2.37

Tuning Interacting Loops, Synchronizing Loops M. RUEL

(2005)

INTRODUCTION

•

The reader is advised to also read Sections 2.6, 2.12, and 2.22. This is desirable to gain a full understanding of the phenomenon of interaction and decoupling; the methods discussed in this section cannot be used in all cases, and a full understanding of the other options for overcoming interactions between control loops can be helpful.

•

• • •

MULTILOOP SYSTEMS When a unit process is controlled by several control loops, there is no magic formula that can tell whether one loop will affect another. This information will only come through an in-depth understanding of the process. If one loop directly interacts with another, oscillation in the first loop will cause oscillation in the second and possibly in other downstream loops. If the same pump feeds two flow loops, oscillation in one loop can cause oscillation in the second. When a loop is cycling, it is essential to determine whether the process is causing cycling, or whether the cycling is attributable to other loops or possibly to the loop itself. To check the cause, one can switch the particular loop to manual mode; if the cycling continues, it is probable that the cycling is being caused by an external source. There is also hidden cycling, which occurs if a cycle is present but is hidden by noise. To uncover a hidden cycle, the readings should be collected in the manual mode, and power spectral density analysis should be used on the data collected. In that case, the hidden cycles will show up as peaks. In some installations the problem is not that the loops interact, but it is imperative that they respond with the same speed. In either case, one should be knowledgeable about the tools that are available to determine loop health and performance: Control Loop Analysis The following criteria should be met for a control system to perform in an optimal manner: •

The power spectral density should be flat, no cycling present.

442 © 2006 by Béla Lipták

•

•

•

Cumulative power spectral density should be continuous. Statistical analysis: Data distribution should be a bell curve, variability should be small, valve movements should be minimized. Development of a process model is desirable to validate the process and to find tuning parameters. Robustness analysis is recommended to validate tuning parameters. The process should be analyzed to check for hysteresis and backlash, stiction, noise, process model inaccuracy, hidden cycling, and nonlinearities. Oscillation should be evaluated by determining the area under the curve, which is a good indicator of control quality. Cross-correlation and multivariate techniques can be used to measure interaction between signals and loops They can also help to determine whether multivariable control should be considered. Performance indexes, such as variability, IAE, and Harris index, should all be monitored.

INTERACTING LOOPS An example of a control system with potentially interacting multiple loops is illustrated in Figure 2.37a. Here two liquids

FC1 FT 1 PT

FT 2

PC

FC 2

FIG. 2.37a Illustration of potentially interacting control loops.

2.37 Tuning Interacting Loops, Synchronizing Loops

1. Another user valve is suddenly closed and this disturbance causes the line pressure to increase. 2. If the pressure control loop is not faster than the flow loop, the flow through FC1 will increase. 3. To correct for the flow increase, FC1 will close down its valve, which in turn will cause the pressure to rise. 4. Eventually the pressure loop will slow down the pump, which will cause the flow to decrease. 5. As the flow drops, FC1 will open its valve to compensate, which will cause the pressure to decrease. 6. In response to the drop in pressure, the PC will speed up the pump, causing the flow to increase again. In this configuration, if PC is not faster than FC1, steps 3, 4, 5, and 6 will repeat continuously and the two loops will oscillate and potentially resonate. Likewise, since FC1 controls the process fluid feed to the flow loop controlled by FC2, flow loop 1 must be faster than 2. If this is not the case, a disturbance in flow 1 could cause both flow controllers to react, and oscillation would result. Tuning to Eliminate the Interaction When loops interact, it is necessary to make sure that their response speeds are not the same and not even similar because speeds that differ but are close also have the potential to oscillate. To be on the safe side, one should select response

