20130426 Manenti - Process Control

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Optimal control

Industrial applicationsFlavio Manenti , Dept. CMIC “Giulio Natta” ; Politecnico di Milano

Filip Logist, Jan Van Impe, Dept. of Chemical Engineering, KULeuven, University of Leuven



Flavio Manenti, Filip Logist – KU-Leuven

2‘‘Terms and conditions’’

• Acronyms and notations

Advanced conventional process control

Advanced process control Model predictive control

• Model predictive control

Based on linear/linearized models

• Dynamic matrix control (DMC, LMPC, MPC)

• Several commercial packages

Based on nonlinear models

• Model predictive control (MPC, NMPC)

• No commercial packages

• Features of NMPC

A dynamic (convolution) model is used to foresee the future behavior of

the plant on a specific time horizon (prediction horizon, H_P) consistingof p sampling times

Receding horizon methodology (moving horizon, not rolling horizon)

Manenti, Considerations on Nonlinear Model Predictive Control Techniques, COMPUTERS & CHEMICAL

ENGINEERING, 35(11), 2491-2509, 2011.




3Integration Pyramid

PlantManagement

Maintenance

and Production

Management

Enterprise

Management

Field

ConventionalControl

AdvancedControl

(MPC/NMPC)

Real TimeDynamic

Optimization

Scheduling

Planning

SecondsMinutes

Hours - Days

Weeks

Months - Years

1 1

2 2 2

1

min ( ) ( ) ( ) ( 1) p p pk h k h k h

SET TAR

y react react T c c u c c

j k l k i k

T j T F l F F i F i

AdvancedControl

(MPC/NMPC)

Real TimeDynamic

Optimization




4Algorithm

• Model Predictive Control• MPC

Plant




5Receding horizon methodology

t

u1,1

u2,1

u3,1un,1

Set-point

ManipulatedVariable

PLANT

MODEL

Controlled Variable

u1

HPHC

u2

u3

HD

1

HPHC

u1

u2

u3

2

HPHC

u1u2 u3

3




6Industrial perspective

Outlier Detection

Robust methods

Linear/nonlinear Regressions

Performance Monitoring

Yield Accounting

Soft sensing

Data

Reconciliation

Mathematical

Modeling

Dynamic

Simulation

ModelPredictive

Control

Optimization

Model

Reduction

DCS, OTS, Plantwide control,Soft sensing, process transients,

grade/load changes

Solvers

Planning

Scheduling

Dynamic optimization

Distributed predictive control

Nonlinear Systems

Optimizers

Differential systems

Stiff systems

ODE,DAE,PDE,PDAE

Efficiency

DecisionsRaw Data

Parallel

Computing

Uncertainties

Optimal production

Optimal grade changesMulti-objective

Real-time optimization

High accuracy

Reliable process cont rol

Production improvement

Economy

Just in time

Market-driven

Logistics

Corporate

Supply Chain




NMPCPET plant

7

Manenti, Rovaglio

Integrated multilevel optimization in large-scale poly(ethylene terephthalate) plants

Industrial & Engineering Chemistry Research

47(1), 92-104, 2008.




8Case Study: PET Plant




9Jacobian Matrix

• Primary esterifier

• Secondary esterifier

• Low polymerizer

• Intermediate polymerizer

• High polymerizer

• Solid state polymerizer

Resulting DAE:

1356 diff. eqs.

164 alg. eqs.

15 controls 2 controlled

16 constrained




10Frequent Grade Changes

Grade A: PET as textile fibres ( melt process

I.V. = 0.55 ÷ 0.65 dl/g)

Grade B: PET for bottles production ( bottle

grade I.V. = 0.72 ÷ 0.85 dl/g)

Grade C: PET for special fibres ( tire-cord

resins I.V. = 0.95 ÷ 1.05 dl/g)




11Comparison

0.440

0.445

0.450

0.455

0.460

0.465

0.470

0 500 1000 1500 2000 2500 3000

I V I P ( d l / g )

Time (min)

0.600

0.610

0.620

0.630

0.640

0.650

0.660

0.670

0.680

0 500 1000 1500 2000 2500 3000

I

V H P ( d l / g )

Time (min)

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 500 1000 1500 2000 2500 3000

P

H P ( m m H g )

Time (min)

