Real-Time Optimization - CEPACcepac.cheme.cmu.edu/pasi2011/library/biegler/LB_rto.pdf · Dynamic...
Transcript of Real-Time Optimization - CEPACcepac.cheme.cmu.edu/pasi2011/library/biegler/LB_rto.pdf · Dynamic...
6/24/11
1
Real-Time Optimization
Data Reconciliation & Parameter Identification
• Estimation problem formulations • Steady state model • Maximum likelihood objective functions considered to get parameters (p)
Minp Φ(x, y, p, w)
s.t. c(x, u, p, w) = 0 x ∈ X, p ∈ P
Plant
DR-PE c(x, u, p) = 0
RTO c(x, u, p) = 0
APC
y
p
u
w
On line optimization • Steady state model for states (x) • Supply setpoints (u) to APC (control system) • Model mismatch, measured and unmeasured disturbances (w)
Minu F(x, u, w) s.t. c(x, u, p, w) = 0 x ∈ X, u ∈ U
9
RTO Characteristics
Plant
DR-PE c(x, u, p) = 0
RTO c(x, u, p) = 0
APC
y
p
u
w
• Data reconciliation – identify gross errors and consistency in data • Periodic update of process model identification • Usually requires APC loops (MPC, DMC, etc.) • RTO/APC interactions: Assume decomposition of time scales
• APC to handle disturbances and fast dynamics • RTO to handle static operations
• Typical cycle: 1-2 hours, closed loop 10
6/24/11
2
RTO Consistency (Marlin and coworkers)
• How simple a model is simple?
• Plant and RTO model must be feasible for measurements (y), parameters (p) and setpoints (u)
• Plant and RTO model must recognize (close to) same optimum (u*) => satisfy same KKT conditions
• Can RTO model be tuned parametrically to do this?
11
RTO Stability (Marlin and coworkers)
• Stability of APC loop is different from RTO loop
• Is the RTO loop stable to disturbances and input changes?
• How do DR-PE and RTO interact? Can they cycle?
• Interactions with APC and plant? • Stability theory based on small
gain in loop < 1. • Can always be guaranteed by
updating process sufficiently slowly.
Plant
DR-PE c(x, u, p) = 0
RTO c(x, u, p) = 0
APC
y
p
u
w
12
6/24/11
3
RTO Robustness (Marlin and coworkers)
• What is sensitivity of the optimum to disturbances and model mismatch? => NLP sensitivity
• Are we optimizing on the noise?
• Has the process really changed?
• Statistical test on objective function => change is within a confidence region satisfying a χ2 distribution
• Implement new RTO solution only when the change is significant
• Eliminate ping-ponging 13
6
REACT OR E FFL UENT FROM LOW PRES SURE S EPARATOR
PREFLASH
MAIN FRA
C.
RECYCLEOIL
REFORMERNAPHT HA
C3/C4
SPLITTER
nC4
iC4
C3
M IXED LPG
FUE L GAS
LIGHT NAPHT HA
ABSO
RBER/
STRIPP
ER
DEBUTA
NIZER
DIB
• square parameter case to fit the model to operating data. • optimization to determine best operating conditions
Existing process, optimization on-line at regular intervals: 17 hydrocarbon components, 8 heat exchangers, absorber/stripper (30 trays), debutanizer (20 trays), C3/C4 splitter (20 trays) and deisobutanizer (33 trays).
Real-time Optimization with rSQP Sunoco Hydrocracker Fractionation Plant
(Bailey et al, 1993)
6/24/11
4
7
Model consists of 2836 equality constraints and only ten independent variables. It is also reasonably sparse and contains 24123 nonzero Jacobian elements.
