dycops pi tuning

7/17/2019 Dycops PI Tuning

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The setpoint overshoot method:A simple and fast closed-loop approach for PI/PID tuning

Mohammad ShamsuzzohaSigurd Skogestad

Department of Chemical Engineering

Norwegian University of Science and Technology (NTNU)Trondheim

Dycops symposium, Leuven, July 2010


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Desborough and Miller (2001): More than 97% of controllers are PID

Vast majority of the PID controllers do not use D-action.

PI controller: Only two adjustable parameters

but still not easy to tune

Many industrial controllers poorly tuned

Ziegler-Nichols closed-loop method (1942) is popular, but

Requires sustained oscillations

Tunings relatively poor

Big need for a fast and improvedclosed-loop tuning procedure

Motivation


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Outline

1. Existing approaches to PI tuning

2. SIMC PI tuning rules

3. Closed-loop setpoint experiment

4. Correlation between setpoint response and SIMC-settings

5. Final choice of the controller settings (detuning)

6. Analysis and Simulation

7. Conclusion


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Step 1: Open-loop experiment: Most tuning approaches are based on open-loop plant model

gain (k),

time constant ( ) time delay ( )

Problem: Loose control during identification experiment

Step 2: Tuning

Many approaches

IMC-PID (Rivera et al., 1986): good for setpoint change

SIMC-PI (Skogestad, 2003): Improved for integrating disturbances

IMC-PID (Shamsuzzoha and Lee, 2007&2009) for disturbance rejection

1. Common approach:

PI-tuning based on open-loop model

-ske

g(s)= s+1


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Ziegler-Nichols (1942) closed-loop method

Step 1. Closed-loop experimentUse P-controller with sustained oscillations. Record:1. Ultimate controller gain (Ku)

2. Period of oscillations (Pu)

Step 2. Simple PI rules:Kc=0.45Kuand I=0.83Pu.

Advantages ZN:

Closed-loop experiment

Very little information required Simple tuning rules

Disadvantages:

System brought to limit of instability Relay test (strm) can avoid this problem but requires the feature of switching to on/off-

control

Settings not very good: Aggressive for lag-dominant processes (Tyreus and Luyben) andquite slow for delay-dominant process (Skogestad).

Only for processes with phase lag > -180o(does not work on second-order)

Alternative approach:

PI-tuning based on closed-loop data only


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Want to develop improved and

simpler alternative to ZN:

Closed-loop setpoint response

with P-controller

Use P-gain about 50% of ZN Identify key parametersfrom

setpoint response:

Simplest to observe is first

peak!

This work.

Improved closed-loop PI-tuning method

Idea: Derive correlation between key parameters and SIMC PI-

settingsfor corresponding process


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2. SIMC PI tuning rules

First-order process with time delay:-ske

g(s)=s+1

PI controller:

( ) cI

1c s =K 1+

s

SIMC PI controller based on direct synthesis:

c =

( )c c

K = k + { }I c =min , 4( +)

Fast and robustsetting:


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Procedure: Switch to P-only mode and make

setpoint change Adjust controller gain to get

overshoot about 0.30 (30%)

Record key parameters:

1. Controller gain Kc02. Overshoot = (yp-y)/y3. Time to reach peak (overshoot), tp4. Steady state change, b = y/ys.

Estimate of y

without waiting to settle:

y

= 0.45(yp+ yu)

Advantages compared to ZN:

* Not at limit to instability

* Works on a simple second-order process.

3. Closed-loop setpoint experiment

Closed-loop step setpoint response with P-only control.


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Various overshoots (10%-60%)

10 1

se

gs

=+

0 5 10 15 20 25 300

0.25

0.5

0.75

1

1.25

time

OUTPUTy

Setpoint

/=1 (Kc0

=0.855)

/=0.4 (Kc0

=0.404)

/=100 (Kc0

=79.9)

/=2 (Kc0

=1.636)

/=5 (Kc0

=4.012)

/=10 (Kc0

=8.0)

/=0.2 (Kc0

= 0.309)

/=0 (Kc0

= 0.3)

Closed-loop setpoint experiment

Overshoot of 0.3 (30%) with different s

30%

=0

=100

=2

Small : Kc0small and b small

0 5 10 15 20 250

0.25

0.5

0.75

1

1.25

1.5

time

OUTPUT

y

oe!"#oot=0.10 (Kc0

=5.64)

oe!"#oot=0.20 (Kc0

=6.87)

oe!"#oot=0.30 (Kc0

=8.0)

oe!"#oot=0.40 (Kc0

=9.1)

oe!"#oot=0.50 (Kc0

=10.17)

oe!"#oot=0.60 (Kc0

=11.26)

"etpoint


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Estimate of yusing undershoot yu

Data: 15 first-order with delay processes using 5 overshoots each (0.2, 0.3, 0.4, 0.5, 0.6). y s=1

Conclusion:

y 0.45( yp+yu)


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4. Correlation between Setpoint response

and SIMC-settings

Goal: Find correlation between SIMC PI-settings and keyparameters from 90 setpoint experiments.

