Dycops_PI-Tuning [Compatibility Mode]

8/8/2019 Dycops_PI-Tuning [Compatibility Mode]

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

Mohammad Shamsuzzoha

Sigurd Skogestad

Department of Chemical Engineering Norwegian University of Science and Technology (NTNU)Trondheim

1 Dycops symposium, Leuven, July 2010


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Vast majority of the PID controllers do not use D-action. PI controller: Only two adjustable parameters

u s no easy o une Many industrial controllers poorly tuned

Ziegler-Nichols closed-loop method (1942) is popular, but Requires sustained oscillations Tunings relatively poor

Big need for afast and improvedclosed-loop tuning procedure

2


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utl ne

1. Existing approaches to PI tuning2. SIMC PI tuning rules. -

4. Correlation between setpoint response and SIMC-settings

5. Final choice of the controller settings (detuning)6. Analysis and Simulation7. Conclusion

3


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1. Common approach:

PI-tuning based on open-loop model

Step 1: Open-loop experiment: Most tuning approaches are based on open-loop plant model , time constant ( ) time delay ( )

Problem: Loose control durin identification ex eriment

Step 2: TuningMan a roaches IMC-PID (Rivera et al., 1986): good for setpoint change SIMC-PI (Skogestad, 2003): Improved for integrating disturbances

4


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Alternative approach:

Ziegler-Nichols (1942) closed-loop method

-tun ng ase on c ose - oop ata on y

Step 1. Closed-loop experimentUse P-controller with sustained oscillations. Record:1. Ultimate controller gain (K u)2. Period of oscillations (Pu)

Step 2. Simple PI rules: K c=0.45K u and 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

5

e ngs no very goo : ggress ve or ag- om nan processes yreus an uy enand quite slow for delay-dominant process (Skogestad).

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


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This work.

- -

Want to develop improved and

y

simpler alternative to ZN: Closed-loop setpoint response

with P-controller Use P-gain about 50% of ZN

Identify key parameters fromset oint res onse:

p y y s y

u y

Simplest to observe is first peak! pt

t 0t =

Idea: Derive correlation between key parameters and SIMC PI-settingsfor corresponding process

6


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2. IM PI tun ng rules

First-order process with time delay:- skeg(s)=

sPI controller:

( ) c I1

c s =K 1+ s

SIMC PI controller based on direct synthesis:

c

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

=

c

Fast and robust setting:

7

c


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-Procedure:

s y

-

setpoint change Adjust controller gain to getovershoot about 0.30 (30%)

p y

y

s y

u y

Record key parameters:

1. Controller gainK c0= -

. p 3. Time to reach peak (overshoot),t p4. Steady state change, b = y / ys.

pt

t 0t =

s ma e o y w ou wa ng o se e: y = 0.45( y p + yu )

Advantages compared to ZN:

8

ot at m t to nsta ty* Works on a simple second-order process.

ose - oop s ep se po n response w -on y con ro .


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-

-

Overshoot of 0.3 30% with different s

se= 1.5

10 1 s +

1

1.25

Setpoint

/ =100 (Kc0

=79.9)

/ =10 (Kc0

=8.0)

=1001

1.25

y

0.5

0.75

O U T P U T y

/ =1 (Kc0

=0.855)

/ =2 (Kc0

=1.636)

/ =5 (Kc0

=4.012)

=2

0.5

0.75

O U T P U T

overshoot=0.10 (K c0=5.64)



0

0.25

/ =0.4 (Kc0=0.404)

/ =0.2 (Kc0

= 0.309)

/ =0 (Kc0

= 0.3) =0

0

0.25

overshoot=0.40 (Kc0

=9.1)



setpoint

9

time

Small : K c0 small and b small

0 5 10 15 20 25time


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Est mate o y us ng undershoot yu1,2

overshoot=0.6 y

1

overshoot=0.5

overshoot=0.4overshoot=0.3

overshoot=0.2

s y

Line: y = 0.8947( yp+ yu )/2

0,6

,

y

p y y s y

u

0,4 pt

t 0t =

0

0,2 Conclusion: y 0.45( yp+ yu)