© 2006 by Béla Lipták

speeds that differ by a factor of three to five. If speeds are closer than 3:1, loops may one day start to oscillate. In case of loops that are highly interactive, a speed ratio of up to 10:1 may be required to fully decouple them. For the control system described in Figure 2.37a, this means that the response time of the pressure loop will determine the response time of flow loop #1, and the response time of flow loop #1 will determine the response time of flow loop #2. In tuning interacting loops, one would do that by placing the downstream loop in manual while tuning the upstream loop; once the upstream loop’s speed of response is determined, use a multiple of that to set the downstream controller. So, for the control system in Figure 2.37a, one would place FC1 and FC2 in manual, while aggressively tuning the pressure controller to provide a high speed of response. The response time of the pressure control loop will determine the system response time. Once the PC is tuned, one would place the pressure loop in automatic so that to the rest of the control system, it would seem as if it were part of the process. Flow controller FC1 is tuned next, while FC2 is still in manual. FC1 must be tuned for a response time that is at least three times slower than that of the pressure loop response time. For ideal separation it should be 5 to 10 times slower. Once FC1 is tuned, both the PC and FC1 are left in automatic, while FC2 is being tuned. Again, FC2 should be tuned for a response time which is at least 3 times (ideally 5 to 10 times) slower than flow loop FC1. Therefore, one can sum up the tuning of the three interacting loops into the following three steps: Step 1. Tune PC for quick response, while other loops are in manual mode. For the purposes of an example, assume that the settling time of this fastest loop turns out to be 30 seconds (Figure 2.37b). Step 2. Tune FC1 for moderate response, while PC remains in automatic and FC2 in manual mode. Tune FC1 for a settling time of at least three times that of the PC, or at least 90 seconds (Figure 2.37c). Step 3. Tune FC2 for a slow response while PC and FC1 both remain in the automatic mode. The settling time of FC2 should be at least three times that of the FC1, or at least 270 seconds (Figure 2.37d) .

30 s Process variable

are being mixed. The expensive process fluid is controlled by FC1 at a flow rate of 100 GPM. The second flow controller (FC2) adds water to dilute the process fluid by maintaining the total flow between 200 and 400 GPM. All three of these loops have the potential to be fast. A response time of less than 30 seconds is attainable on all three loops, but which loop should be the fastest? What is the logic behind this decision and why should one be faster than the others in the first place? The reason why the speeds should be different is because if they are not, the loops can oscillate whenever an upset occurs because the correction generated by one loop upsets the others and this generates cycling. As to which loop should be the fastest, one should evaluate the process to determine which controlled variable needs to be constant in order for the other loop(s) to operate properly. In Figure 2.37a, by observing the process we would conclude that in order for the flow loop (FC1) to function properly, the upstream pressure to its control valve has to be constant. Because that upstream pressure has to be constant regardless what the flow is, therefore, the pressure loop must be faster than flow loop #1. If this was not the case, if the pressure loop and the #1 flow loop were tuned to have the same speed of response, they may work for a while, but eventually, when a disturbance occurs, it will cause the two loops to oscillate. For example the following sequence of events could cause oscillation in this control configuration:

443

50

42 40

80

120

160

200

240

280

FIG. 2.37b After the fastest loop is tuned, measuring its response time (settling time), which in this case is 30 seconds.

444

Control Theory

Process variable

90 s

TABLE 2.37e The Sequence of Steps to be Used in Tuning Any Number of Interacting Control Loops

50

Fast

42

Slow 40

80

120

160

200

240

280

FIG. 2.37c Tuning the less fast loop for a response time (settling time) that is three times that of the fastest loop or in this case is 90 seconds.

Steps

Loop1

Loop2

Loop3

...

Loopn

1

Tune

Manual

Manual

Manual

Manual

Tune

Manual

Manual

Manual

Tune

Manual

Manual

...

...

...

2 Automatic

3 Automatic Automatic

For a summary of the steps required in tuning any number of interacting loops, refer to Table 2.37e. The method of removing interaction by reducing the speed of response has disadvantages because this can cause the control loops to become sluggish and unable to effectively correct upsets and disturbances. If this is the case the use of more sophisticated techniques of decoupling is recommended, as discussed in Section 2.12. Cascade loops is another case of interacting loops. Hopefully, in a cascade system, the inner loop has to be faster than the outer loop. (See Section 2.6.) SYNCHRONIZING LOOPS In some control systems, the loops do not interact but they do work together. Such configurations are called synchronized loops, and it is desirable for such loops to have the same response time. It is important to note that synchronized loops should be so designed that there is no physical link between them that could cause interaction. Batch mixing is one example of a control system that should be synchronized. Figure 2.37f illustrates a control system for mixing three ingredients in a mix tank. The goal of such a control system is to maintain the required ratio of the ingredients even during startup or shutdown or when the rate of production changes. Because the control valves and pipe volumes associated with the three flow control loops are substantially different, it is probable that their process gains, dead times, and time con-

...

