ChE 491 / 433

transcript

ChE 491 / 433

22 Oct 12

ChE 491 / 43322 Oct 12

Ziegler-Nichols (ZN I)

(QDR or QAD Tuning)

(Ultimate Gain)

sE+ sR sC)(sM

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Feedback Controller Tuning: (General Approaches)

1) Simple criteria; i.e QAD via ZN I, tr, etc• easy, simple, do on existing process• multiple solutions

2) Time integral performance criteria• ISE integral square error• IAE integral absolute value error• ITAE integral time weighted average error

3) Semi-empirical rules• FOPDT (ZN II)• Cohen-Coon

4) ATV, or Autotuning5) Trial and error6) Rules of thumb

Procedure, done closed loop (on-line):

Ziegler Nichols I (Ultimate Gain Method)

• P-Only (switch off integral & derivative modes)• Controller in Auto mode (closed loop)• Adjust Kc

o “bump” process with small setpoint changeo Find Kc where loop response is undamped

Time Time Time

Dynamic Changes as Kc is Increased for a FOPDT Process

gainultimateKCU

Procedure, done closed loop (on-line):

• P-Only (switch off integral & derivative modes• Controller in Auto mode (closed loop)• Adjust Kc

o “bump” process with small setpoint changeo Find Kc where loop response is undamped

• Record Kc (call it Kcu – the ultimate gain)• Measure Tu (the ultimate period)• Use Table 7-1.1 to get tuning constants• Adjust controller settings to calculated values• Test to see if need to make fine adjustments

Quarter-decay-ratio response (sometimes called QAD)

Response to disturbance should be close to QDR (QAD)

• Don’t need to know mathematical models• Easy to use• Use on any process you can get to oscillate

Advantages:

• Must force loop / process to oscillate (operating close to unstable)• Tuning constants not unique, except for P-only

Disadvantages:

Quarter Decay Ratio (QAD)

• Good for load disturbances• Prevents large initial deviations w/o too much oscillations• Gives good “Ball Park” values; leading to fast responses

for most processes

Advantages:

• For SP changes, may overshoot too much

• Parameters for PI, PID, not unique

• May be too aggressive for cases where K or to change.

Disadvantages:

PS Exercise: Tuning Two Tanks in Series

• Launch Loop Pro Trainer• Select Case Studies• Select Gravity Drained Tanks

• Press the pause button• Adjust controller output to 50%• Press run (continue) button and let run till achieve steady

state• Click the rescale button to re center the plot• Adjust controller output to achieve a level in tank 2 of 2

meters• Click the controller button and turn to PID control (P-Only)

• You may have to turn the Integral part off; and Kc = 4 %/m

• Press run button and adjust the disturbance up and down 0.5 l/min

• Then adjust the set point up and down 0.5 m• Observe how the system behaves.

Loop Pro Trainer (process simulator):

• Now, double Kc and observe effect.• Double it again…• Try it at Kc = 2 %/m

• Now turn on the Integral term (tI should be 4.0 min) and do the same adjustments, observing the behavior of the system.

• You may need to adjust the History to see the full change.

• Change tI and observe the effect.• Make sure you are back to the original settings (SP = 2m,

Level at 2 m, etc) when you start and end with the PI controller.

• Now turn on the Integral term (tI should be 4.0 min) and do the same adjustments, observing the behavior of the system.

• You may need to adjust the History to see the full change.

• Change tI and observe the effect.• Make sure you are back to the original settings (SP = 2m,

Level at 2 m, etc) when you start and end with the PI controller.

Now let’s tune the controller.• Use the Ziegler Nichols I method to find Kcu and Tu.• Tune the controller for:

• P – only control• And then for PI control.

Loop-Trainer

Kcu ~ 72, delta R = 4 –> 4.5

Kcu ~ 72, delta R = 4 –> 4.5…set Kc = 1/2Kcu = 36

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22 Oct 12

PS Exercise: Tuning Two Tanks in SeriesDifferent opinions:1. Different correlations will give different constants in the controller

equations. D. Cooper suggests if one is uncertain, to start conservative, i.e. with the smallest controller gain and the largest integral (reset) time, thus, giving the least aggressive controller. Final controller tuning may best be performed on-line by trial and error, using experience and knowledge of the process, to obtain the desired controller performance.

