Introduction and basics of performance assessment of ...teacher.buet.ac.bd/shoukat/CPM.pdfControl Loop Performance Assessment 14 October, 2012 1 Introduction and basics of performance

Control Loop Performance Assessment 14 October, 2012

1

Introduction and basics of performance

assessment of univariate loops

Prof. M.A.A. Shoukat Choudhury

Department of Chemical Engineering

BUET, Dhaka


2Organization

Introduction and motivation

MV Benchmark basics

Time-domain analysis

Spectral analysis

Concluding remarks


3Main message

Maintenance is an important part of the asset life cycle.

Maintenance costs can constitute anywhere from 3 to 50 percent of production costs. „Fail and Fix‟ is OUT.

„Predict and Prevent‟ is IN.

Paradigm shift underway in process operation: „Listen‟ to your data and use it to monitor the performance of your process.

Examine data in a multivariate framework


4The Technology

Data fusion: Combine/fuse information

from all pertinent sensors (multivariate

data analysis) + information from the

peripheral production system

Predictive Maintenance

Smart

Sensors

Convert process

data into

information

Produce

‘Machine Health’

Information or index


5Information-based Decision Support System

Data

Action

D

C

S

P

R

O

C

E

S

S

Data

Processing

Know ledge

Extraction

Conditioned

data

Know ledge

metricsDecision

Support

Direct action

through DCS or

through operator

Operating personnel ,

engineer, or m anagement

Information flow in a real-time information-based decision support system.


6

Why monitor loop performance?


7Eastman loop “demographics”

Flow

32%

Pressure

15%Level

18%

Temperature

20%

Other

15%

Percent of 14,000 loops by type

Percent of 8,500 loops by performance

Best

25%

Good

33%

Fair

32%

Poor

10%

Credits: Michael A. Paulonis and John W. Cox, Eastman Chemical Company, USA


8Why monitor controller performance?

PID controllers are the „workhorses‟ of process industry

More than 90% of the controllers are PI(D)s

More than 30% of PIDs operate in manual

More than 30% of loops increase short-term variability

About 25% of loops use default settings

About 30% of loops have equipment problems

APCs are not useful when PIDs are badly tuned


Performance Assessment

Q. Is your controller doing a satisfactory job?

A. Compare it with a benchmark

What benchmarks?

Best achievable control

• for the process

• amongst a class of controllers

User specified benchmarks etc.


10

Remember that:

)variablescontrolled(

1Pr

VarianceofitandQuality

Quality and Variance


11How well is your controller performing?

Good, bad or optimal ?

Look at variance of the controlled variable to measure performance.

But this by itself does not provide a measure of performance.

We need a yardstick or a metric to compare this number.

1

)(

)( 1

2

2

N

yy

yVar

N

iy


12

Actual variance :

Lowest achievable variance is:

One measure of performance is:

2

y

2

mv

2

2

y

mv

NOTE: The Performance Index is not a measure of variability. It is a

measure of the potential that exists for improving current controller

performance.

Controller Performance Assessment


13Why monitor controller performance?

time / min

0 2000 4000 6000 8000 100000

10

20

30

40

50

60

70

Le

ve

l

Change in the operating target due to

reduced variance

Constraint

OPPORTUNITY


14

The case for reducing variability

time / min

0 2000 4000 6000 8000 100000

10

20

30

40

50

60

70

Le

ve

l

Constraint

μpresent

μnew

newnewpresentpresent 33Constraint

)(3 newpresetpresentnew

HOW MUCH ?

presentnewyopportunit

2

2

present

MVC


15Performance monitoring & the role of FB control

Smaller Variability

Typical variability decrease with on-line monitoring: 30 %

Fre

qu

en

cy

Upper Spec Low Spec Target

Before Advanced

Control

After Advanced

Control


16

Loop to be evaluated

Schematic Diagram of an Industrial Process

Look at a real industrial process


17

0 2 4 6 8 10 12 14 16280

290

300

310

Te

mp

era

ture

hrs

How good a job are we doing in regulating this temperature ?

Can we do any better ?

Can this variance be reduced

by retuning this loop?

What is the lowest possible variance that we can achieve

for this loop?

Quality and Variance


18Performance Assessment : SISO System

0 2 4 6 8 10 12 14 16280

290

300

310

Temperature

after tuningbefore tuning

hrs

02 4 6 8 10 12 14 16

0

0.2

0.4

0.6

hrs

Performance Index

Tighter temperature

regulation resulted in

22% increase in catalyst

life


19

ProcessController

dr u y

Performance of univariate or multivariate controllers ???

Simplistically ask: How “healthy” is your controller?

Performance assessment

Main benefit: Develop a tool that would help towards

low maintenance and optimal process performance.


20Summary so far

With easy data access:

Routine controller monitoring can

answer the following questions: How

well is your controller tuned: Good, bad

or optimal? Can performance be

improved?

Main issue: How to have a reliable APC

asset base with low maintenance?