...

n Automatic Automatic Automatic Automatic

Tune

n + 1 Automatic Automatic Automatic Automatic Automatic

stants also differ. In such cases, if all three loops were tuned for 10% overshoot (or any other criterion), the response times of the loops would not be the same. Therefore, when the rate of production rises and the level controller calls for increased flows, the recipe flow ratios will be out of balance until all three flows reach their new set points and regain stability. To ensure that all three loops move at the same speed, one should determine the response time of the slowest loop and match the response times of the others to it. Normally, the slowest loop is also the one with the largest dead time. The steps involved in tuning synchronizing loops are: 1. Apply an upset (bump test) to each loop. This can be a temporary change of set point.

FC 3 FT 3 FC2

1"

FC 1

FT 2

FT 1 Process variable

270 s

6"

50 10"

42 LC 40

80

120

160

200

240

280

FIG. 2.37d Tuning the least fast loop for a response time (settling time), which is three times that of the less fast loop or in this case is 270 seconds.

© 2006 by Béla Lipták

LT

FIG. 2.37f In order to keep the ratio of ingredients constant during load changes, the loops have to be synchronized (their speed of response has to be the same).

2.37 Tuning Interacting Loops, Synchronizing Loops

software, the expected speed can be specified. If done by hand, techniques such as pole placement, Internal Model Control, or Lambda tuning should be used.

TABLE 2.37g Summary of Steps Required in Tuning to Synchronize Control Loops Steps 1

Loop1

Loop2

Loop3

...

Test

Test

Test

Test

2

4

Loopn Test

Slowest Tune at maximum speed

3

Tune at same speed

5 Automatic Automatic Automatic Automatic Automatic

2. From the responses of the loops, determine which is slowest. 3. Tune the slowest loop for maximum speed of response and measure the response time that results. 4. Adjust the tuning parameters of the other loops so that they will also have approximately the same response time. When tuning loops that need to work in harmony, select tuning parameters that give similar response times. If this is done using

© 2006 by Béla Lipták

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Bibliography Astrom, K. J., PID Controllers: Theory, Design, and Tuning, 2nd ed., Research Triangle Park, NC: Instrument Society of America, 1995. Corripio, A. B., Tuning of Industrial Control Systems, Research Triangle Park, NC: Instrument Society of America, 1990. Gerry, J. P., “Tune Loops for Load Upsets vs. Setpoint Changes,” Control Magazine, September 1991. Levine, W., The Control Handbook, Boca Raton, FL: CRC Press, 1996. Lipták, B. G. (Ed.), Instrument Engineers’ Handbook: Process Software and Digital Networks, Boca Raton, FL: CRC Press, 2002. McMillan, G. K., Tuning and Control Loop Performance, 3rd ed., Research Triangle Park, NC: ISA, 1994. Ruel, M., “Loop Optimization: Before You Tune,” Control Magazine, Vol. 12, No. 3 (March 1999), pp. 63–67. Ruel, M., “Loop Optimization: Troubleshooting,” Control Magazine, Vol. 12, No. 4 (April 1999), pp. 64–69. Ruel, M., “Loop Optimization: How to Tune a Loop,” Control Magazine, Vol. 12, No. 5 (May 1999), pp. 83–86. Ruel, M., “Plantwide Control Loop Optimization,” Chapter 5.9 in B. G. Lipták, Ed., Instrument Engineers’ Handbook, 3rd ed., Boca Raton, FL: CRC Press, 2002. Shinskey, F. G, Process Control Systems, 4th ed., New York: McGraw-Hill, 1996.