Predictive Control From Practice to Theory - …jbr · Predictive Control From Practice to Theory James B. Rawlings Department of Chemical and Biological Engineering November 18,

Predictive Control From Practice to Theory

James B. Rawlings

Department of Chemical and Biological Engineering

November 18, 2008Systems and Control Centennial Session

AICHE Annual MeetingPhiladelphia, PA

Rawlings Predictive Control From Practice to Theory 1 / 27

Outline

1 Model Predictive Control

2 From Practice . . .

3 To Theory . . .

4 And Back Again

Not to be confused with a paper of similar title, “There and Back Again,”B. Baggins (Middle Earth)


Outline

1 Model Predictive Control

2 From Practice . . .

3 To Theory . . .

4 And Back Again

Not to be confused with a paper of similar title, “There and Back Again,”B. Baggins (Middle Earth)


The power of abstraction

process

sensorsactuators

dx

dt= f (x , u)

y = g(x , u)


The model predictive control framework

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MeasurementMH Estimate

MPC controlForecast

t time

Reconcile the past Forecast the future

sensorsy

actuatorsu


Predictive control

The future influences the present just as much as the past does.

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MPC controlForecast

t time


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Predictive control

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MPC controlForecast

t time


sensorsy

actuatorsu

minu(t)

∫ T

0|ysp − g(x , u)|2Q + |usp − u|2R dt

x = f (x , u)

x(0) = x0 (given)

y = g(x , u)Rawlings Predictive Control From Practice to Theory 5 / 27

State estimation

When I want to understand what is happening today or try to decide whatwill happen tomorrow, I look back.

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MPC controlForecast

t time


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State estimation

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MPC controlForecast

t time


sensorsy

actuatorsu

minx0,w(t)

∫ 0

−T|y − g(x , u)|2R + |x − f (x , u)|2Q dt

x = f (x , u) + w (process noise)

y = g(x , u) + v (measurement noise)


Feedback

One technique for obtaining a feedback controller synthesis fromknowledge of open-loop controllers is to measure the currentcontrol process state and then compute very rapidly for theopen-loop control function.

The first portion of this function isthen used during a short time interval, after which a newmeasurement of the process state is made and a new open-loopcontrol function is computed for this new measurement. Theprocedure is then repeated.

— Lee and Markus (1967)Foundations of Optimal Control Theory

Everything has been thought of before, but the problem is tothink of it again.

— Goethe


Feedback

One technique for obtaining a feedback controller synthesis fromknowledge of open-loop controllers is to measure the currentcontrol process state and then compute very rapidly for theopen-loop control function. The first portion of this function isthen used during a short time interval, after which a newmeasurement of the process state is made and a new open-loopcontrol function is computed for this new measurement.

Theprocedure is then repeated.



— Goethe


Feedback

One technique for obtaining a feedback controller synthesis fromknowledge of open-loop controllers is to measure the currentcontrol process state and then compute very rapidly for theopen-loop control function. The first portion of this function isthen used during a short time interval, after which a newmeasurement of the process state is made and a new open-loopcontrol function is computed for this new measurement. Theprocedure is then repeated.



— Goethe


Feedback




— Goethe


Feedback




— Goethe


Industrial practice of MPC

Validation

Planning and Scheduling

Reconciliation

Model UpdateOptimizationSteady State

Plant

Controller

Two layer structure

Steady-state layerI RTO optimizes steady state

modelI Optimal setpoints passed to

dynamic layer

Dynamic layerI Controller tracks the setpointsI Linear MPC

(replaces multiloop PID)


Industrial practice of MPC

Validation


Reconciliation


Plant

Controller

Two layer structure

Steady-state layerI RTO optimizes steady state

modelI Optimal setpoints passed to

dynamic layer

Dynamic layerI Controller tracks the setpointsI Linear MPC

(replaces multiloop PID)


Large industrial success story!

Linear MPC and ethylene manufacturing

Number of MPC applications in ethylene: 800 to 1200

Credits 500 to 800 M$/yr (2007)

Achieved primarily by increased on-spec product, decreased energy use

Eastman Chemical experience with MPC

First MPC implemented in 1996

Currently 55-60 MPC applications of varying complexity

30-50 M$/year increased profit due to increased throughput (2008)

Praxair experience with MPC

Praxair currently has more than 150 MPC installations

16 M$/year increased profit (2008)





Credits 500 to 800 M$/yr (2007)













Credits 500 to 800 M$/yr (2007)













Credits 500 to 800 M$/yr (2007)













Credits 500 to 800 M$/yr (2007)













Credits 500 to 800 M$/yr (2007)













Credits 500 to 800 M$/yr (2007)













Credits 500 to 800 M$/yr (2007)










Impact for 13 ethylene plants (Starks and Arrieta, 2007)