0.60

0.80

1.00

1.201.40

1.60

1.80

2.00

0 500 1000 1500 2000 2500 3000

P I P ( m m

H g )

Time (min)

NMPC

NMPC




12Comparison

0.640

0.650

0.660

0.670

0.680

0.690

0.700

0.710

0 500 1000 1500 2000 2500 3000

I V P H C R

( d l / g )

0.760

0.770

0.7800.790

0.800

0.810

0.820

0.830

0.840

0 500 1000 1500 2000 2500 3000

I V S S

P ( d l / g )

NMPC

NMPC

Time (min)

Time (min)




NMPCEthylene splitter

Eni, Italy

13




14The C2-splitter

Column design:

•Total tray number : 110

•Feed : tray #55 (*)

•Ethylene cut : tray #104(*)

Feed composition (**) :

•C2H4 – 79%

•C2H6 – 19%

•Others – 2% (H2, CO,

CO2, CH4, C3H8, C3H6)

(*) bottom-up numeration

(**) molar basis




15Validation

Reflux flowrate change effect on overhead

composition and on temperature at tray #5

0,0

100,0

200,0

300,0

400,0

500,0

600,0

700,0

800,0

900,0

1000,0

89,40 89,60 89,80 90,00 90,20 90,40 90,60

O v e r h e a d

i m p u r i t i e s

[ p p m

]

Reflux flowrate [ton/h]

Reflux flowrate change effects on overhead

stream impurities

Simulation

Plant

‐41,00

‐40,00

‐39,00

‐38,00

‐37,00

‐36,00

‐35,00

89,60 89,80 90,00 90,20 90,40 90,60

T r a y

5

t e m p e r a t u r e

[ ° C ]

Reflux flowrate [ton/h]

Reflux flowrate change effects on temperature at

tray #5

Simulation

Plant

0,0

200,0

400,0

600,0

800,0

1000,0

1200,0

96,60 96,80 97,00 97,20 97,40 97,60

O v e r h e a d

i m p u r i t i e s [ p p m ]

Boil‐up flowrate [ton/h]

Boil‐up flowrate change effects on overhead

stream impurities

Smulation

Plant

‐41,00

‐40,00

‐39,00

‐38,00

‐37,00

‐36,00

‐35,00

‐34,00

96,60 96,80 97,00 97,20 97,40 97,60

T r a y

5 t e m p e r a t u r e

[ ° C ]

Boil‐up flowrate [ton/h]

Boil‐up flowrate change effects on temperature at

tray #5

Simulation

Plant

Boil-up flowrate change effect on overhead

composit ion and on temperature at tray #5




16Servo-mechanism problem

9000

9200

9400

9600

9800

10000

10200

10400

10600

0,0 5,0 10,0 15,0 20,0 25,0 30,0

R e f l u x f l o w

r a t e [ l b m o l / h ]

Time [h]

Reflux flow rate

PI

DMC

NMPC

0,9600

0,9650

0,9700

0,9750

0,9800

0,9850

0,9900

0,0 5,0 10,0 15,0 20,0 25,0 30,0

E t h y l e n e m

o l a r f r a c t i o n [ ‐ ]

Time [h]

Ethylene molar fraction in cut stream

PI

DMCNMPC

SP Distillate

0,8600

0,8700

0,8800

0,8900

0,9000

0,9100

0,9200

0,9300

0,9400

0,9500

0,0 5,0 10,0 15,0 20,0 25,0 30,0

E t h a n e m o l a r f r a c t i o n [ ‐ ]

Time [h]

Ethane molar fraction in bottom stream

PI

DMC

NMPC

SP Bottom

43,20

43,40

43,60

43,80

44,00

44,20

44,40

44,60

44,80

45,00

0,0 10,0 20,0 30,0 40,0 50,0 60,0 R e b o i l e r t h e r m a l d u t y [ 1 . E + 0 6 B T U / h ]

Time [h]

Reboiler thermal duty

PI

DMC

NMPC




17Servo-mechanism problem

0,8600

0,8700

0,8800

0,8900

0,9000

0,9100

0,9200

0,9300

0,9400

0,9500

0,0 5,0 10,0 15,0 20,0 25,0 30,0

E t h a n e m o l a r f r a c t i o n [ ‐ ]

Time [h]