Consider 15 first-order plus delay processes:

/ = 0.1, 0.2, 0.4, 0.8, 1, 1.5, 2, 2.5, 3, 5, 7.5, 10, 20, 50, 100

For each of the 15 processes:

Obtain SIMC PI-settings (Kc,I)

Generate setpoint responses with 6 different overshoots (0.10,0.20, 0.30, 0.40, 0.50, 0.60)and record key parameters(Kc0,overshoot, tp, b)

-

( ) 1

se

g ss

=

+


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Fixed overshoot:

Slope Kc/Kc0= A approx. constant,

independent of the value of /

c

c0

K=A

K

Correlation Setpoint response and SIMC PI-settings

Controller gain (Kc)

Kc0

Kc10%:

A=0.87

30%:

A=0.63

60%:

A=0.45

Agrees with ZN (approx. 100% overshoot):

Original: Kc/Kcu= 0.45

Tyreus-Luyben: Kc/Kcu= 0.33

90 cases: Plot Kcas a function of K

c0


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0.1 0.2 0.3 0.4 0.5 0.60.4

0.5

0.6

0.7

0.8

0.9

oe!"#oot ($!%ction%&)

'

'=1.152(oe!"#oot)21.607(oe!"#oot)1.0

2A= 1.152(overshoot) - 1.0!(overshoot) + 1.0 Overshoots between 0.1 and 0.6(should not be extended outside this range).

Conclusion: Kc= Kc0A

A = slope

overshoot


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( )I1

" =2A

1-"

SIMC-rules

Case 1 (large delay): I1=

Case 2 (small delay): I2= 8

Case 1 (large delay):

= 2kKc (substitute = I into the SIMC rule for Kc)

c c0 c c0 c0kK =kK K K kK A =

c0

"

kK = (1-")

Correlation Setpoint response and SIMC PI-settings

Integral time (I

)

(from steady-state offset)

Conclusion so far:

Still missing: Correlation for

c

0.5K =

k

( )c

c

K = k +

c =

{ }I c =min , 4( +)


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0.1 0.3 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Oe!"#oot

/t

p

0.43 (*1

)

0.305 (*2

)

/=0.1

/=8

/=100

/=1

( )I I1 I #2 #

" =min( , ) min 0.$A t t, 2.44

1-"

=

Correlation betweenand tp

/tp

overshoot

Use:

/tp= 0.43 for I1 (large delay)

/tp

= 0.305 for I2

(small delay)

Conclusion:

tp


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%hoice o& 'etning &ctor F*

F=1 !ood tradeoff "et#een fast and ro"ust (I/% ith $c=%

F&1:moother contro ith more ro"ustness

F'1to speed upthe cose'-oo# res#onse.

0c cK = K A F

( )#I # =min 0.$A ,

"

t t1-" 2.44

F

2A= 1.152( ) - 1.overshoot overs0!( ) + 1.0hoot

From P-control setpoint experiment record key parameters:1. Controller gain Kc02. Overshoot = (yp-y)/y3. Time to reach peak (overshoot), tp4. Steady state change, b = y/ys

Proposed PI settings (including detuning factor F)

5. Summary setpoint overshoot method


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6. Analysis: Simulation PI-control

5 1

se

gs

=+

First-order + delay process

0 20 40 60 800

0.25

0.5

0.75

1

1.25

time

OUTPUT

y

P!opo"e+ met#o+ ,it# -=1 (oe!"#oot=0.10)



S*/ (c==1)

t=0: Setpoint change t=40: Load disturbance

in training setsimilar response as SIMC


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sg e

=

Pure time delay process

0 6 12 18 24 300

0.5

1

1.5

2

time

OUTPUT

y




S*/ (c==1)

Analysis: Simulation PI-control

in training set


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sg e s

=

Integrating process

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3

time

OUTPUT

y


P!opo"e+ met#o+ ,it# -=1 (oe!"#oot=0.302)P!opo"e+ met#o+ ,it# -=1 (oe!"#oot=0.60)

S*/ (c==1)


in training set


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( ) ( )

1

1 0.2 1g

s s=

+ +

Second-order process

0 2 4 6 8 100

0.25

0.5

0.75

1

1.25

1.5

time

OUTPUT

y



S*/ (c=

e$$ectie=0.1)


Not in training set


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21Responses for PI-control of high-order process g=1/(s+1)(0.2s+1)(0.04s+1)(0.008s+1).

