valve stiction

Valve Stiction - Definition, Modeling, Detection,

Quantification and Compensation

Dr. M. A. A. Shoukat ChoudhuryDepartment of Chemical Engineering

Bangladesh University of Engineering & Technology (BUET)Dhaka, BANGLADESH

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M. A. A. Shoukat Choudhury2KFUPM, Nov, 2008

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BUETControl Loop Demographics

Acc

epta

ble,

16%

Excellent, 16%

Open Loop, 36%

Poor, 10%

Fair,

22%

(Desborough and Miller, 2002)

valve problems30%

design problem20%

well performing20%

poor tuning30%

(Bialkowski, 1992)


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cause oscillation(s) in process variablespoor controller performance shorten the life of control valvesmay lead to process upsetsnon-uniform end-productsmore off-spec productslarger rejection ratesreduced profitabilityso on ...

Motivation


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BUETA CONTROL VALVE


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Stiction (Static Friction)SaturationHysteresisOversized valve Corroded plug/seatRuptured diaphragmDeadzone so on….

Control Valve Problems


BUETISA Terminology

InstrumentInput Output


BUETInput - Output Plot of Instruments


BUETWhere is Valve Stiction?

CONTROLLERSP

+PV

-PROCESSVALVE

Disturbance

CO / OP MV

SP – Set PointCO – Controller Output (also called OP)MV – Valve output or valve positioner signalPV – Process Variable (Controlled)


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Instrument Society of America (ISA)(ANSI/ISA- S51.1-1979): ``Stiction is the resistance to the start

of motion, usually measured as the difference between the driving values required to overcome static friction upscale and downscale''. The definition was first proposed in 1963 in American National Standard C85.1-1963.

What is Stiction?Stiction = Static Friction


BUETInside a Valve

Stiction

Fluid in out


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In process industries, stiction is measured as a certain % of the valve travel or the span of the control signal.

For example:

2% stiction means that when valve gets stuck it will start moving only after the cumulative change of its control signal is greater than or equal to 2%. If the range of the control signal is 4 to 20 mA then 2% stiction means a cumulative change of the control signal less than 0.32 mA in magnitude will not be able to move the valve.

Stiction in Real Process Industry


BUETStiction in a Level Control Loop

65 70 75 80 85 9060

62

64

66

68

70

72

74va

lve

posi

tion,

mv

controller output, op


BUETProposed Input – Output Plot for Stiction

valv

e ou

tput

(mv)

valve input (op)

deadband stickband

slip jump, j

stickband

+ deadband

mov

ing p

hase

A BC

D

EF

G

s

1. Choudhury, M. A. A. S., Nina F. Thornhill and Sirish L. Shah (2005). Modelling valve stiction, 13, 641-658


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BUETStiction Models

Mechanistic ModelsData Driven Models


BUETLooking Inside a Valve!

Stiction

Fluid in out


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Ff = -Fc sgn(v) - v Fv if v >= 0

-(Fa + Fr ) if v = 0 and |Fa + Fr|<= Fs

-Fs sgn(Fa + Fr ) if v = 0 and |Fa + Fr| > Fs

Fr = - k yFa = A Pa

M d2y

dt2= Fa + Fr +Ff + Fp + Fi

Disadvantages:1. Difficult to simulate 2. Need tailoring for each valve

because the model needs mass and force terms.3. Friction force term is complicated

Mechanistic Model for a Valve


BUETOther Data-Driven Stiction Models

One parameter Model by Hagglund


BUETBasis of Two-Parameter Stiction Model


BUETTwo-parameter Stiction Model


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valve input and valve output (red)

0 50 100 150 200time/s

valve output vs. valve input

linear

deadband

stiction (undershoot)

stiction (no offset)

stiction (overshoot)

Various Types of Stiction


BUETVarious Types of Stiction

J = 0 Pure Deadband

J < S Stiction (Undershoot): Valve output can never reach the valve input

J = S Stiction (Stick-Slip): Valve output reaches the valve input

J > S Stiction (Overshoot): Valve output crossesthe valve input


BUETSimulation using Two Parameter Stiction Model

stiction

deadband stiction

stiction


BUETConcentration Loop

Process:

