instrumentation tuning theory

8/13/2019 Instrumentation Tuning Theory

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hapter S ontroJ er TuningModule Ultimate Sensitivity ethod

H PTER : ONTROLLER TUNINGMODULE : ULTIM TE SENSITIVITY METHOD

IntroductionWe have seen that a typical controller, either pneumatic or electronic, can finish up with three adjustableparameters, proportional, integral, and derivative . The adjustment of these parameters is often poorlyunderstood, and incorrect settings can result in a poorly performing feedback control system.In the module on proportional control the accepted ideal setting was one that produced a 1/4 decaycharacteristic Figure 1

A 4There is no realmathematical justificationfor this response, but itdoes represent a goodcompromise betweenspeed of response andstability. This criterionshould be the cornerstoneof controller tuning.

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A/16 J L ~ ~ , 4 ~ ~ : : : ~ ~ l I l = = = = * = = ime

Figure 1: Typical 1/4 Decay Response.

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hapter : ontroller uningodule : Ultimate Sensitivity ethodThe Control LoopThe controller is but one piece o hardware in a typical control loop. The other items are also involved in theoverall balance o the loop. It is convenient or the purposes o discussing controller tuning to divide theloop into two sections, controller and every thing else (process, pipes, valves, pumps, etc.).

P - Process ~ r . ~ ~ ]ontroller PipesPumps Sensor In the section on process dynamics wediscussed the problems o capacitance Sand dead time causing a lag .inresponse. Recall that an additional 180 o lag,

over and above the inherent 180 lagintroduced by proportional control, andwe no longer have a negative feedbacksystem. Figure 2: Simplified Control Loop. We have feedback in phase with theinput signal and, provided the gain is sufficient, have potential for oscillation. In practice it can be stated that all control loops have the ability to introduce more than 180 o lag. The limiting factor to prevent oscillation is the controller gain setting. This should explain why controllersmust be tuned on site, each process is different from any other.

There are several methods available for tuning controllers. a loop Is performing reasonably satisfactorily, acomplete retuning may not be necessary, but t may be possible able t Improve the loop s performance bymaking small adjustments and observing the results. However, such a trial and error process does require agood deal o experience o instrumentation systems to carry outwithout upsetting the process too much.The method which best illustrates the principle o controller tuning is the one developed and described byZiegler and Nichols in 1942 This is termed the Ultimate Sensitivity Method.

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hapter : Oniviler TuningModule : Ultimate Sensitivity ethodUltimate Sensitivity Ziegler-Nichols) Method

Time

I Step Disturbance

One attraction o the Ziegler-Nichols method is that it was empirically derived as a result o observationscarried out on many control loops. It is based on the fact, as described above, that any control system inclosed loop mode automatic) can be made to oscillate i the controller gain Is Increased progressively. If thesystem is made to oscillate at constant amplitude the overall loop gain is one. The setting of controller gainat this point is termed the Ultimate Proportional Band UPB . If the proportional gain is further increased theamplitude o the oscillations will progressivelyincrease and i the gain is reduced theoscillations will eventually die out This isshown in Figure 3.

SP ~ : : ; ;

Low Gain PBSP 1 - - - -

a:i SP OptimumThere is another piece o information availableat this point. t is the period o oscillation andit is representative o the natural frequency othe system. We will require this to determinereset and derivative settings which are timerelated.

Time

Figure 3: Responses to Varying Proportional Gains.pageB 3


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Methodhapter om oller TuningModule Ultimate ensitivity Method

1. While in manual mode turn off, r increase reset time to maximum if in MPR r decrease reset rateRPM to minimum. Similarly switch off derivative rreduce derivative time to minimum value.

2. With the controller in automatic mode, and with the proportional control set at some r i ~ r r y wide PBsetting, sUbject the process to a small upset move setpoint to a new value for a few seconds and thenreturn to original setting .3. If the response curve obtained from step 2, on the process recorder, does not damp out then the gain istoo high PB too narrow . The gain setting should be reduced, try halving, when in manual mode and

then step 2 should be repeated.4. I f the response curve in step 2 damps out upper and centre graphs the gain is too low PB too wideand the gain must be increased.5 . Repeat the process with different gains until constant amplitude cycling is obtained. The PB at whichthis occurs is recorded, and is the Ultimate Proportional Band UPB . Also recorded is the UltimatePeriod Pu , the time taken, in minutes, rone cycle oscillation.

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Applying the Ziegler and Nichols formulae.1 . For Proportional control only:

A 1/4 decay curve will be obtained the UPS is doubled, gain halved.PB = 2.0 UPB

hapter : onrroller uningodule :Ultimate ensitivity ethod

2 . Proportional plus Reset. P + IRecall reset adds lag to the system, i.e., less stable, therefore overall gain must be reduced slightly.

PB =2.2 UPBReset = Pu MPR2

3 . Proportional Plus Derivative P + DDerivative action reduces lag, i.e., system slightly more stable, more gain can be used.

PB = 1.6 UPBDerivative = Mins

4 . Proportional Plus Reset Plus Derivative P + I + DPB = 1.6 UPBReset = Pu MPR

Derivative = g MinsRemember the above equations were essentially empirically derived and exceptions are possible. They aredesigned to prc.duce a quarter decay ratio. A_major disadvantage is that the loop must be made to oscillate.In a working plant this is not always possible.

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hapter: omllJl eruningodule : Ultimate Sensiiivity MethodExampleA temperature control loop is to be tuned by the Ziegler-Nichols method. The process cycled, at constantamplitude, with a UPB of 12 and an ultimate period of 22 minutes. What would lJe the control settings for athree mode P I D controller?For three mode controller:P 1.6 UPB Pu MPR)

u Mins)Proportional setting 1.6 x 1219.2Reset setting MPRDerivative setting = = 2.75 Minutes


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Setting the Gains on ControllersChapter : al _er TuningModule : Ultimate Sensitivity Method

The problem now arises in putting these figures obtained into practice. For example the process iscontrolled by a Fischer Porter electronic controller. We find that to set the PB setting at 19 2 will require agood deal of guesstimation ; the control is not that precisely calibrated. The switched reset control gives a choice of 12 MPR or 6MPR there is no position for 11 minutes. The rate controller setting has figures of 4 Minutes or 2 Minutes. Which settings should be used? The example used a temperature control process, a typically sluggish system. With sluggish systemsreset windup is a potential problem set the reset to 12 minutes. Sluggish systems generally benefit from derivative action, set D to 4 minutes increased derivative) andcheck for stability. fthere is evidence of instability due to the increased derivative action the setting willhave to be reduced to the 2 minute setting.

Decisions of this type must be based upon both the type of process being controlled and previousexperience. In general it can be said that:Temperature Processes are generally sluggish. They are more tolerant of high derivative settings than highreset settings.Flow Processes are fast ctingtolerant with respect to higher reset settings, hardly if ever feasible to usederivative action.Level Processes response dependent upon capacitance of system each case must be considered on itsmerits.Note: We have discussed only one possibly the best known and widely accepted as one of the best) tuningtechnique. There are many other techniques available which vary considerably in approach andimplementation. Tuning controllers is as much an art as it is a science.

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instrumentation tuning theory

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