PI

DMC

NMPC

SP Bottom

39,50

40,00

40,50

41,00

41,50

42,00

42,50

43,00

43,50

44,00

44,50

45,00

0,0 5,0 10,0 15,0 20,0 25,0 30,0 R e b o i l e r t h e r m a l d u t

y [ 1 . E + 0 6 B T U / h ]

Time [h]


PI

DMC

NMPC

9000

9200

9400

9600

9800

10000

10200

10400

10600

0,0 5,0 10,0 15,0 20,0 25,0 30,0

R e f l u x f l o w


Time [h]

Reflux flow rate

PI

DMC

NMPC

0,9600

0,9650

0,9700

0,9750

0,9800

0,9850

0,9900

0,0 5,0 10,0 15,0 20,0 25,0 30,0

E t h y l e n e m


Time [h]


PI

DMCNMPC

SP Distillate

0,9800

0,9850

0,9200

0,9250




18Regulation problem (feedcomposition disturbance)

0,9890

0,9895

0,9900

0,9905

0,9910

0,9915

0,9920

0,0 10,0 20,0 30,0 40,0 50,0 60,0

E t h y l e n e m


Time [h]


PI

DMCNMPC

SP Cut

0,8800

0,8900

0,9000

0,9100

0,9200

0,9300

0,9400

0,9500

0,9600

0,9700

0,0 10,0 20,0 30,0 40,0 50,0 60,0

E t h a n e m o l a r

f r a c t i o n

[ ‐ ]

Time [h]


PI

DMC

NMPC

SP Bottom

9950,00

10000,00

10050,00

10100,00

10150,00

10200,00

10250,00

10300,00

10350,00

0,0 10,0 20,0 30,0 40,0 50,0 60,0

R e f l u x f l o w


Time [h]

Reflux flow rate

PI

DMC

NMPC

43,20

43,40

43,60

43,80

44,00

44,20

44,40

44,60

44,80

45,00

0,0 10,0 20,0 30,0 40,0 50,0 60,0

R e

b o

i l e r t h e r m

a l d u t y

[ B T U / h ]

Time [h]


PI

DMC

NMPC




19Regulation problem (feedcomposition disturbance)

0,9890

0,9895

0,9900

0,9905

0,9910

0,9915

0,9920

0,0 10,0 20,0 30,0 40,0 50,0 60,0

E t h y

l e n e m

o l a r

f r a c t i o n

[ ‐ ]

Time [h]


PI

DMCNMPC

SP Cut

0,8800

0,8900

0,9000

0,9100

0,9200

0,9300

0,9400

0,9500

0,9600

0,9700

0,0 10,0 20,0 30,0 40,0 50,0 60,0

E t h a n e m o l a r

f r a c t i o n

[ ‐ ]

Time [h]


PI

DMC

NMPC

SP Bottom

9950,00

10000,00

10050,00

10100,00

10150,00

10200,00

10250,00

10300,00

10350,00

0,0 10,0 20,0 30,0 40,0 50,0 60,0

R e f l u x f l o w


Time [h]

Reflux flow rate

PI

DMC

NMPC

43,20

43,40

43,60

43,80

44,00

44,20

44,40

44,60

44,80

45,00

0,0 10,0 20,0 30,0 40,0 50,0 60,0

R e

b o

i l e r t h e r m

a l d u t y

[ B T U / h ]

Time [h]


PI

DMC

NMPC

0,9900

0,9905

0,9500

0,9550

0,9500

0,9550




Self-adaptive NMPC

Deisobutanizer

Mongstad Refinery, Norway

20

Dones, Manenti, Preisig, Buzzi-FerrarisNonlinear Model Predictive Control: a Self-

Adaptive ApproachIndustrial & Engineering Chemistry Research

49(10), 4782-4791, 2010




Unit 21




Spoiled Jacobian 22




Results

• Use of compartmental models

• Model self-adaptation

To the problem

To the dynamic

To the computational effort

• Benefits

Accurate when needed

Fast when possible

(viceversa)

23

93

93.5

94

94.5

95

95.5

0 500 1000 1500 2000 2500 3000

c o n c e n t r a t i o n i C 4 t o p [ % ]

time [s]

NMPC with full dynamic model

NMPC with 5-dynamic-trays model

ANMPC

360

365

370

375

380

385

390

395

400

0 500 1000 1500 2000 2500 3000

r e f l u x s t r e a m [ m o l / s ]

time [s]