1103)(

10

+=

−

sesG

s

Obtained from Eborn & Olsson (1995) and Horch & Issakson (1998)

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ssC

10112.0)(

Controller:


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0 100 200 300time/s




mv (red) and op (black) mv (red) and op (black) mv vs. op

0 100 200 300

time/s

mv vs. op

Comparison of Closed Loop Behavior

Data-driven model Mechanistic model


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pv (red) and op (black)

0 100 200 300time/s

pv vs. op




Closed Loop PV-OP Plot


BUETOther Data-Driven Stiction Models

Manabu Kano Model – same as the two parameter model, notations are different.Peter He Model – same as the one parameter model


BUETAssymetric Stiction Modelva

lve

outp

ut (m

v)

valve input (op)

slip jump, JU

SD

mov

ing p

hase

SU

JDJD

JU

JUkd ku

Six parameters – SU, SD, JU, JD, kd, ku


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BUETA CHEMICAL PLANT


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data matrix

poor controllertuning

oscillatorydisturbances nonlinearities Other causes …

diagnosis

Poor performance?

Why?

data

Objectives


BUETNonlinearities

stictioncorroded valve plug/seatoversized valvesaturationdeadzone so on….

nonlinearities

processnonlinearities

valvenonlinearities

Static Friction


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S

S

X1

X2

Y1

Y2

What is Nonlinearity?

If Y=Y1+Y2 and Z=a Y1 S is Nonlinear

SX1+X2 Y

Sa X1 Z


BUETA Simple Example

Squaring function

Y1 = X12

Y2 =X22

Squaring function X1 +X2 Y = X1

2+ X22

+2 X1 X2

a X1 Z = a2 X12

Squaring function

Squaring function

Y=Y1 +Y2 and Z=a Y1 S is NON-LINEAR

X1

X2


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-4 -2 0 2 40

50

100

150

200

250

300 H is togram

X

Num

ber o

f occ

uren

ce

1st moment,m1 = μ = E(x)It represents the mean of the data

2nd moment,m2 (k)= E {x(n) x(n+k)} It represents the spread of the distribution

Second Order Statistics (SOS)

-5 -3 -1 0 1 3 50

0.1

0.2

0.3

0.4

x

pdf

std = 2

-5 -3 -1 0 1 3 50

0.1

0.2

0.3

0.4

x

pdf

std = 2std = 1.5

-5 -3 -1 0 1 3 50

0.1

0.2

0.3

0.4

x

pdf

std = 2std = 1.5std = 1


BUETFourier Transform


BUETDFT


BUETData Representation

0.01 0.1 1.0

3

2

1

Frequency (cycles/time)

Frequency Domain (Power Spectrum)Time-domain trends

0 2000

3

2

1

Samples

Z1 = sin(2*π*0.05*t) + Noise

Z2 = cos(2*π*0.3*t) + Noise

Z3 = 0.5*Z1 + 0.5*Z2

P(f)=DFT {m2(k)}= E[X(f) X(f)*]


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5000-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

erro

r

0 1000 3000

time

error signal to controller

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

mag

nitu

de o

f erro

r

no. of occurence

0

0 100 200 300 400 500

Histogram of error signal

Real flow loop data Almost Gaussian distributionSecond order statistics are sufficient to describe the distribution

5000-2.5

-2

-1.5

-1

-0.50

0.5

1

1.5

2

2.5

erro

r

0 1000 3000time

error signal to controller

1500-2.5

-2

-1.5

-1

-0.50

0.5

1

1.5

2

2.5

mag

nitu

de o

f erro

r

0 500 1000no. of occurence

Histogram of error signal

Real flow loop data Skewed distributionNeeds higher moments to characterizethe distribution for further analysis of this data

Why Look at Higher Moments


BUETDouble Fourier transform

(F)i(F)