Hydrocarbons AC&O 17

Advanced ControlAdvanced Control& Optimization& Optimization

We’re Doing it For the Money

$0

$10,000,000

$20,000,000

$30,000,000

$40,000,000

$50,000,000

$60,000,000

1Q 2

000

3Q 2

000

1Q 2

001

3Q 2

001

1Q 2

002

3Q 2

002

1Q 2

003

3Q 2

003

1Q 2

004

3Q 2

004

1Q 2

005

3Q 2

005

1Q200

6

3Q200

6

$0

$100,000,000

$200,000,000

$300,000,000

$400,000,000

$500,000,000

$600,000,000

Cumulative Quarterly


Maintaining technology (Starks and Arrieta, 2007)

Hydrocarbons AC&O 10

Advanced ControlAdvanced Control& Optimization& Optimization

Challenges (continued 1)

2006 Average DMC Service Factors (per plant)

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

A B C D E F G H I J K L M

Plant

DM

C S

ervi

ce F

acto

r (%

)

Plants L & M experienced APC personnel changes


Broader industrial impact (Qin and Badgwell, 2003)

Area Aspen Honeywell Adersa PCL MDC TotalTechnology Hi-Spec

Refining 1200 480 280 25 1985

Petrochemicals 450 80 - 20 550

Chemicals 100 20 3 21 144

Pulp and Paper 18 50 - - 68

Air & Gas - 10 - - 10

Utility - 10 - 4 14

Mining/Metallurgy 8 6 7 16 37

Food Processing - - 41 10 51

Polymer 17 - - - 17

Furnaces - - 42 3 45

Aerospace/Defense - - 13 - 13

Automotive - - 7 - 7

Unclassified 40 40 1045 26 450 1601

Total 1833 696 1438 125 450 4542

First App. DMC:1985 PCT:1984 IDCOM:1973 PCL: SMOC:IDCOM-M:1987 RMPCT:1991 HIECON:1986 1984 1988

OPC:1987

Largest App 603x283 225x85 - 31x12 -


Are all the problems solved?

Some questions to consider

Has the application base stopped growing?

Is the technology mature?

Is the theory complete?

Do we have tools to decompose large-scale systems into manageableproblems?

Do we have tools to optimize dynamic economic operation?

Have control researchers stopped working on linear systems?
















































A report & a presentation prepared by:

Available for download: http://www.decision.eu/smart2007.htm

European CommissionDG information Society & Media

Monitoring and control: today's market, its evolution till 2020 and the impact of ICT on

these

Workshop:

9th of October 2008



EC – DG INFSO – SMART 2007/047Monitoring and control: today's market, its evolution till 2020 and the impact of ICT on these

2

Intentionally blank

2

WORKSHOP: Brussels the 9th of October 2008Rawlings Predictive Control From Practice to Theory 14 / 27

Has the application base stopped growing?A report & a presentation prepared by:



Bottom-up analysis: no overlap between markets• The results of our analysis is a global and exhaustive estimate of the Monitoring &

Control market situation with a cohesive 2 axis breakdown by product and solution, and by application market showing current values and trend potential.

• Our approach was designed to evaluate the global market value with appropriate scales to avoid all major sources of overlapping:

– First level: a bottom up analysis of 30 separate markets.

– Second level: application market definitions linked to the hypothesis of the existence of:

• A dedicated specific market such as Embedded solutions;

• Vertical applications specific markets such as Factory automation;

• Horizontal product layer oriented market such as ERP.

WORKSHOP: Brussels the 9th of October 2008

23




3. Worldwide Monitoring & Control Market• The worldwide market for Monitoring & Control products and

solutions is around 188 billion euros.

• This represents 8% of total ICT expenditures worldwide.

• In the field of ICT, this is comparable to:

– the whole semiconductor industry world revenues;

– twice the world mobile phone manufacturers revenues.

• Services, with more than 50% of the market value, have the biggest share.

• The 3 larger sub markets represent together over 100 billion euros, namely:

– integration, installation & training services with 38 billion euros;

– control hardware with 36 billion euros;

– maintenance, repair & overall services with 30 billion euros.

• The 3 larger application markets are Vehicles, Process and Manufacturing industries.

• Europe represents 32 % of the world total market value.

35%

12%

53%

Hardware Soft Services

Definitions- bundle OS & drivers included in hardware- application development included in services


24

Total world: €187,9 bn






European Monitoring & Control Market

• The European M&C market is around 62 billion euros:

- In relative terms, compared to the European economy, this is more than 1 day of the total EU-27 yearly Gross Domestic Product.

- Compared to services businesses, it represents 8% of the EU-27 Telecoms & Transport sector gross value-added.

- Compared to total employment inside EU-27 and with a value added share of 70%, it is worth 750 000 jobs.

• Structural European details are quite comparable to Worldwide ones:

- More than 50% of services.

- 3 same major application markets.

- 3 same majors product and solutions sub segments.

32%

12%

56%

Hardware Soft Services

Definitions- bundle OS & drivers included in hardware- application development included in services


25

Total Europe: €61,5 bn




Worldwide Monitoring & Control Marketsby application

• Factory automation, the sum of Manufacturing plus Process industries, remains the main market with 58 billion euros, comparable to Vehicles (56 billion):

– With 38 billion euros out of 58, Services dominates with 2/3 of total Factory Automation market.