NMPC with full dynamic model

NMPC with 5-dynamic-trays model

ANMPC

4

6

8

10

12

14

16

0 500 1000 1500 2000 2500 3000

n u m b e r o f d y n a m i c t r a y s u

s e d i n t h e m o d e l

time [s]




D-RTO

Olefins plant

Invensys, USA

24

Manenti et al.Process Dynamic Optimization Using ROMeo

Computer Aided Chemical Engineering

29, 452-456, 2011




25Industrial perspective

Outlier Detection

Robust methodsLinear/nonlinear Regressions


Yield Accounting

Soft sensing

Data

Reconciliation

Mathematical

Modeling

Dynamic

Simulation

ModelPredictive

Control

Optimization

Model

Reduction


grade/load changes

Solvers

Planning

Scheduling



Nonlinear Systems

Optimizers


Stiff systems

ODE,DAE,PDE,PDAE

Efficiency

DecisionsRaw Data

Parallel

Computing

Uncertainties

Optimal production

Optimal grade changes

Multi-objective


High accuracy



Economy

Just in time

Market-driven

Logistics

Corporate

Supply Chain

Dynamic Optimization




26Tools

Outlier Detection



Yield Accounting

Soft sensing

Data

Reconciliation

MATHEMATICAL

MODELING

Dynamic

Simulation

Dynamic

Optimization

Optimization

Model

Reduction

DCS, OTS, Plantwide control,Soft sensing, process transients,grade/load changes

Solvers

Enterprise-wide

Planning

Scheduling

Nonlinear Systems

Optimizers


Stiff systems

ODE,DAE,PDE,PDAE

Efficiency

DecisionsRaw Data

Parallel

Computing

Supply Chain

Management

Uncertainties

Optimal production


Multi-objective


High accuracy



Just in time

Market-driven

Conscious MGM

Mathematical

Modeling

Dynamic

Simulation

Optimization

DYNSIM

ROMeo




27Tools

Outlier Detection



Yield Accounting

Soft sensing

Data

Reconciliation

MATHEMATICAL

MODELING

Dynamic

Simulation

DynamicOptimization

Optimization

ModelReduction

DCS, OTS, Plantwide control,Soft sensing, process transients,grade/load changes

Solvers

Enterprise-wide

Planning

Scheduling

Nonlinear Systems

Optimizers


Stiff systems

ODE,DAE,PDE,PDAE

Efficiency

DecisionsRaw Data

Parallel

Computing

Supply Chain

Management

Uncertainties

Optimal production


Multi-objective


High accuracy



Just in time

Market-driven

Conscious MGM

Is it possible?

DYNSIM

Mathematical

Modeling

Dynamic

Simulation

DynamicOptimization

Optimization

ROMeo




28The Idea

• On-line Optimization

• Nonlinear MPC

• Data Reconciliation

T

min

. . : 0; 0

R

M R M R

i i i ii x x x x

s t f g

x W

x x

,min

. . : , 0

, 0

;n m

Z Profits Costs

s t f

g

R N

x b

x b

x b

x b

1 2, ,min ... ...

. . : 0; , 0

0; , 0

; ;

n

n p m

Z

s t f f

g g

R R N

x u b

x x x

x x x

x u b

• Dynamic Optimization

T

min

. . : , 0

, 0

R SET R SET

i i i i

i

x x x x

s t f

g

u

W

x x

x x




29Example

• Series of three ideal CSTRs

Open-loop

Closed-loop

P-7

P-16

P-21




30Open-loop in C++

Key-component molar flow

exiting the reactor:

• #1

• #2• #3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5

[ m o l / s ]

Time




31Open-loop in DYNSIM

UAM MODELS insertedinto the ICON PALETTE

(C++ dynamic library)

32




32Open-loop in DYNSIM

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5

[ m o l / s ]

Time

33




33Using BzzMath in DYNSIM

No changes at theDYNSIM’s interface

34l d l i




34Closed-loop in C++

0.398

0.4

0.402

0.404

0.406

0.408

0.41

0.412

0.414

0.416

0.418

0 10 20 30 40 50

[ m o l / s ]

Time

0.198

0.199

0.2

0.201

0.202

0.203

0.204

0.205

0 10 20 30 40 50

[ m o l / s ]

