1

New Vistas for Process Control: Integrating Physics and Communication Networks

B. Erik Ydstie

K. Jillson, E. Dozal, M. Wartmann

Chemical Engineering

Carnegie Mellon University

2

Process

u y

•What is a Process Network?

•What is an observation (signal)?

• Is there a difference between process and information flow?

• Is a Process Network passive?

Controller

Information Network(process data, pictures, sound,..)

Process Network (energy and materials)

A1

A2

A3

A4A5

A41

A42

A43

r1

r2

s3 = r3

s4 = r4

s5 = r5

s5s41 = r41

T3

T2

T1

r4

signals

3

Passivity Based Control

u yControl system:

nsobservatio )(

system control ),()(

xhy

uxgxfdt

dx

=

+=

S

χ

α

χ

VV

vχvm

rFv

rvr

ii

i

ii

iii

3

)(

=

−+=

+=

&

&

&

Example: MD with thermostat

strain

friction

4

0 if ve)(dissipati passive ,2

2≥−≤ βςβyu

dt

dV T

x if passivestrictly State

if passivestrictly Output

if passivestrictly Input

→

→

→

ςςς

y

u

)Invariant"" is an,(Hamiltoni Lossless , Vyudt

dV T=

u y

S

Definitions:

0/Rx: :Function Storage +→V

0>β

5

Passivity Theorem (Input-Output Theory)

S

eC

A Feedback connection of a passive/lossless system S and a

strictly input passive control system C is finite gain stable.

n1

+

+

-

+n2

u

y

0 if passiveinput strictly , 00 >= gegu

u’

6

Proof

controller )(

system control ,)(

2

01

2

2

egunydt

dW

ynudt

dV

−+−≤

−+≤ βς

passive is system loop closed ,)( 22

0

2

1 βς−−

≤

+eg

u

y

n

n

dt

WVdT

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Q1. What Is a Process Network?

A1

A2

A3

A4A5

A41

A42

A43

r1

r2

s3 = r3

s4 = r4

s5 = r5

s5s41 = r41

T3

T2

T1

r4

Graph, G = (P,T,F)

� Vertices (Processes, Pi, i=1,…,nP)

� Vertices (Terminals connect to other processes, Ti, i=1,…,nT)

� Edges (Flows, Fi, i=1,…,nF)

A1: It is a network of (chemical) processes

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Processes

• Inventory Z(x) (material, energy, moles, charge,..) - HD1

• Potentials w (value, pressure, temp) - HD0

Conservation laws:

signals - nsobservatio ),(

system process ,)()(

Zhw

ufZpdt

dZ

i

i

=

+= ∑

A1: Z represents the state

A2: Exists S(Z), concave HD1

Z and w are dual (Legendre transform)

9

Q2: Is there a Difference between Process

and Information Flow?

B Signal Flow:

• Directed Graph

• A: x=z=y copy (intensive)

• B: x+y+z=0 conservation (extensive)

• Block Diagram Algebra

• SIMULINK

A Process Flow :

• Graph

• A and B: x+y+z=0

• A and B: u+v+w=0

• Bond graphs/circuits

• MODELICA

G A

BC

A2: Yes

e

y

y*

-

+

10

The Two Port Representation:

Transformation Processes

C

Resources Products

SActuators

u

Measurements

y

Communication

network

Signals are the Legendre

transform of process variables

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∑∑∑ −−−=terminalssconnectionprocesses

pwfwpwdt

dV TTT

∑ ZfwpXfwf i aaaa , , ,

Possibilities for passive feedback/feedforward

Theorem:

Like a Tellegen Theorem

Intensive variable control

(Dual space)

Inventory control

(Primal space)

Q3: Is a Process Network Passive?

A3: Qualified Yes, Depends on How Measurements and Actuators are Placed

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Literature Background

• Circuit theory and analog computers (1950ies)

• Irreversible thermodynamics (1950 - 60ies)

• Bond graphs (1960’ies)

• Thermodynamic networks (1960 - 70ies)

Application Domains

• Power Plant Control

• Decentralized Adaptive Control

• (Particulate systems/stat .mech.)

