Integrated Process Networks:Nonlinear Control System Design

for Optimality and Dynamic Performance

Michael Baldeaa,b and Prodromos Daoutidisa

aUniversity of Minnesota, Minneapolis, MN 55455bPraxair, Inc., Tonawanda, NY 14150

Antonio C. Brandao Araujo and Sigurd SkogestadNorwegian University of Science and Technology

NO-7491 Trondheim, Norway

Chemical Plant

• Material recycle• Heat integration

• Feedback interactions within the plant

Control of Tightly Integrated Plants:Challenging and Important!

• Decentralized control: inherent limitations

• Fully centralized control: generally impractical– Size / complexity of dynamic models– Ill-conditioning

• Efficient transient operation : critical – Moves across product slate due to frequent

changes in market conditions and economics– Going beyond regulatory control…– Accounting for ‘network’ dynamics

Research on Integrated Process Networks

Dynamic Analysis:– Slow response, high sensitivity to disturbances,

instability (Gilliland et al. ’64, Denn & Lavie ’82, Skogestad & Morari ’87,

Luyben ’93, Mizsey & Kalmar ’96)

– Nonlinear dynamics (Morud & Skogestad ’94, ’96, Bildea et al. ’00, Kiss et al. ’06)

Research on Integrated Process Networks

Control– Interaction of design and control for reaction-separation

networks (Luyben ’93, Luyben M. & Floudas ’94, Yin & Luyben ‘97)

– Plant-wide control(Price & Georgakis ’93, Luyben et al. ’97, Ng & Stephanopoulos ’98, Zheng et al. ’99)

– Applications to benchmark problems (McAvoy & Ye, ’94, Ricker, ’96, Ricker and Lee, ’95, Larsson et al. ’01, Jockenhovel et al. ’03)

– Self – optimizing control (Morari et al. ’80, Skogestad ’00)

– Partial control (Shinnar et al. ’96, Tyreus ’99, Kothare et al. ’00)

– Passivity based stabilization (Ydstie et al. ’98, ’99) – Dynamic optimization

(Tosukhowong et al. ’04)– Time-scale analysis / nonlinear model reduction and control

(Kumar and Daoutidis ’02, Baldea et al. ’06, Baldea and Daoutidis ’05 ’06)

Present Work

• Combining time-scale analysis (dynamics)

and self-optimizing control (steady state

economics):

– Control structure design– Nonlinear supervisory control

• Prototype reactor-separator-recycle network

Plant-wide ControlHierarchy of Decisions(Larsson and Skogestad, 2000)

I. TOP-DOWN

Step 1. DEGREES OF FREEDOMStep 2. OPERATIONAL OBJECTIVESStep 3. CONTROLLED VARIABLES Step 4. PRODUCTION RATE

II. BOTTOM-UP

Step 5. REGULATORY CONTROL LAYER (PID) Step 6. SUPERVISORY CONTROL LAYER (MPC) Step 7. OPTIMIZATION LAYER (RTO) Can we do without?

Planning(months - years)

What should we control?

Optimization level: Solve

Optimal solution: usually at constraints– most degrees of freedom are used to satisfy “active

constraints”

• Control active constraints!– Implementation usually simple

• What else should we control?– Variables for remaining unconstrained degrees of

freedom: acceptable losses in the presence of disturbances and implementation errors

00 0 0min ( , , )

uJ x u d

0 0

0 0

( , , ) 0

( , , ) 0

f x u d

g x u d

Self-optimizing Control

Principle:

(Economically) acceptable operation (loss) should be achieved using constant set points for the controlled variables, without the need to re-optimize when disturbances occur.

c=cs

Planning(months - years)

Identify degrees of freedom, disturbances

Define economics,operational constraints

Optimize for the various disturbances

Identify (and control) active constraints

Identify “self-optimizing” controlled variables for remaining degrees of freedom

“Bottom-up” design regulatory/stabilizing structure

Multiple possible supervisory configurations

Performance assessment: Dynamic simulation

No a-priori performance indication

Controlled Variables

Selection of Controlled Variables

Integrated Process Network:Multiple Time Scale Dynamics

•Low single pass conversion - high recycle rate

•Impurities present in the feed – small amount

•Impurities do not separate readily -small purge stream

Baldea and Daoutidis, Comp. Chem. Eng., 2006.