Time

0.0982

0.0984

0.0986

0.0988

0.099

0.0992

0.0994

0.0996

0.0998

0.1

0.1002

0 10 20 30 40 50

[ m o l / s ]

Time

CV

(SP: 0.1 mol/s)

35F ll I t ti (All i )




35Full Integration (All-in-one)

36D & D




36Drag & Drop

DYNSIM

37D & D




37Drag & Drop

DYNSIM

38Drag & Drop




38Drag & Drop

ROMeo

39Drag & Drop




39Drag & Drop

ROMeo

40Smart Dynamic Simulation with




40Smart Dynamic Simulation withROMeo

41D-RTO with Multiple Shooting




D-RTO with Multiple Shooting

42Friendly Interface for D-RTO




Friendly Interface for D-RTO

Possibility to give the user to enter

any kind of data for D-RTO

Specific

D-RTOTAB

43Preliminary Comparison




Preliminary Comparison

RTO vs D-RTO

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0 10 20 30 40 50 60 70 80 90

'checkdrto.ris' u 1:4'check.ris' u 1:4

Traditional approach

Two-shooting

Multiple-shooting

44Validation Case (Olefins)




Validation Case (Olefins)

• Cracking Furnace (SPYRO-based D-RTO)

45Stack




SteamCrackingFurnaceFeed

Stack

Damper

Breeching

ConvectionSection

Radiant

Section

Burners / Air Blowers

Coil Outlet

Temperature

(COT)

Steam

Transfer Line

Exchanger (TLE)

High

Pressure

Steam

Main

Factionator

>800°C 400°C

COT

Olefins

TC

FC

Fuel

Air

PV

PV

OUT

OUT

SP

Temperature

Controller

Flowrate Ratio

Controller

RADIANT SECTION

PV

46Software Integration




D-RTO- ROMeo (OPERA) -

Software Integration

All-in-one tool for SPYRO-based smart dynamic simulation and

optimization of olefins plant

SPYRO- FORTRAN -

• SPYRO (FORTRAN)

Mixed-language (FORTRAN-C++)

• Cracking furnace SPYRO-based dynamic model

(C++)

Very performing ODE/DAE solver (BzzOde,

BzzDae, BzzDaeSparse… BzzMath)

• Smart dynamic simulation (grade change,

DYNSIM)

Full integration in DYNSIM

• Dynamic real-time optimization (multiple

shooting, ROMeo)

Full integration and OPERA synchronization

BzzMath

- C++ -

Dynamic Model- DYNSIM -

47SPYRO-based (Smart) Dynamic




( ) ySimulation

• C3H6/C2H4 Severity Change from 0.62 to 0.67

FUEL FLOWRATE[kg/h]

DUTY [kcal/h] CH4/C3H6SEVERITY

COIL OUTLETTEMPERATURE (COT)

[°C]

WALLTEMPERATURE

[°C]

C3H6/C2H4SEVERITY

Initial Severity

Arrival Severity

1.34e+007

1.35e+007

1.36e+007

1.37e+007

1.38e+007

1.39e+007

1.4e+007

0 20 40 60 80 100 120

Time [min]

0.9

0.92

0.94

0.96

0.98

1

1.02

1.04

0 20 40 60 80 100 120

Time [min]

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0 20 40 60 80 100 120

Time [min]

786

788

790

792

794

796

798

800

802

0 20 40 60 80 100 120

Time [min]

1088

1090

1092

1094

1096

1098

1100

1102

1104

0 20 40 60 80 100 120

Time [min]

3450

3500

3550

3600

3650

3700

3750

3800

0 20 40 60 80 100 120

Time [min]

48SPYRO-based (Smart) Dynamic




• Severity Change Convergence

3450

3500

3550

3600

3650

3700

3750

3800

0.9 0.92 0.94 0.96 0.98 1 1.02 1.043450

3500

3550

3600

3650

3700

3750

3800

0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69

Fuel Flowrate vs

CH4/C3H6 Severity

Fuel Flowrate vs

C3H6/C2H4 Severity

( ) ySimulation

49SPYRO-based (Smart) D-RTO




( )

As per DYNSIM, UAM

inserted into the ICON

PALETTE (C++ dynamic

library)