10

0 0,2 0,4 0,6 0,8 1 1,2

( yp+ yu )/2

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


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4. Correlation between Set oint res onseand SIMC-settings

Goal: Find correlation between SIMC PI-settings and key parameters 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

-

( )1

se g s

s

=

+

For each of the 15 processes: Obtain SIMC PI-settings (K c, I) Generate setpoint responses with 6 different overshoots (0.10,

0.20, 0.30, 0.40, 0.50, 0.60) and recordkey parameters(K c0,overshoot, t p, b)

11


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Correlation Setpoint response and SIMC PI-settings

Controller gain (K c)90 cases: Plot K as a function of K

40

50 0.10 overshootkKc=0.8649kK c00.20 overshootkKc=0.7219kK c00.30 overshootkKc=0.6259kK c0 K

K c 10%:A=0.8730%:A=0.63

60%:A=0.45

30

k K

c

0.40 overshootkKc=0.5546kK c00.50 overshootkKc=0.4986kK c00.60 overshootkK

c=0.4526kK

c0

2

2.5

c

c0

=AK

10

20

0.5

1

1.5

0 20 40 60 80 100 1200

kKc0

0 1 2 3 4 5 60

K c0

12

Slope K c/K c0 = A approx. constant,independent of the value of /

.Original: K c/K cu = 0.45

Tyreus-Luyben: K c/K cu = 0.33


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0.9

= 2 -

onclus on: K c = c0

0.7

0.8

. - . .

A = slope

0.6

.

A

0.1 0.2 0.3 0.4 0.5 0.60.4

0.5

overshoot (fractional)

overshoot

2A= 1.152(overshoot) - 1.607(overshoot) + 1.0

13

Overshoots between 0.1 and 0.6

(should not be extended outside this range).


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Correlation Setpoint response and SIMC PI-settings

Integral time ( I)

SIMC-rules

Case 1 (large delay): I1 = ase sma e ay: I2 Case 1 (large delay) :

= 2kK c (substitute = I into the SIMC rule for K c)

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

c0 bkK = (from steady-state offset)

( )I1 b

=2A1-b

-

Conclusion so far:

14 Still missing: Correlation for


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0.5 / =0.1

orrelat on between and t p

0.4

0.43 ( I1)

/ =8

/ =1

/t p p y y s yu y

s

0.2

0.3 / t

p

. I2 =

pt

t 0t =

t p

0.1

overshoot

Use: /t p = 0.43 for I1 (large delay) /t p = 0.305 for I2 (small delay)

0.1 0.3 0.5 0.6Overshoot

b Conclusion:

15 ( )I I1 I p2 p =m n , m n . , .

1-b

=


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From P-control setpoint experiment record key parameters:1. Controller ainK

.

c2. Overshoot = ( y p- y )/ y3. Time to reach peak (overshoot),t p4. Steady state change, b = y / ys

0c cK =K A F

Proposed PI settings (including detuning factor F)

=min 0.86A b t t2.44

F

2A= 1.152( ) - 1.6overshoot overs07( ) + 1.0hoot

Choice of detuning factor F :

1-b

16

F=1. Good tradeoff between fast and robust (SIMC with c= )

F>1: Smoother control withmore robustness F


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6. nalys s: mulat on PI-control1.25

se=

First-order + delay process

1

5 1 s +0.75

U T P U T

y

in trainin set

0.25

0.5

Proposed method with F=1 (overshoot=0.10)Proposed method with F=1 (overshoot=0.298)

similar response as SIMC

0 20 40 60 800

time

ropose me o w = overs oo = .SIMC ( c==1)

17

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


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2

nalys s: mulat on PI-control

Pure time delay process

1.5

g e=

1 T P U T

y

in trainin set

0.5

O

Proposed method with F=1 (overshoot=0.10)

0 6 12 18 24 300

.Proposed method with F=1 (overshoot=0.60)SIMC ( c==1)

