model predictive control of distributed and hierarchical systems leuven, february 15, 2007 process...
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Model Predictive Controlof Distributed and
Hierarchical Systems
Leuven, February 15, 2007
Process Systems Engineering
RWTH Aachen University
Johannes Gerhard, Jan Busch
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 2
The Current Business Climate
From growing market volume and limited competition
to market saturation and global competition in the 21st century:
• internet and e-commerce facilitate complete market transparency,
• transportation cost continue to decrease,
• engineering and manufacturing skills are available globally.
Economic success requires to quickly transform new ideas into
marketable products:
• product innovation to open-up new market opportunities,
• process design for best-in-class plants to maximize lifecycle profits,
• efficient, robust, and agile manufacturing to make best use of existing assets.
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 3
General Objective
Drive the manufacturing process to its economical optimum anytime !
decision making on process operations
market
process uncertainties& disturbances
constraints• equipment, safety, environment• capacity, quality, reproducability
time-varying profiles
manipulatedvariables
observedvariables
d
Φ
h
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 4
Real-Time Business Decision Making
Real-time business decision making (RT-BDM)
• the set of activities performed by humans and assisting processoperation support technology
• to manage a manufacturing process
• for profibability and agility
increasingdegree ofautomation
cor-porate
planning
set-point optimization
field instrumentation and base layer control
advanced control
planning &scheduling
site, enterprise
plant, packagedunit
unit, groupof units
field
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 5
A Systems View on Manufacturing
processing subsystem the process plant – materials processing entities
operating subsystem the „control system“ – monitoring, controlling and automated decision making
managing subsystem the „plant operators“ – all humans participating in decision making and execution
towards higher levels of automation !
split of work ?
process
pla
nt operations
support system
decision maker
(Schuler, 1992, Backx et al., 1998)
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 6
RT-BDM – An Integrated Approach
dynamic data recon-
ciliation
decision maker
optimal control
process including
base control
c)(tuc
)(td
)(tdr
)( cr tx
c
)(t
h,optimizing feedbackcontrol system
optimizing feedbackcontrol system
process includingbase layer control
• optimal output feedback structure
• solution of optimal controlreconciliation problems atcontroller sampling frequency
• computationally demanding, limited by model complexity
• lack of transparency,redundancy and reliability
(Terwiesch et al., 1994;Helbig et al., 1998;Wisnewski & Doyle, 1996;Biegler & Sentoni, 2000Diehl et al., 2002,
van Hessem, 2004)
plant
operation support system
process
decision maker
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 7
Horizontal (Functional) Decomposition
• decentralization typically oriented at functional constituents of the plant
• coordination strategies enable approximation of”true” optimum
• not adequately covered inoptimization-based controland operations yet
• (Mesarovic et al., 1970;Findeisen et al., 1980;Morari et al., 1980;Lu, 2000; Venkat et al., 2006)
decision maker
subprocess 2
h,
)(2 tdsubprocess
1
coordinator
optimizing feedback
controller 2
optimizing feedback
controller 1
)(1 td
2,c)(2 t
)(2, tuc
1,c)(1 t
)(1, tuc
optimizing feedbackcontrol system
co co
subprocess 2subprocess 1
see technical presentation !
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 8
Vertical (Time-Scale) Decomposition
• generalizes steady-state real-time optimization and
constrained predictive control
• generalizes cascaded feedback control structure
• requires (multiple) time-scale separation, e.g.d(t) = d0(t) + d(t)with trend d0(t) and zero mean fluctuation d(t)
(Helbig et al., 2000,Kadam et al., 2003)
decision maker
tracking controller
h,
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scale dynamic data reconciliation
short time scale dynamic data reconciliation
time scale
separator)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
optimizing feedbackcontrol system
process including
base control
)(td
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 9
decision maker
tracking controller
h,
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scale dynamic data reconciliation
short time scale dynamic data reconciliation
time scale
separator)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
Dynamic Real-time Optimization
• dynamic optimization - a versatile means for problem formulation
• economical objectives and constraints
• still a challenge for numerical methods
optimizing feedbackcontrol system
process including
base control
)(td
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 10
decision variables: u(t) time-variant control variables
p time-invariant parameters
tf final time
Mathematical Problem Formulation
))((min,),(
ftptu
txf
objective function (e.g. economics)
endpoint constraints (e.g. specs.)))((0
,],[),,,,(0
,)(0
,],[),,,,(
0
00
0
f
f
f
txE
ttttpuxP
xtx
ttttpuxFxM
DAE system (process model)
path constraints (e.g. temp. bound)
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 11
Sequential Solution Strategy
Control vector parameterization
ik
kikii tctu )()( ,,
)(, tki parameterizationfunctions
kic , parameterst
ui(t)
i,k(t)
ci,k
Reformulation as nonlinear programming problem (NLP) )),,((min
,,f
tpctpcx
f
))((0
,),,,,(0
f
ii
txE
ttpcxP
s.t.