To changes in the setpoint or load disturbances:• if the process response is sluggish; Kc is too small and/or tI is

too large.• if the process response is too quick and perhaps oscillating is

not desired; Kc is too large and/or tI is too small.2. Ziegler-Nichols may be too aggressive for many ChE applications. Luyben

(Plantwide Dynamic Simulators in Chemical Processing and Control, Wiley, 2002) suggests for PI controller Kc = Ku / 3.2 and tI = 2.2 * Tu .

Step Change Responses:

Is Kc or tI too high?

Kc too large Properly tuned

controller

tI too large

COortm %)(

PVortc )(

COortm %)(

PVortc )(

3) Semi-empirical rules; FOPDT fit to Open Loop Step Test • Ziegler-Nichols Open Loop (ZN II)• Cohen-Coon

Ziegler Nichols II (ZN II)

Fit response to FOPDT model

sE+ sR sC)(sM

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tKinallKKK PTV ,,

Procedure, usually done open loop:

Ziegler Nichols II (FOPDT fit)

• Put controller in Manual mode• Manually make step change in controller output• Observe (record) data and fit to FOPDT model

seKfit

timedeadprocesseffectivettconstatimeprocesseffective

gainSSprocessK

Open-Loop Step Test……..FOPDT

Open-Loop Step Test……..FOPDT: Loop Pro Method

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Open-Loop Step Test……..FOPDT: Smith & Corripio Method

ot&tOpen-Loop Step Test……..FOPDT: Smith & Corripio Method

Estimation of Fit 3 suggested for non-integrating processes:

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Fit 3: 7-2.16 p 239

ot&tOpen-Loop Step Test……..FOPDT: Smith & Corripio Method

Estimation of Fit 1 suggested for integrating processes.

outF = constant

non-integrating process(self-regulating)

)(tuAFif in

integrating process

What happens to h ??

Procedure in open loop:Ziegler Nichols II (FOPDT fit)

• Put controller in Manual mode• Manually make step change in controller output• Observe (record) data and fit to FOPDT model

seKfit

t timedeadprocesseffectivettconstatimeprocesseffective

gainSSprocessK

nt5.01.0

Procedure same as for ZN II (open loop step test):

Cohen-Coon: • The Ziegler-Nichols rules are more sensitive to the ratio of dead time to

time constant, and work well only on processes where the dead time is between 1/4 and 2/3 of the time constant.

• The Cohen-Coon tuning rules work well on processes where the dead time is between 1/10 and 4 times the time constant.

• “Quarter-amplitude damping-type tuning also leaves the loop vulnerable to going unstable if the process gain or dead time doubles in value.” Smuts suggests reducing Kc by ½ to avoid problems later on.

* Jacques F. Smuts, Process Control for Practitioners, Opticontrols, Inc (2011)

PS Exercise: Compare “Loop Pro” and “Fit 3” FOPDT Methods

• Press the pause button• Adjust controller output to 51%• Tune controller for operation around a tank level of 2 meters

PS Exercise: Use The Step Test (ZN II, or Open Loop FOPDT Fit) to Tune The PI

Controller

ChE 491 / 433 29 Oct 12

• disturbance/load change

• setpoint change

Time Integral Performance Criteria

)(tc )(oldSP

Integrate error from old SP

)(tc SPnew

Integrate error from new SP

Smith/Murrill developed unique tuning relationships

• IAE (Integral of the Absolute value of the Error)

• ITAE (Integral of the Time-weighted Absolute value of the Error)

)( dtteIAE

)( dttetITAE

• Determine type of input/forcing function (i.e. purpose of controller)• maintain c(t) at setpoint (“Regulator” controller)• c(t) track setpoint signal (“servo” control)

Eqn: 7-2.17 p 245

PS EX: Find PI Parameters for IAE Criteria

• Put your PI tuning parameters into the simulator controller and check tuning.

• Do the parameters need to be adjusted?