( ) ( ) ( ) ( )

1

1 0.2 1 0.04 1 0.00$ 1g

s s s s=

+ + + +

High-order process

0 5 10 15 200

0.25

0.5

0.75

1

1.25

time

OUTPUT

y



S*/ (c=

e$$ectie=0.148)


Not in training set


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( )2

1

1g

s s

=+

Third-order integrating

process

0 40 80 120 160 2000

1

2

3

4

5

time

OUTPUT

y




S*/ (c=

e$$ectie=1.5)


Not in training set


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5 1

se

g

s

=

First-order unstable process

0 20 40 60 800

0.5

1

1.5

2

time

OUTPUT

y





Not in training setNo SIMC settings available


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0 2 4 6 8 100

0.25

0.5

0.75

1

1.25

time

OUTPUT

y

-=1.0 (oe!"#oot=0.322)

-=2.0 (oe!"#oot=0.322)

-=3.0 (oe!"#oot=0.322)

-=0.8 (oe!"#oot=0.322)

Kc

I

/s

0.$ 11.23 0.!! 1.3

1.0 3.01 0.35$ 1.!4

2.0 4.52 1.32 1.

.0 .01 2.$! 1.24

Effect of detuning factor F

Second-order process

( ) ( )

1

1 0.2 1

g

s s

=+ +



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6. Conclusion

From P-control setpoint experiment obtain:

1. Controller gain Kc0

2. Overshoot = (yp-y)/y

3. Time to reach peak (overshoot), tp

4. Steady state change, b= y/ys,

Estimate: y= 0.45(yp+ yu)

PI-tunings for Setpoint Overshoot Method:

c c0K = K A ,F 2A= 1.152(overshoot) - 1.0!(overshoot) + 1.0

( )I # #

" =min 0.$A t , 2.44t

1-"

F

F=1:oo' tr'e-o&& "eteen #er&ormnce n' ro"stness

F&1:moother

F'1:#ee' #

Probably the fastest PI-tuning approach in the world

(Shamss setpoint method)


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REFERENCES

strm, K. J., Hgglund, T. (1984). Automatic tuning of simple regulators with specifications onphase and amplitude margins,Automatica,(20), 645651.

Desborough, L. D., Miller, R. M. (2002). Increasing customer value of industrial control performancemonitoringHoneywells experience. Chemical Process ControlVI (Tuscon, Arizona, Jan. 2001),AIChE Symposium Series No. 326. Volume 98, USA.

Kano, M., Ogawa, M. (2009). The state of art in advanced process control in Japan, IFAC symposium

ADCHEM 2009, Istanbul, Turkey. Rivera, D. E., Morari, M., Skogestad, S. (1986). Internal model control. 4. PID controller design,Ind.

Eng. Chem. Res.,25 (1) 252265.

Seborg, D. E., Edgar, T. F., Mellichamp, D. A., (2004). Process Dynamics and Control, 2nd ed., JohnWiley & Sons, New York, U.S.A.

Shamsuzzoha, M.,Skogestad. S. (2010). Report on the setpoint overshoot method(extended version)http://www.nt.ntnu.no/users/skoge/.

Skogestad, S., (2003). Simple analytic rules for model reduction and PID controller tuning, Journal ofProcess Control,

13, 291309. Tyreus, B.D., Luyben, W.L. (1992). Tuning PI controllers for integrator/dead time processes,Ind.Eng. Chem. Res.26282631.

Yuwana, M., Seborg, D. E., (1982). A new method for on-line controller tuning,AIChEJournal28(3) 434-440.

Ziegler, J. G., Nichols, N. B. (1942). Optimum settings for automatic controllers. Trans.ASME, 64,759-768.


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Scaled proportional and integral gain for SIMC tuning rule.

On dimensionless form,

the SIMC (c= )

6

c c

K =kK =0.5

6 cI

I

kK 1K = =m)7 0.5,

1

I c IK =K is known as the integral gain.

Note:Integral term (KI?) is most important for delay dominant processes ( /


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Abstract

The PI controller is widely used in the process industries due to simplicity androbustness, It has wide ranges of applicability in the regulatory control layer.

The proposed method is similar to the Ziegler-Nichols (1942) tuning method.

It is faster to use and does not require the system to approach instability withsustained oscillations.

The proposed tuning method, originally derived for first-order with delayprocesses and tested on a wide range of other processes and the results arecomparable with the SIMC tunings using the open-loop model.

Based on simulations for a range of first-order with delay processes, simplecorrelations have been derived to give PI controller settings similar to those ofthe SIMC tuning rules.

The detuning factor F that allows the user to adjust the final closed-loopresponse time and robustness.

The proposed method is the simplest and easiest approachfor PI controllertuning available and should be well suited for use in process industries.

dycops pi tuning

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