508-shoots flowsheet




5132-shoots flowsheet




No changes at theROMeo’s interface

52Converging Path




2000

3000

4000

5000

6000

7000

8000

9000

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05

F U E L F L O W R A T E

4 SHOOTS

16, 32 SHOOTS

TRADITIONAL

STARTINGPOINT

OPTIMUM

C3H6/C2H4 SEVERITY

No changes at the

traditional control level

53High Benefits, Few Shoots




3200

3250

3300

3350

3400

3450

3500

3550

3600

3650

3700

3750

0.6 0.65 0.7 0.75 0.8 0.85 0.9

F U E L

F L O W R A T E

32 SHOOTS

16 SHOOTS

C3H6/C2H4 SEVERITY

54Market dynamics




0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

1.05

0 20 40 60 80 100 120

Time [min]

0.5

0.6

0.7

0.8

0.9

1

1.1

0 20 40 60 80 100 120

Time [min]

• Market dynamics (the current market condition is a higher demand of propylene, thus higher price) imposes a severity change in ethylene/propyleneproduction:

TRADITIONAL

4 SHOOTS

TRADITIONAL

4 SHOOTS

CH4/C3H6C3H6/C2H4

16, 32 SHOOTS

16, 32 SHOOTS

55Severity change




2000

3000

4000

5000

6000

7000

8000

9000

0 20 40 60 80 100 120

Time [min]

700

720

740

760

780

800

820

0 20 40 60 80 100 120

Time [min]

Coil outlet temperature [°C] of theradiant section of the cracking furnace

Fuel flowrate [kg/h] entering thecracking furnace

TRADITIONAL

4 SHOOTS

TIME [min]

TRADITIONAL

4 SHOOTS

Supposed practical upper bound 16, 32 SHOOTS

16, 32 SHOOTS

56Quantitative comparison




3000

3200

3400

3600

3800

4000

0 50 100 150 200 250 300

Traditional RTO

TIME [min]

32-shoots D-RTO

2000

2500

3000

3500

4000

4500

5000

0 50 100 150 200 250 300

D-RTO off-spec time

RTO off-spec time

TIME [min]

F U E L F L O W R A T E

• To operate at the optimum conditions dictated by the market, the RTO requiresmore than 2h to accomplish the severity change, whereas the D-RTO requiresabout 1h.

• Consider that severity changes are not only imposed by market dynamics, buteven by feedstock changes, load changes… As a result, frequent severity

changes are required in each coil of each cracking furnace of each olefins plants

1-step traditional RTO

2-steps traditional RTO

32-shoots D-RTO F U E L F L O W R A T E

57Industrial feasibility9000




D-RTO with ROMeo

• Feasible

• D-RTO is more stable than RTO

• D-RTO halves off-spec periods

• On-line feasibility for the industrial scale

• Computational times are comparable

• No visible changes to the user in ROMeo environment

• No changes to the existing control scheme

• Easy-to-use when implemented (few parameters to be defined)

SEVERITY

2000

3000

4000

5000

6000

7000

8000

0.5 0.6 0.7 0.8 0.9 1 1.1

Upper bound

F U E

L F L O W R A T

E

Corporate level 58




• Case: Eni Versalis 17 sites, European area (large-scale)

59




Corporate optimal control

Air separation units

Air Liquide, ItalyLinde Gas, Italy

Manenti et al.Raising the decision-making level to improve the

enterprise-wide production flexibilityAIChE J ournal

59(5), 1588-1598, 2013

Just a premise 60




• High flexibility/operatibility is useless without corporate control The case of Linde Gas, Terni’s site:

Test preliminare (offline Munich-Arluno-Terni)

Single-site Corporate

Industrial viewpoint 61




Outlier Detection

Robust methods

Linear/nonlinear Regressions


Yield Accounting

Soft sensing

Data

Reconciliation

Mathematical

Modeling

Dynamic

Simulation

Model

Predictive

Control

Optimization

ModelReduction


grade/load changes

Solvers

Planning

Scheduling



Nonlinear SystemsOptimizers


Stiff systems

ODE,DAE,PDE,PDAE

Efficiency

DecisionsRaw Data

ParallelComputing

Uncertainties

Optimal production


Multi-objectiveReal-time optimization

High accuracy



Economy

Just in time

Market-driven

Logistics

Corporate

Supply Chain

62




Available for questions:

[email protected]

Documents

20130426 Manenti - Process Control