In-Class EX: Loop Pro Demo Fitting

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• Single step; can be analyzed by hand• Pulse, doublet, pseudo-random binary sequence (PRBS) tests;

require computer tools for analysis

Step Testing Thoughts

Data collected should meet these criteria:• Process at steady state before data collected• Signal to noise ratio should be 10 or greater• Collected data should be done when no disturbances were present• After fitting, the model appears to fit the data visually

Step Testing ThoughtsSingle step+ simple, graphical analysis can be done- long time away from desired operating level (DLO; or SP)- Data only on one side of DLO

Pulse (two step tests in rapid succession; 1 up and 1 back down)+ only need to let measured process variable show a clear response- long time away from desired operating level (DLO; or SP)- Data only on one side of DLO

Step Testing ThoughtsDoublet Test+ two pulse tests; one up; one down; ending at beginning level+ obtain data on both sides of DLO+ relatively quickly return to normal operation level+ a preferred method of some in industry for open loop tests- since done open loop; could be concern for certain systems

Step Testing ThoughtsPRBS Test (pseudo-random binary sequence )+ theoretically PV shouldn’t vary far from DLO- need a well defined, random test- should have some idea of process gain, time constant, and

deadtime- might take longer than a doublet test

Step Testing Comparisons

Doublet

• Can do closed loop studies, and fit to FOPDT• Controller aggressive enough for 10 times S to N response• Data should begin and end at steady state• No load disturbances should occur• Do step, pulse, doublet changes to the set point.• Fit data to FOPDT; check tuning parameters on the process

Step Testing Thoughts

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Relay feed back test or ATVAuto-Tune Variation (ATV)*

+ Keeps process close to normal operation+ More efficient for process with long time constant.

* Åström and Hägglund (1983);* Luyben & Luben (1997)

General method:• determine reasonable h value to move FCE (3 – 10 % change)• Input the change +h• When PV starts to move, input change of –2h• When PV cross the set point, input change of +2h• When PV re-crosses the set point, input change of –2h• Repeat until constant oscillations of PV are maintained (~3-4 cycles)• Record amplitude (a) and period of oscillation (Pu)

)(tc sp

Auto-Tune Variation (ATV)

• Calculate Ku from ATV results.*

• ZN settings

• TL settings** (less aggressive and recommended for more sluggish processes)

2.1/45.0 uZNIu

ZNc PKK t

45.0/31.0 uTLIu

TLc PKK t

* Riggs & Karim (2006)** TL = Tyreus & Luben

Relay feed back test or ATVAuto-Tune Variation (ATV)

+ Keeps process close to normal operation+ More efficient for process with long time constant.

0 20 40 60Time (hours)

Open Loop Test

ATV Test

Riggs & Karim (2006)

PS EX: Find PI Parameters using the ATV Method

Auto-Tune or Self-Tuning Controllers

General loop auto-tuning:• On demand or on-the-fly (continuous updating)• Can be simple step test or pulse doublet• Can be sophisticated self-tuning for difficult processExample single point industrial controllers:

http://www.watlow.com/downloads/en/manuals/945e_a.pdf

Example single point industrial controllers:

• Select the tuning criterion for the control loop.• Apply filtering to the sensor reading• Determine if the control system is fast or slow

responding.– For fast responding, field tune (trail-and-error)– For slow responding, apply ATV-based tuning

Trial and Error (field tuning)*

* J.B. Riggs, & M.N. Karim Chemical and Bio-Process Control, 3rd ed. (2006)

• Turn off integral and derivative action.• Make initial estimate of Kc based on process knowledge.• Using setpoint changes, increase Kc until tuning criterion

is met

• Decrease Kc by 10%.• Make initial estimate of tI (i.e., tI=5tp).• Reduce tI until offset is eliminated• Check that proper amount of Kc and tI are used.

Trial and Error (field tuning)*

* J.B. Riggs, & M.N. Karim Chemical and Bio-Process Control, 3rd ed. (2006)

Kc and tI levels good?

Rules of Thumb

• Flow Loops: typically PI controllers; PB ~ 150;• Level Loops: PI for tight control; P for multiple tanks in series;• Pressure Loops: can be fast or slow (like P control by controlling

condenser)• Temperature Loops: typically moderately slow; typically might use PID

controller; PB fairly low (depends on gains); integral time on order of process time constant, with faster process derivative time ~ ¼ the process time constant.

* D.A.Coggan, ed., Fundamentals of Industrial Control, 2nd ed., ISA, NC (2005)

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min1.0It

** W.L.Luyben, Process Modeling, Simulation and Control for Chemical Engineers, 2nd ed., McGraw-Hill (1990)

Higher Order Process

ChE 491 / 433

ChE 491 / 433

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