DAE system solved by
underlying numerical
integration
Gradients for NLP solver typically obtained by integration of sensitivity systems
State and sensitivity integration dominate computational effort!
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 12
Improved Algorithms – Sequential Approach
Sensitivity integrationis expensive
Reduce numberof sensitivity parameters
Improve efficiency of sensitivity integration
Reduce model complexity
State integration is expensive
Control gridadaptation strategy
),(f
1
11 zX
h
MAA
h
MAA
h
MA
XX k
jn
j
j
kk
z
New methods forfirst and second-ordersensitivity integration
Methods formodel reduction
2x
1x
2z 1z
*x
Schlegel et al., 2003Hannemann & M., 2007
Schlegel et al., 2001,Romijn et al., 2007
Schlegel & M., 2004,…,Hartwich & M., 2006
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 13
Optimization under uncertainty (CNLD)
Optimization under parametric uncertainty• e.g. reaction kinetics, drifting catalyst activity …
Constructive nonlinear dynamics (CNLD)
Normal vector constraints guarantee minimal distance to critical manifolds• Optimum is robust w.r.t. to uncertain parameters • General concept of critical manifolds allows
different problem formulations• close relationship to semi-infinite programming
a
k
ProblemOptimum may be unstable, constraints may be violated because of uncertainty.
a,k
Process properties defined by critical manifolds in the parameter space
r F
k
Tasks addressed with CNLD
• robust stability• robust performance• robust process constraints• robust optimal control (cf. technical presentation)
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 14
decision maker
tracking controller
process including
base control
h,
c)()()( tututu cc
)(td
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scale dynamic data reconciliation
short time scale dynamic data reconciliation
time scale
separator)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
Integration of Control and Optimization
• type of controller? • control problem formulations: models, constraints, algorithms, …?
• how to reconcile control and optimization levels?
• how to account for process and model uncertainty?
• ...
optimizing feedbackcontrol system
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 15
Trajectory Tracking Predictive Control
• dynamic real-time optimization (D-RTO) on slow time-scale
• model predictive control (MPC)on fast time-scale– time-variant linear model
from linearization and linear model reduction
– some constraints (which?)– control performance
monitoring
• works well in (simulated) Bayer polymerization process (Dünnebier et al., 2004)
t
t~
D-RTO
MPC
refref uy ,
t~
t
updated
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 16
t
t~ MPC
Tight Integration of Control and Optimization
refref uy ,updated
fast trajectory updates
reoptimization with refinement of control discretization
reoptimization with coarse control discretization
linear time-varyingMPC in delta-modefor trajectory tracking,
dynamic real-time optimization (D-RTO), trajectory updates when necessary
D-RTO
linear time-varying controller
neighboring extremal update,when possible
Kadam et al. (2003)Kadam & M. (2004)
sensitivityanalysis
with changing active set
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 17
A Radically Different Approach
Do you solve optimal control problems when you drive a car?
Join in my driver‘s contest!
Finish
.)(,0)(ftff xtxtv
Start
0)0(),0( vx
Slope of street uncertain
max)( vtv
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 18
Solution Model
0),,,,( s.t.
min,
avxvxf
t fta f
Finish
.)(,0)(ftff xtxtv
Start
0)0(),0( vx
Slope of street uncertain
max)( vtv
0 10 20 30
-1
-0.5
0
0.5
1MAX
MIN
PATH
acceleration a
time [second]0 10 20 30
0
2
4
6
8
10
0 10 20 300
50
100
150
200
250
velocity vdistance x
time [second]
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 19
0 10 20 300
2
4
6
8
10
0 10 20 300
50
100
150
200
250
velocity vdistance x
1 2
NCO Tracking
• assume non-changing switchingstructure due to uncertainty:parametric but no structuralchanges in the solution model
• parameterize nominal
optimal control profiles (sequence & type of arcs): the solution model
• implement a (linear) multi-variable (decentralized switching) controlsystem with solution model as setpoint: track the NCO
(Bonvin, Srinivasan et al., 2003)
• automatically detect switching structureby numerical optimization:facilitate solution model generation
(Schlegel & Marquardt, 2004, Hartwich & M., 2006)
tracking activeconstraint
adjust switching time
close to optim
al perfo
rmance
without o
n-line optim
ization
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 20
decision maker
tracking controller
process including
base control
h,
c)()()( tututu cc
)(td
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scale dynamic data reconciliation
short time scale dynamic data reconciliation
time scale
separator)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
Integration with Planning and Scheduling
• models, formulations, algorithms, ...
