valve stictionteacher.buet.ac.bd/shoukat/valvestiction.pdf · m. a. a. shoukat choudhury 4 kfupm,...
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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
BUET
M. A. A. Shoukat Choudhury2KFUPM, Nov, 2008
BUET
M. A. A. Shoukat Choudhury3KFUPM, Nov, 2008
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)
M. A. A. Shoukat Choudhury4KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury5KFUPM, Nov, 2008
BUET
M. A. A. Shoukat Choudhury6KFUPM, Nov, 2008
BUETA CONTROL VALVE
M. A. A. Shoukat Choudhury7KFUPM, Nov, 2008
BUET
Stiction (Static Friction)SaturationHysteresisOversized valve Corroded plug/seatRuptured diaphragmDeadzone so on….
Control Valve Problems
M. A. A. Shoukat Choudhury8KFUPM, Nov, 2008
BUETISA Terminology
InstrumentInput Output
M. A. A. Shoukat Choudhury9KFUPM, Nov, 2008
BUETInput - Output Plot of Instruments
M. A. A. Shoukat Choudhury10KFUPM, Nov, 2008
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)
M. A. A. Shoukat Choudhury11KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury12KFUPM, Nov, 2008
BUETInside a Valve
Stiction
Fluid in out
M. A. A. Shoukat Choudhury13KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury14KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury15KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury16KFUPM, Nov, 2008
BUET
M. A. A. Shoukat Choudhury17KFUPM, Nov, 2008
BUETStiction Models
Mechanistic ModelsData Driven Models
M. A. A. Shoukat Choudhury18KFUPM, Nov, 2008
BUETLooking Inside a Valve!
Stiction
Fluid in out
M. A. A. Shoukat Choudhury19KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury20KFUPM, Nov, 2008
BUETOther Data-Driven Stiction Models
One parameter Model by Hagglund
M. A. A. Shoukat Choudhury21KFUPM, Nov, 2008
BUETBasis of Two-Parameter Stiction Model
M. A. A. Shoukat Choudhury22KFUPM, Nov, 2008
BUETTwo-parameter Stiction Model
M. A. A. Shoukat Choudhury23KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury24KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury25KFUPM, Nov, 2008
BUETSimulation using Two Parameter Stiction Model
stiction
deadband stiction
stiction
M. A. A. Shoukat Choudhury26KFUPM, Nov, 2008
BUETConcentration Loop
Process:
1103)(
10
+=
−
sesG
s
Obtained from Eborn & Olsson (1995) and Horch & Issakson (1998)
⎟⎟⎠
⎞⎜⎜⎝
⎛+=
ssC
10112.0)(
Controller:
M. A. A. Shoukat Choudhury27KFUPM, Nov, 2008
BUET
0 100 200 300time/s
stiction (undershoot)
stiction (no offset)
stiction (overshoot)
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
M. A. A. Shoukat Choudhury28KFUPM, Nov, 2008
BUET
pv (red) and op (black)
0 100 200 300time/s
pv vs. op
stiction (undershoot)
stiction (no offset)
stiction (overshoot)
Closed Loop PV-OP Plot
M. A. A. Shoukat Choudhury29KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury30KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury31KFUPM, Nov, 2008
BUET
M. A. A. Shoukat Choudhury32KFUPM, Nov, 2008
BUETA CHEMICAL PLANT
M. A. A. Shoukat Choudhury33KFUPM, Nov, 2008
BUET
data matrix
poor controllertuning
oscillatorydisturbances nonlinearities Other causes …
diagnosis
Poor performance?
Why?
data
Objectives
M. A. A. Shoukat Choudhury34KFUPM, Nov, 2008
BUETNonlinearities
stictioncorroded valve plug/seatoversized valvesaturationdeadzone so on….
nonlinearities
processnonlinearities
valvenonlinearities
Static Friction
M. A. A. Shoukat Choudhury35KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury36KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury37KFUPM, Nov, 2008
BUET
-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
std = 2
-5 -3 -1 0 1 3 50
0.1
0.2
0.3
0.4
x
std = 2std = 1.5
-5 -3 -1 0 1 3 50
0.1
0.2
0.3
0.4
x
std = 2std = 1.5std = 1
M. A. A. Shoukat Choudhury38KFUPM, Nov, 2008
BUETFourier Transform
M. A. A. Shoukat Choudhury39KFUPM, Nov, 2008
BUETDFT
M. A. A. Shoukat Choudhury40KFUPM, Nov, 2008
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)*]
M. A. A. Shoukat Choudhury41KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury42KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury43KFUPM, Nov, 2008
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)
M. A. A. Shoukat Choudhury44KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury45KFUPM, Nov, 2008
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)
M. A. A. Shoukat Choudhury46KFUPM, Nov, 2008
BUET
stiction
It is seldom ONE single problem
tuningdisturbance
non- linearity
M. A. A. Shoukat Choudhury47KFUPM, Nov, 2008
BUET
- 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
M. A. A. Shoukat Choudhury48KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury49KFUPM, Nov, 2008
BUETBicoherence of a linear and nonlinear Signal
M. A. A. Shoukat Choudhury50KFUPM, Nov, 2008
BUET
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.
M. A. A. Shoukat Choudhury51KFUPM, Nov, 2008
BUET
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)
M. A. A. Shoukat Choudhury52KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury54KFUPM, Nov, 2008
BUET
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)
M. A. A. Shoukat Choudhury55KFUPM, Nov, 2008
BUET
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 %
M. A. A. Shoukat Choudhury56KFUPM, Nov, 2008
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)
M. A. A. Shoukat Choudhury57KFUPM, Nov, 2008
BUET
M. A. A. Shoukat Choudhury58KFUPM, Nov, 2008
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.
M. A. A. Shoukat Choudhury59KFUPM, Nov, 2008
BUET
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 %
M. A. A. Shoukat Choudhury60KFUPM, Nov, 2008
BUETIndustrial Loop Analysis
M. A. A. Shoukat Choudhury61KFUPM, Nov, 2008
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
M. A. A. Shoukat Choudhury62KFUPM, Nov, 2008
BUET
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
M. A. A. Shoukat Choudhury64KFUPM, Nov, 2008
BUET
M. A. A. Shoukat Choudhury65KFUPM, Nov, 2008
BUETQuestions?