21Organization


MV Benchmark basics


Concluding remarks


22How well is your controller performing?

Good, bad or optimal ?

Look at variance of the controlled variable to measure performance.

But this by itself does not provide a measure of performance.

We need a yardstick or a metric to compare this number.

1

)(

)( 1

2

2

N

yy

yVar

N

iy


23

Actual variance :

Lowest achievable variance is:

One measure of performance is:

2

y

2

mv

2

2

y

mv

NOTE: The Performance Index is not a measure of variability. It is a

measure of the potential that exists for improving current controller

performance.

Controller Performance Assessment


Closed - loop response: yN

q TQat d t

1~

write

where

and is a transfer function

N F q R

F F Fq F q

R

d

d

d

0 1

1

1

1 ( )

q Td ~Q

y t-

N

Preliminaries

at


25

Cold WaterFaucet

Hot WaterHot

Water

Tank

Transportation Lag

Delays pose fundamental limitations to

achievable control performance


yN

q TQa

F q R

q TQa

F q TQ q R FTQ

q TQa

F qR FTQ

q TQa

F a Fa F a L a

t d t

d

d t

d d

d t

d

d t

t t d t d

e

t d

t

1

1

1

1

1

0 1 1 1 1 0

~

~(

~) (

~)

~

(

~

~ )

1 24444 34444

L a

e Fa Q

w

t d

w

t t

t d

t d

1 1

1 2444 3444

where is independent of the control law

while is dependent on the control law

Preliminaries …contd


y e wt t t d

Controller Invariant Term

Var y Var e Var w Var et t t d t( ) ( ) ( ) ( )

Since is independent of the controller,

this lower bound is achieved if and only if

. This yields the minimum

variance control law as

Var e

Var w

QR

TF

t

t d

( )

( )

~

0

Preliminaries …contd


28Preliminaries …contd

y e wt t t d

y2

Control loop performance measure: 1)(2

2

y

mvd

Var y Var e Var w Var et t t d t( ) ( ) ( ) ( )

Controller Invariant Term

)()()( dttt wVareVaryVar

Total Variance Achievable Minimum Variance

mv2


29The FCOR algorithm for univariate processes

The IIR model between the output and the white

noise disturbance is:

Multiplying the above equation by at ,at-1 , …at-d+1

respectively and then taking the expectation of both

sides of the equation yields:

t

d

d

d

dt aqfqfqfqffy )( )1(

1

2

2

1

10

2

11

2

22

2

11

2

0

][)1(

][)2(

][)1(

][)0(

addttya

attya

attya

attya

fayEdr

fayEr

fayEr

fayEr



The controller invariant or minimum variance portion

of the output is:

The minimum variance of the output is:

t

d

d

d

dt aqfqfqfqffy )( )1(

1

2

2

1

10

mvy

2222

2

2

2

2

2

2

2

22

1

2

2

2

1

2

0

2

/)1()1()0(

)1()1()0(

)(

ayayaya

a

a

ya

a

ya

a

ya

admv

drrr

drrr

ffff



If the controller performance index is defined as:

; Note that this index is a function of the delay order ’d’ &

The index can be expressed as:

Where Z is the cross-correlation coefficient vector

between and for lags 0 to (d-1), i.e.

2

2

)(y

mvd

1)(0 d

T

yayaya

ayyayaya

ZZ

d

drrrd

)1()1()0(

/)1()1()0()(

222

22222

)]1()1()0([ dZ yayaya


y t

at

a t

controller process-

disturbance

corr y at t( )

corr y at t( )1

corr y at t d( ) 1

q 1

q 1

ya d( )1

ya ( )1

ya ( )0

time series analysis

Steps:

1) time series analysis

2) correlation

3) obtain

The FCOR Algorithm


33The FCOR Algorithm:

Filter design: Univariate AR or ARMA

modeling to estimate the white noise

sequence.

Correlation analysis between the estimated

white noise sequence and the measured

output.

Inner product of the correlation coefficients

yields SISO performance index.


34

0.00

0.05

0.10

0.15

0.20

0.25

0.30

PI(var) vs. Delay: MOIC25276P.PV

PI(var)

Delay 10 11 12 13 14 15 16 17 18 19 20Delay

PI(var) 0.126 0.142 0.159 0.176 0.194 0.213 0.232 0.252 0.272 0.291 0.310

Performance Index of the new controller using

The MV benchmark


35Organization


MV Benchmark basics


Concluding remarks


36Concluding Remarks

Detailed time-domain analysis gives insight into loop performance.

Engineering knowledge is important in drawing meaningful conclusions from the analysis.

“Bottom-up” approach is important.

Start with the lowest level loops to ensure that APC algorithms and optimizers can actually deliver optimum performance.

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Introduction and basics of performance assessment of ...teacher.buet.ac.bd/shoukat/CPM.pdfControl Loop Performance Assessment 14 October, 2012 1 Introduction and basics of performance