• integrated ordecomposed
problem formulations
• how to account for process performance and uncertainty on the planning level• ...
optimizing feedbackcontrol system
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 21
Scenario-based Decision Making
Situated action: adjust operational strategy to context !
scenario (market, suppliers,demand, state of plant ...)
strategy 1
strategy 2
...
stra. ...
tft0
strategy 2
stra. ...
strategy 1
tft0
strategy 2strat. 3strategy 1
optimal changeover &automatic sequencing
...
Min cost
Max flexibility
different objectives
…
...
product A
product B
different products
…
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 22
Disjunctive Programming Formulation
,,0),()(
,0,,
,],,[,0,,,
,],,[,0,,,,..
1
00
1
1
mkkkkdk
kkkkk
kkkkkk
Kkptzmtz
pzzl
Kkttttpuzg
Kkttttpuzzfts
• Dynamic model:
• Constraints:
• Initial conditions:
• Stage transition conditions:
• Objective:
s
kk
n
kkkkk
Ypuztptz
1,,,
,,)(:min
• Propositional logic: .)( TrueY
(MLDO)
,0
,0)](
,,[
,
,0),()(
,0,,
,0,,,
,0,,,,
1
,
1
00
,
,
i
Tkk
TTkik
i
ii
kkikk
dk
i
kkik
kkkik
i
b
tz
puB
Y
b
ptzvtz
pzzs
tpuzr
tpuzzq
Y
• Disjunctions:
Yn
iib
1
Raman, Grossmann (1994), Oldenburg et al. (2003)
Dynamic optimizatio
n / MLDO
implemented in
DyOS
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 23
decision maker
tracking controller
process including
base control
h,
c
)(td
c
optimaltransitions
med. time scale dynamic data reconciliation
short time scale dynamic data reconciliation
time scale
separator0
0
Real-time Business Decision Making
optimizing feedback control system on different time-scales
planning &scheduling
long time scale dynamic data reconciliation
implementation requires …
• process systems methods and tools
• technology platforms for product packaging and implementation
• business platforms for market penetration
s s
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 24
Technology Platform Prerequisites
• Computing power– hardware: processor– networks: bus systems– software
high computing performantcomputing: no saturation yet
communication networks: field bus systems, LAN, WAN etc. are in place
software platform: management execution systems link ERP and manufacturing levels
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 25
INCA Software Platform
IPCOSOPC Server
Matlab – StateEstimation
gPROMS – processsimulation 2
PLS
DyOS – Real TimeOptimization
Matlab - MPC
gPROMS – processsimulation 1
• INCOOP, PROMATCH EU-projects• modular design• easy plant / simulator replacement
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 26
Research Interests
sub-system 1 sub-
system 2
coordination
• coordination – from the linear to the nonlinear case
• robustness – NLD for distributed (linear) controllers
open issues
technicalpresentations
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 27
Research Interests
sub-system 1 sub-
system 2
• coordination – from the linear to the nonlinear case
• robustness – NLD for distributed (linear) controllers
• use of overall process models?
open issues
D-RTO
scheduling
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 28
Research Interests
coordination
• coordination – from the linear to the nonlinear case
• robustness – NLD for distributed (linear) controllers
• use of overall process models?
• hierarchy in subsystems
• coordination in 2-dim space
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
open issues
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
coordination
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
MPC of Distributed and Hierarchical Systems – Leuven, 15.2.2007 29
Research Interests
coordination
• coordination – from the linear to the nonlinear case
• robustness – NLD for distributed (linear) controllers
• use of overall process models?
• hierarchy in subsystems?
• coordination in 2-dim space?
• NCO tracking – a promising alternative for subsystem optimization?
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
open issues
coordination
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
trackingcontroller
c)()()( tututu cc
)(0 td
)(0 ctx
c
optimal trajectory
design
long time scaledynamic datareconciliation
short time scaledynamic datareconciliation
time scaleseparator
)(td)(0 ctx
)(),(),( tutytx ccc
)(0 t
)(t
00
processincluding
base control
)(td
NCO tracking