P = ziCi
G
i!G
" + ziCi
E
i!E
" + ziCi
Pm
m=1
NP
" # U
Cases Considered:
1. Normal Base Case Operation
2. Simulate fouling by reducing the heat exchange coefficients for the debutanizer
3. Simulate fouling by reducing the heat exchange coefficients for splitter feed/bottoms exchangers
4. Increase price for propane
5. Increase base price for gasoline together with an increase in the octane credit
Optimization Case Study Characteristics
8
6/24/11
5
Real-time Optimization: Components
Plant
DR-PE c(x, u, p) = 0
RTO c(x, u, p) = 0
APC
y
p
u
w
• Data reconciliation – identify gross errors and inconsistency in data • Periodic update of process model identification • Usually requires APC loops (MPC, DMC, etc.) • RTO/APC interactions: Assume decomposition of time scales
• APC to handle disturbances and fast dynamics • RTO to handle static operations
• Typical cycle: 1-2 hours, closed loop • What if steady state and dynamic models are inconsistent?
10
Dynamic On-line Optimization?
Plant
DR-PE c(x, x’, u, p) = 0
D-RTO
c(x, x’, u, p) = 0
PC
y
p
u
d
m
Goal: Integrate On-line Optimization with Advanced Process Control +Consistent, first-principle dynamic models +Prediction and extrapolation – not fitting and interpolation +Links to Off-line Decision-making - Leads to increase in computational complexity - Requires time-critical calculations
Essential for: • Inherently Dynamic processes • Nonstandard operations • Optimal disturbance rejection
6/24/11
6
11
Dynamic Real-time Optimization Integrate On-line Optimization/Control with Off-line Planning • Consistent, first-principle models • Consistent, long-range, multi-stage planning • Increase in computational complexity • Time-critical calculations
Applications • Batch processes • Grade transitions • Cyclic reactors (coking, regeneration…) • Cyclic processes (PSA, SMB…)
Continuous processes are never in steady state: • Feed changes • Nonstandard operations • Optimal disturbance rejections
Simulation environments (e.g., ACM, gPROMS) and first principle dynamic models are widely used for off-line studies
8
Some DRTO Case Studies • Integrated grade transitions
– MINLP of scheduling with dynamics (Flores & Grossmann, 2006, Prata et al., 2007)
– Significant reduction in transition times • Dynamic Predictive Scheduling
– Processes and supply chains need to optimally respond to disturbances through dynamic models
– Reduction in energy cost by factor of two • Cyclic Process Optimization
– Decoking scheduling – SMB optimization – PSA optimization – Productivity increases by factor of 2-3
9
6/24/11
7
13
On-line Issues: Model Predictive Control (NMPC)
Process
NMPC Controller
d : disturbances z : differential states y : algebraic states
u : manipulated variables
ysp : set points
( )( )dpuyzG
dpuyzFz,,,,0,,,,
=
=′
NMPC Estimation and Control
!
minu
J(x(k)) = "(zl ,ul )+F(zN )l= 0
N
#
s.t.zl+1 = f (zl ,ul )
z0 = x(k)
Bounds
NMPC Subproblem
Why NMPC? Track a profile – evolve from
linear dynamic models (MPC) Severe nonlinear dynamics (e.g,
sign changes in gains) Operate process over wide range
(e.g., startup and shutdown)
Model Updater
( )( )dpuyzG
dpuyzFz,,,,0,,,,
=
=′
14
MPC - Background Motivate: embed dynamic model in moving horizon framework to drive
process to desired state • Generic MIMO controller • Direct handling of input and output constraints • Slow time-scales in chemical processes – consistent with dynamic
operating policies
Different types • Linear Models: Step Response (DMC) and State-space • Empirical Models: Neural Nets, Volterra Series • Hybrid Models: linear with binary variables, multi-models • First Principle Models – direct link to off-line planning NMPC Pros and Cons + Operate process over wide range (e.g., startup and shutdown) + Vehicle for Dynamic Real-time Optimization - Need Fast NLP Solver for Time-critical, on-line optimization - Computational Delay from On-line Optimization degrades performance
6/24/11
8
15
Tennessee Eastman Process
Unstable Reactor
11 Controls; Product, Purge streams
Model extended with energy balances
16
Tennessee Eastman Challenge Process