)sin(),()cos(),(

),(),( )(

ℑ+ℜ

=+++

==

∫ ∫∫ ∫

∫ ∫∞

∞−

∞

∞−

∞

∞−

∞

∞−

∞

∞−

∞

∞−

+−

dxdyvyuxyxfidxdyvyuxyxf

dxdyeyxfvuF vyuxi

often described by magnitude ( )and phase ( )

) (1

0

1

0

Nnl

MmkiM

k

N

lklmn efF

+−−

=

−

=∑∑=

π

In the discrete case with values fkl

of f(x,y) at points (kw,lh) fork= 1..M-1, l= 0..N-1

)()( 22 FF ℑ+ℜ

))()(arctan(

FF

ℜℑ


BUETStiction Detection – Problem Formulation

CONTROLLERSP

+PV

-PROCESSVALVE

Disturbance

CO / OP MV

SP – Set PointCO – Controller Output (also called OP)MV – Valve output or valve positioner signalPV – Process Variable (Controlled)


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200 400 600 800 10001.1

1.12

1.14

x 104

PV

and

SP

PVSP

200 400 600 800 100038

38.2

38.4

38.6

38.8

CO

sampling instants

CO

200 400 600 800 1000

-0.2

0

0.2

PV

and

SP

PVSP

200 400 600 800 100042

44

46

48

CO

sampling instants

CO

A flow loop in a refinery A level loop in a power plant

Data from Industrial Control loops


BUETStiction Detection Methods

Horch’s cross-corelation method (Horch, 2000)Yamashita (2006) pattern based methodSrinivasan et al. (2005 a,b) Qualitative Approach and Hammerstein model methodSinghal and Salsbury (2005) - Aria ratio methodRossi & Scali (2005) relay methodSurrogate data based method (Nina Thornhill)Choudhury et al. (2006) bicoherence based methodChoudhury et al. (2008) Hammerstein model approachJelali (2008), global search algorithmScali and Ghelardoni (2008), qualitative shape based valve stiction for flow loops, CEP, 16(12)Chitralekha, Shah, prakash (2010), stiction detection and quantification by the method of unknown input estimation, JPC, 20(2)Zabiri and Ramasamy (2009), NLPCA as diagnostic tool for valve stiction, JPC, 19(8)Ivan and Lakhms (2009), A new unified approach to valve stiction, I&ECR, 48(7)


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stiction

It is seldom ONE single problem

tuningdisturbance

nonlinearity


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- measures the nonlinear interactions between different frequency components of a signal.

Δ

Bispectrum is normalized to give a new measure called squared Bicoherence. Its magnitude varies from 0 to 1.

bic2(f1

,f2

) = |B(f1

, f2

)|2

E |X(f1

) X(f2

)|2 E |X(f1

+f2

)|2

Bispectrum:

B(f1 , f2 ) = E[X(f1) X(f2) X(f1+ f2)*]

Time Series Nonlinearity


BUETTime Series Nonlinearity (cont’d)

A discrete stationary time series, x(n), is said to be linear if it can be represented by

∑∞

=

−=0

)()()(s

sneshnx

Where, e(s) is a sequence of independent identically distributed random variable with E[e(s)]=0, E[e2(s)]= σe

2, and E[e3(s)]=μ3

= constant

It can be shown that for any linear signal, the squared bicoherence is

bic2(f1 , f2 ) =μ3

2

σe6


BUETBicoherence of a linear and nonlinear Signal


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Based on the squared bicoherence, Non-Gaussianity Index (NGI) and Nonlinearity Index (NLI) have been developed.

NGI <= 0 NGI>0 , NLI=0 NGI>0, NLI>0

Frequency independent Frequency dependent

GaussianLinear

Non-GaussianLinear

Non-GaussianNonlinear

NGI = bic 2 - bic 2crit , NLI = | bic 2

max - ( bic 2 + 2 σbic2 )|

Critical Values of bic2crit is determined at 95% or 99% confidence

interval of the squared bicoherence

Test of Non-linearity (cont’d)Choudhury, M. A. A. S., Sirish L. Shah and Nina F. Thornhill (2004). Diagnosis of poor control loop performance using higher order statistics. Automatica, 40(10), 1719-1728.