18


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3


sIntegrating process2.5

1.5

2

T P U T

y

in trainin set

1

O U

Proposed method with F=1 (overshoot=0.108)= =

0 20 40 60 80 1000

0.5

.Proposed method with F=1 (overshoot=0.60)SIMC ( c==1)

19


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Second-order process1.25

1.5

( )( )1 0.2 1 g

s s=

+ +1

P U T

y

0.5

. O U


ot n tra n ng set

0 2 4 6 8 100

0.25

Proposed method with F=1 (overshoot=0.322)Proposed method with F=1 (overshoot=0.508)SIMC ( c=effective =0.1)

20 Responses for PI-control of second-order process g=1/(s+1)(0.2s+1).

time


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1=

High-order process

1

1.25

1 0.2 1 0.04 1 0.008 1 s s s s+ + + +

0.75 T P U T

y

0.5 O

Proposed method with F=1 (overshoot=0.104)Pro osed method with F=1 overshoot=0.292

ot n tra n ng set

0 5 10 15 200

.

Proposed method with F=1 (overshoot=0.598)SIMC ( c=effective =0.148)

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


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Pro osed method with F=1 overshoot=0.106


5


Proposed method with F=1 (overshoot=0.610)SIMC ( c=effective =1.5)

1=

r -or er n egra ngprocess4

y

( )1 s s +2 O

U T P U T

Not in training set

0 40 80 120 160 2000

1

22

time


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seFirst-order unstable process

2


Proposed method with F=1 (overshoot=0.30)Proposed method with F=1 (overshoot=0.607)

5 1 s 1.5

P U T

y

0.5

O U

No SIMC settings available

0 20 40 60 800

23

me


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1.25

Second-order process

0.75

1

U T

y

F K M

( )( )1 0.2 1 g

s s=

+ +

0.5 O U T

0.8 11.29 0.77 1.96

1.0 9.031 0.958 1.74

0 2 4 6 8 100

0.25

= . overs oot= .F=2.0 (overshoot=0.322)F=3.0 (overshoot=0.322)F=0.8 (overshoot=0.322)

2.0 4.52 1.92 1.363.0 3.01 2.87 1.24

24

time


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6. onclus on

-

From P-control setpoint experiment obtain:

s y

y

. on ro er ga n c02. Overshoot= ( y p- y )/ y3. Time to reach peak (overshoot),t p4. Steady state change, b = y / ys,

p y s yu y

Estimate: y = 0.45( y p + yu )

PI-tunings for Setpoint Overshoot Method :c c0K=K A ,F 2A= 1.152(overshoot) - 1.607(overshoot) + 1.0

pt

t 0t =

( )I p p b =min 0.86A t , 2.44t1-b

F

F=1 : Good trade-off between performance and robustness>

25

F


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REFEREN E strm, K. J., Hgglund, T. (1984). Automatic tuning of simple regulators with specifications on

phase 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, IFACsymposium 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., JohnW ey & Sons, New Yor , 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 of Process Control, 13, 291309.

Tyreus, B.D., Luy en, W.L. 1992 . Tun ng PI contro ers or ntegrator ea t me processes, In . Eng. Chem. Res. 26282631.

Yuwana, M., Seborg, D. E., (1982). A new method for on-line controller tuning, AIChE Journal 28(3) 434-440.

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

26

- .


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'

IM PI tun ng rules

cOn mens on ess orm,

the SIMC ( c = )

'

I K

'c c

K =kK =0.5

' kK 1

I = I 8 =

Scaled ro ortional and inte ral ain for SIMC tunin rule.

II

= =max . , 16

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

Note:

27

Integra term K I s most mportant or e ay om nant processes


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bstract

robustness, 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 with

sustained oscillations. The proposed tuning method, originally derived for first-order with delay

processes and tested on a wide range of other processes and the results arecom arable with the SIMC tunin s usin the o en-loo 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 of the SIMC tuning rules.

e e un ng ac or a a ows e user o a us e na c ose - oopresponse time and robustness.

The proposed method is thesimplest and easiest approach for PI controller tuning available and should be well suited for use in process industries.

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