– Among Services the sub segment Integration, installation and training accounts for 50% of them.

• Together, three application markets, Vehicles, Manufacturing and Process industries represent 60% of total Monitoring & Control market.

• Ranked between 10 and 20 billion euros the next three applications markets are in order :

– Healthcare

– Critical infrastructures

– Logistic & transport

• Last one, Home is, for the moment, a small niche market.

56,4

31,5

26,3

18,3

18,0

10,9

8,6

7,2

7,2

4,3

0,7

Vehicles

IndustryManufacturing

IndustryProcess

Healthcare

CriticalInfrastructures

Logistics &transport

Environment

Power grids

Building

Householdappliances

Homes

HardSoftServ

57,8

26


Total world: €187,9 bn



0

50

100

150

200

250

300

350

400

450

1965 1970 1975 1980 1985 1990 1995 2000 2005

year

papers

year

MPC



0

200

400

600

800

1000

1200

1400

1965 1970 1975 1980 1985 1990 1995 2000 2005

year

papers

year

MPCFB ControlChem Engr


Ratio of MPC papers to feedback control papers

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1965 1970 1975 1980 1985 1990 1995 2000 2005

MPC/FB Control


Decomposing large-scale systems?


Decomposing large-scale systems?

Material flow

Energy flow


Optimizing economics: Current industrial practice

Validation


Reconciliation


Plant

Controller

Two layer structure

Drawbacks

I Inconsistent modelsI Re-identify linear model as

setpoint changesI Time scale separation may not

holdI Economics unavailable in

dynamic layer


Optimizing economics: Current industrial practice

Validation


Reconciliation


Plant

Controller

Two layer structure

DrawbacksI Inconsistent modelsI Re-identify linear model as

setpoint changesI Time scale separation may not

holdI Economics unavailable in

dynamic layer


Optimizing economics: what’s desirable?

-4 -2 0 2 4-4

-20

24

Profit

Input (u)

State (x)

Profit

-4 -2 0 2 4-4

-20

24

Profit

Input (u)

State (x)

Profit


Optimizing economics: what’s desirable?

-4 -2 0 2 4-4

-20

24

Profit

Input (u)

State (x)

Profit

-4 -2 0 2 4-4

-20

24

Profit

Input (u)

State (x)

Profit


Predictive Control. There and Back Again

Optimal dynamic operation of chemical processes has undergone atotal transformation in the last 20 years.

Both in theory and inpractice.

The currently available theory splits the problem into state estimationand regulation. Both are posed and solved as online optimizationproblems. Basic properties have been established. Lyapunov functionsare the dominant theoretical tool for analysis and design.

Industrial implementations and vendor software are basically keepingpace with the best available theory and algorithms. That is asurprising and noteworthy outcome!

Obtaining the dynamic models remains a significant bottleneck.



Optimal dynamic operation of chemical processes has undergone atotal transformation in the last 20 years. Both in theory and inpractice.







The currently available theory splits the problem into state estimationand regulation.

Both are posed and solved as online optimizationproblems. Basic properties have been established. Lyapunov functionsare the dominant theoretical tool for analysis and design.






The currently available theory splits the problem into state estimationand regulation. Both are posed and solved as online optimizationproblems.

Basic properties have been established. Lyapunov functionsare the dominant theoretical tool for analysis and design.






The currently available theory splits the problem into state estimationand regulation. Both are posed and solved as online optimizationproblems. Basic properties have been established.

Lyapunov functionsare the dominant theoretical tool for analysis and design.













Industrial implementations and vendor software are basically keepingpace with the best available theory and algorithms.

That is asurprising and noteworthy outcome!















Critiquing the research enterprise

The abstraction level is high and barrier to entry is significant.

But the barrier is no higher than any other mathematically intensiveresearch field in chemical engineering. Fluid mechanics, statisticalmechanics, molecular dynamics, . . .

Researchers in this community have not done a good jobcommunicating the significant advances in this field to theircolleagues outside the field.

Let’s start the ball rolling by updating and widely communicating Qinand Badgwell (2003).




But the barrier is no higher than any other mathematically intensiveresearch field in chemical engineering.

Fluid mechanics, statisticalmechanics, molecular dynamics, . . .






















Acknowledgments

Don Bartusiak, ExxonMobil

Tom Badgwell, Aspentech

Jim Downs, Eastman Chemical

Larry Megan, Praxair

Rahul Bindlish, Dow

Financial support from NSF #CTS-0825306, 0456694 andTexas Wisconsin California Control Consortium (TWCCC) members


Further reading

S. J. Qin and T. A. Badgwell. A survey of industrial model predictive controltechnology. Control Eng. Prac., 11(7):733–764, 2003.

D. M. Starks and E. Arrieta. Maintaining AC&O applications, sustaining the gain. InProceedings of National AIChE Spring Meeting, Houston, Texas, April 2007.


Predictive Control From Practice to Theory - …jbr · Predictive Control From Practice to Theory James B. Rawlings Department of Chemical and Biological Engineering November 18,

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