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NGI = 0.02 and NLI = 0.55

200 400 600 800 10001.1

1.12

1.14

x 104

PV

and

SP

PVSP

200 400 600 800 100038

38.2

38.4

38.6

38.8

CO

sampling instants

CO

Loop is Nonlinear

1. The process is locally linear in the current operating region2. Disturbances entering the loop are linear

Assumptions:

Flow Control Loop in a Refinery (revisited)


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OP

PV

PV

OP

Pattern of Stiction in PV-OP Plot

apparent stiction = maximum width of the cycles in pv-op plot

Hagglund, 1995Rengaswamy, et. al, 2001


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38.2 38.4 38.6 38.8 391.115

1.12

1.125

1.13

1.135

1.14

1.145

1.15

1.155 x 104 P V -OP p lo t

PV

OP

One possible solution is filtering. We have used frequencydomain band pass Weiner Filter. The filter boundaries can be obtained from the significant peaks of the bicoherence plot

For this example : [fl fh ] = [0.01 0.20]

38 38.2 38.4 38.6 38 .81.1

1.105

1.11

1.115

1.12

1.125

1.13

1.135

1.14

1.145 x 104

PVf

O P f

Flow Control Loop in a Refinery (cont’d)


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4

38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.91.105

1.11

1.115

1.12

1.125

1.13

1.135

1.14

1.145x 10

P Q

a b

α

OP

PV

Quantification of Apparent Stiction

Apparent Stiction=PQ = ( )αcosbαsinaba2

2222 += 0.35 %


BUETDiagnosis of Poor Control Loop Performance

Possible causes: 1. linear external oscillation2. tightly tuned controller3. and so on Nonlinear

Poorly performing control loop data (SP, PV, OP)

Calculate NGI (use sp-pv)

NGI > 0 ?

Non-Gaussian

NLI > 0 ?

Gaussian, Linear

Non-Gaussian, Linear

Calculate NLI

no yes

no yes

Filter PV and OP

Fitted Ellipse/ Fuzzy C-means

Clustering

Elliptic loop inPVf – OPf plot ?

yes

no

Valve Problems other than Stiction

Apparent Stiction % (unit of OP)


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BUETLevel Control Loop (revisited)

200 400 600 800 1000

-0.2

0

0.2

PV

and

SP

PVSP

200 400 600 800 100042

44

46

48

CO

sampling instants

CO

NGI = -0.02Non-linearity is not a cause for oscillation(s)

This is a level control loop which controls the level of condensate in the outlet of a turbine in a power plant by manipulating the flow rate of the liquid condensate.


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This is a level control loop which controls the level of condensate in the outlet of a turbine in a power plant by manipulating the flow rate of the liquid condensate.

200 400 600 800 1000-0.5

00.5

PV a

nd S

P PVSP

200 400 600 800 100070758085

OP

sampling instants

CO

Level Control of Turbine Condensate

NGI = 0.04 NLI = 0.61 [fl fh ] = [0.01 0.1] Apparent Stiction ≈

11%

6 5 7 0 7 5 8 0 8 5 9 0- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

PV

f

O P f

a= 7.75, b= 0.55, α

= 4.0

Apparent Stiction ≈

11%65 70 75 80 85 90

60

62

64

66

68

70

72

74valve charac teris tics

valv

e po

sitio

n

contro ller output

≈

11 %


BUETIndustrial Loop Analysis


BUETStiction Compensation

Repair the valveUse a knocker in the control algorithm (Hagglund, 2002)Increase the proportional controller gain, KRemove the integral time constant, or use a large value of integral time constantUse the derivative component


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Definition of Stiction is discussedData Driven Model of Stiction has been presented Two indices, NGI and NLI, for detecting nonlinearities in control loop have been developed and applied successfully to simulated as well as industrial data.Filtered pv-op characteristic plots are useful for diagnosis of non-linearities.Ellipse fitting technique has been demonstrated to be successful in automatically quantifying the amount of stiction.Methods for Stiction Compensation are discussed.

Summary


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BUETQuestions?

valve stiction

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