Dynamic Model

: scaled inputs : large recycle loop flowrates : scaled inputs : medium flowrates : scaled input : small purge flowrate : small parameter – ratio of throughput to recycle

: small parameter – ratio of purge to throughput states

terms: stiffness, multiple time scales

lusu

1pu

1

2 2

1( , ) ( )

( ) ( ) ( )

s l l

Io I p P

x f x u g x u

g x g x g x u

2

(1), ( ), (1/ )O O O

N C

Model ReductionTime Scale Decomposition

• Fast time scale (process units)

• Intermediate time scale (network)

• Slow time scale (impurity levels)

( )l ldxg x u

d 0 ( )l lg x u

lu

1/t dimensional

Equilibrium manifold

Manipulated inputs

( 1)S C

dimensional

Equilibrium manifold

Manipulated inputs

( 1) 1N S C ˆ ( , )s

df u

dt

su

0 ( , )sf u

1-dimensional

Manipulated input

2t

pu ˆ( ) ( )Io p Pdg x g x u

d

t

Hierarchical Controller Design

PRODUCT PURITYPRODUCTION RATE

HOLDUPSSTABILIZATION

HOLDUPSSTABILIZATION

LA

YE

RS

SU

PE

RV

ISO

RY

REGULATORYLAYER

IMPURITY LEVELS

SUPERVISORY CONTROL

SLOW TIME SCALESUPERVISORY CONTROL

INTERMEDIATE T.S.

OP

TIM

IZA

TIO

NL

AY

ER

FA

ST

ER

TIM

E S

CA

LE

FAST TIME SCALEDISTRIBUTED CONTROL

INTERMEDIATE T.S.SUPERVISORY CONTROL

NETWORK LEVELOPTIMIZATION

pu

,

s

L sp

uy

su

Lu

Manipulated inputsControl objectives (broad)

Optimality and Dynamic Performance

Self Optimizing Control– economic insight– selection of controlled

variables

Time Scale Analysis– dynamic perspective– selection of manipulated

inputs

Combining:

control designs with inherent optimality and good dynamic performance

Case StudyGeneric Reactor – Condenser Network

• Slow reaction , large recycle• Product nonvolatile• Volatile impurity present in the feed

• Degrees of freedom: R (W), F, P, L

A B

IB

Insights from Time-scale Analysis

• Control objectives: vapor holdups (pressures) stabilization (fast), liquid holdup stabilization, X B (intermediate) impurity levels (slow)

• Available degrees of freedom: R,F (fast) L, M RSP, M CSP (intermediate) P (slow)

Hierarchical Controller Design (I)(Baldea and Daoutidis C&ChE, 2006)

Time scale Controlled output

Manipulated

Input

Controller

Fast Reactor holdup Reactor effluent Proportional

Fast Condenser vapor holdup

Recycle rate Proportional

Intermediate Liquid holdup Liquid flowrate Proportional

Intermediate Product purity Reactor holdup

Set point

Nonlinear, model-based, cascade

Slow Inert levels in reactor

Purge flowrate Nonlinear, model-based

Control Structure I

• Reactor pressure allowed to vary • Compressor/pressure constraints?

Insights from Self-optimizing Control

• Disturbances: FO, yA,O, yI,O, xB,TR ,k1

• Cost function: J = pW*W - pL*L + pP*L• Active constraints: Reactor pressure, product purity• Self-optimizing variable: W

Self-optimizing Control Structure (II)

• No control of impurity• Poor dynamics: small purge controls product purity

Hierarchical / Self-optimizing Controller Design (III)

Time scale Controlled output

Manipulated

Input

Controller

Fast Reactor holdup Reactor effluent Proportional

Condenser vapor holdup

Recycle rate

(compressor power)

Proportional

Intermediate Liquid holdup Liquid flowrate Proportional

Product purity Condenser vapor holdup

set point

Nonlinear, model-based, cascade

Slow Compressor power

Purge flowrate Proportional Integral

5% increase in purity setpoint

5% increase in purity setpoint

20% increase in production rate

20% increase in production rate

Concluding Remarks

• Self-optimizing control / time-scale analysis: complementary perspectives

steady-state economics vs dynamics

controlled variables vs manipulated inputs

• Control configurations that are self-optimizing and have good closed - loop response characteristics

• Well-conditioned nonlinear supervisory controllers

based on reduced order models

Acknowledgements

• National Science Foundation

• MB partially funded by a University of Minnesota Doctoral Dissertation Fellowship

Integrated Process Networks:Nonlinear Control System Design

for Optimality and Dynamic Performance

Michael Baldeaa,b and Prodromos Daoutidisa

aUniversity of Minnesota, Minneapolis, MN 55455bPraxair, Inc., Tonawanda, NY 14150

Antonio C. Brandao Araujo and Sigurd SkogestadNorwegian University of Science and Technology

NO-7491 Trondheim, Norway