• (Supply chains)

• Financial and Business systems

• Integrated Operation

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C

Resources

(coal, air)

Products

(electricity)

SActuators

u

Measurements

y

Communication

network

Power Plant ControlPower Plant Control

Emerson TIE Seminar – May 2007

Power Plant ControlPower Plant ControlPower Plant Control

� Decentralized Modeling and synchronization

� Unit Coordinated control

Emerson TIE Seminar – May 2007

Integrated Unit Master ApproachIntegrated Unit Master ApproachIntegrated Unit Master Approach

� Provides index for total control of unit

� Allows operator entered megawatt target and ramp rate

� Provides seven modes of unit operation

� Allows operator entered high and low limits

� Provides local and remote unit dispatch

� Built-in unit runbacks, rundowns and inhibits

Load Demand Dispatch

Emerson TIE Seminar – May 2007

Emerson TIE Seminar – May 2007

Area Regulation Test Decentralized Inventory ControlArea Regulation Test Area Regulation Test Decentralized Inventory ControlDecentralized Inventory Control

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Decentralized Adaptive Control

Plant()

Plant()

?

1. Does control performance improve with communication?

?

2. Are (un-modeled) interconnections always bad?

Adaptive

Controller

Adaptive

Controller

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Financial and Business Systems

Intrinsic value S(Z)

(Warren Buffet)

=

l

axZ )(

assets

liabilities

Investment Operations Financing

Assets:

Current Assets

Fixed Assets

+ Other Assets

= Total Assets

Income:

Revenues

- Cost of Sales

= Gross Margin

- Operating Expenses

= Operating Result

- Taxes

= Net Profit (Loss)

Liabilities/Net Worth:

Current Liabilities

Long-term Liabilities

+Shareholder equity

= Total Liabilities

and Net Worth

Total Assets = Total Liabilities and Net Worth

The state of the company:

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Investment Operations Financing

Assets:

Current Assets

Fixed Assets

+ Other Assets

= Total Assets

Income:

Revenues

- Cost of Sales

= Gross Margin

- Operating Expenses

= Operating Result

- Taxes

= Net Profit (Loss)

Liabilities/Net Worth:

Current Liabilities

Long-term Liabilities

+Shareholder equity

= Total Liabilities

and Net Worth

Total Assets = Total Liabilities and Net Worth

Flow of products and services

(2nd Law of Thermo-All activities incur cost)Flow of cash

1stLaw of T

herm

o

cash of value,

)(intensiveinventory of ue val,

S

ET

Z

SwT

∂∂

=

∂∂

=

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Oilfield Review 2006

Faster decisions – Higher precision

Integrated Operation (IO) – Statoil-Hydro

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• Conservation Laws (KCL = 1st Law of Thermo)

• Dissipation (KVL = Second Law of Thermo)

Market

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Decentralized Decision Making The chemical plant

tank

tank

mixer

reactor

column

column

column

product

product

waste

supply

supply

recycle stream

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controller

controller

controllercontroller controller

controller

controller

Decentralized Decision-making:

Coordination- Move the Smarts Down

Coordination

Other processes

The Market

Power plants

• Coal

• IGCC (DOE)

• Acad. Prblms/

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Nature is Self-Optimizing

(“All Smarts Local”)

� Maxwell’s “theorem” of minimum heat (1871)

� Prigogine’s “theorem” of minimum entropy production (1947)

� Minimum dissipation and optimality in electrical circuits

(Desoer/Director 1960ies-70ies)

� Thermodynamic networks (1970ies)

Resistor 1

Resistor 2 V1 V2

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Network Theory: Optimality Top Down

=AF 0

T=W A w

1a) Conservation laws (KCL):

1b) Loop equations (KVL):

2) Constitutive equations:

=F WΛΛΛΛ3) Boundary conditions

The optimization problem:

1

fn

T

i i

i

W F=

=∑ W Fmin

Primal

Dual

Coordination

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Network Theory: Optimality Top Down

=AF 0

T=W A w

1a) Conservation laws (KCL):

1b) Loop equations (KVL):

2) Constitutive equations:

=F WΛΛΛΛ3) Boundary conditions

The optimization problem:

1

fn

T

i i

i

W F=

=∑ W Fmin

Primal

Dual

Coordination

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Network Theory: Optimality Bottom Up

=AF 0

T=W A w

1a) Conservation laws (KCL):

1b) Loop equations (KVL):

2) Constitutive equations:

=F WΛΛΛΛ3) Boundary conditions

The optimization problem:

1

fn

T

i i

i

W F=

=∑ W Fmin

Primal

Dual

Coordination

Optimization build into “control” structure(Toyota, GE 6-sigma, Alcoa,…..)

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Conclusions

• Two port description proposed to represent the interface between

(process) systems and signals (the information system)

• Conservation laws and passivity theory can be applied for

stability analysis of process networks

• Stability and (Global) optimality follows from passivity theory if

flow is derived from a “convex potential”