new vistas for process control - carnegie mellon...
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New Vistas for Process Control: Integrating Physics and Communication Networks
B. Erik Ydstie
K. Jillson, E. Dozal, M. Wartmann
Chemical Engineering
Carnegie Mellon University
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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
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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
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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
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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’
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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)
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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*
-
+
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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
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Emerson TIE Seminar – May 2007
Power Plant ControlPower Plant ControlPower Plant Control
� Decentralized Modeling and synchronization
� Unit Coordinated control
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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
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Emerson TIE Seminar – May 2007
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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”