nd

SetPoint

Time (sec)

Figure 8-3.2 Response to a disturbance and set point changes at 600 gpm

Figure 8-3.3 shows the responses when the process flow is changed to 400 gpm. This time

unstable responses are obtained. Obviously some of the KPI, such as absolute error or loop

oscillating, will alert operations.

0

10

20

30

40

50

60

70

80

50

60

70

80

90

100

110

0 500 1000 1500 2000 2500 3000 3500

ControllerOutput

PVa

ndS

etPoint

Time(sec)

Process flow changed

from 600 to 400 gpmUnstable response

Controller set inmanual

Set point

changed from 90

to 92 F

Figure 8-3.3 Responses at the 400 gpm level.


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8-10

The reason for the nonlinearity and therefore instability is that the process behaves differently at

different process flow rates. As the fluid flow slows through the cooler, the residence time

increases, so more heat is transferred; this makes the process gain larger. The time between when

the temperature valve moves and the measurement indicates a change is also longer; this is the

process dead time. Both gain and dead time affect the tuning as we have learned. Thus, this

situation requires re-tuning the controller

Example 8-3.2

Consider the reactor shown in Fig. 8-3.4 where an exothermic reaction occurs and it is cooled

using cooloing water. Depending on the type of product the reactor runs at temperatures

between Fo

119 and Fo149 . The most common temperature is F

o3.134 and the controller was

tuned for that condition.

TC

SP

Product

Reactor

Cooling

water

101

TR

TT101

Process

Fluid

Figure 8-3.4 Chemical reactor

Figure 8-3.5a shows the response of the temperature to a step change in set point of two

degrees up and down. The figure shows a stable fast response. Figure 8-3.5b shows the

response when the set point decreases by 10oF at a rate of 0.05

oF/min, and Figure 8-3.5c shows

a similar decrease by 13

o

F. Both responses are stable however, it seems that as the temperaturemoves away from the original set point of 134.3 oF where the controller was tuned, the process

response lags the set point more.


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8-11

0 50 100 150 200 250 300133

133.5

134

134.5

135

135.5

136

136.5

137

137.5

138

Temperature,

oF

Time, min

Reactor

Temperature

Set Point

Figure 8-3.5a Temperature response to set point changes

0 50 100 150 200 250 300 350 400 450 500 550124

126

128

130

132

134

136

Reactor

Temperature

Time, min

Tempera

ture,

oF

Figure 8-3.5b Process response to a decrease of 10oF in set point at a rate of 0.05

oF/min


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8-12

Set

Point

0 100 200 300 400 500 600 700 800120

122

124

126

128

130

132

134

136

ReactorTemperature

SetPoint

Time, min

Temperature,

oF

Figure 8-3.5c Process response to a decrease of 13 oF in set point at a rate of 0.05 oF/min

Figure 8-3.5d shows the response when the set point increases by 10oF at a rate of 0.05

oF/min, and Figure 8-3.5e shows a similar decrease by 13

oF. The first response, Fig. 8-3.5d,

shows a few oscillations at the new set point but recovers and controls. The response in Fig. 8-

3.5d is unstable. Obviously the process characteristics at this temperature are different enough

than before yielding an unstable system with the original tunings.

0 50 100 150 200 250 300 350 400 450 500 550

134

136

138

140

142

144

Time, min

Temperature,

oF

Reactor

Temperature

Figure 8-3.5d Process response to an increase of 10oF in set point at a rate of 0.05

oF/min


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8-13

0 50 100 150 200 250 300 350 400 450 500

134

136

138

140

142

144

146

148

150

Temperature,

oF ReactorTemperature

Time, min

Figure 8-3.5e Process response to an increase of 13oF in set point at a rate of 0.05

oF/min


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control performance

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