Method of Full Discretization of State and Control Variables
Large-scale Sparse block-diagonal NLP
DAE Model Number of differential equations 30
Number of algebraic variables 152
Number of algebraic equations 141
Difference (control variables) 11
NLP Optimization problem Number of variables of which are fixed
10920 0
Number of constraints 10260
Number of lower bounds 780
Number of upper bounds 540
Number of nonzeros in Jacobian 49230
Number of nonzeros in Hessian 14700
6/24/11
9
17
Setpoint change studies
Setpoint changes for the base case [Downs & Vogel]
Process variable Type
Magnitude
Production rate change Step
-15% Make a step change to the variable(s) used to set the process production rate so that the product flow leaving the stripper column base changes from 14,228 to 12,094 kg h-1
Reactor operating pressure change Step
-60 kPa Make a step change so that the reactor operating pressure changes from 2805 to 2745 kPa
Purge gas composition of component B change Step
+2% Make a step change so that the composition of component B in the gas purge changes from 13.82 to 15.82%
18
Case Study: Change Reactor pressure by 60 kPa
Control profiles
All profiles return to their base case values
Same production rate
Same product quality
Same control profile
Lower pressure – leads to larger gas phase (reactor) volume
Less compressor load
6/24/11
10
19
TE Case Study – Results I
Shift in TE process
Same production rate
More volume for reaction
Same reactor temperature
Initially less cooling water flow (more evaporation)
20
Case Study- Results II
Shift in TE process
Shift in reactor effluent to more condensables
Increase cooling water flow
Increase stripper steam to ensure same purity
Less compressor work
6/24/11
11
21
Case Study: Change Reactor Pressure by 60 kPa
Optimization with IPOPT
1000 Optimization Cycles
5-7 CPU seconds
11-14 Iterations
Optimization with SNOPT
Often failed due to poor conditioning
Could not be solved within sampling times
> 100 Iterations
22
What about Fast NMPC? Fast NMPC is not just NMPC with a fast solver
Computational delay – between receipt of process measurement and injection of control, determined by cost of dynamic optimization
Leads to loss of performance and stability (see Findeisen and Allgöwer, 2004; Santos et al., 2001)
As larger NLPs are considered for NMPC, can computational delay be overcome?
6/24/11
12
23
NMPC – Can we avoid on-line optimization? Divide Dynamic Optimization Problem:
• preparation, feedback response and transition stages • solve complete NLP in background (‘between’ sampling times) as part of preparation and transition stages • solve perturbed problem on-line • > two orders of magnitude reduction in on-line computation
Based on NLP sensitivity of z0 for dynamic systems • Extended to Collocation approach – Zavala et al. (2008, 2009) • Similar approach for MH State and Parameter Estimation – Zavala et al.
(2008)
Stability Properties (Zavala et al., 2009) • Nominal stability – no disturbances nor model mismatch
– Lyapunov-based analysis for NMPC • Robust stability – some degree of mismatch
– Input to State Stability (ISS) from Magni et al. (2005) • Extension to economic objective functions
24
NLP Sensitivity Parametric Programming
NLP Sensitivity Rely upon Existence and Differentiability of Path Main Idea: Obtain and find by Taylor Series Expansion
Optimality Conditions
Solution Triplet
6/24/11
13
25
NLP Sensitivity
Optimality Conditions of
Obtaining
Already Factored at Solution
Sensitivity Calculation from Single Backsolve
Approximate Solution Retains Active Set
KKT Matrix IPOPT
Apply Implicit Function Theorem to around
26
Solve NLP(k) in background (between tk and tk+1)
Advanced Step Nonlinear MPC (Zavala, B., 2008)
!
min J(x(k), u(k)) = F(xk+N |k ) + "(xl |k,vl |k )l= k+1
k+N#1
$
s.t. xk+1|k = f (x(k),u(k))
xl+1|k = f (xl |k,vl |k ), l = k +1,...k +N -1
xl |k % X, vl |k %U, xk+N |k % X f
Solve NLP in background (between steps, not on‐line) Update using sensiHvity on‐line
tk tk+1 tk+2
u(k)
x(k)
tk+N
xk+1|k
6/24/11
14
27
Solve NLP(k) in background (between tk and tk+1) SensiHvity to update problem on‐line to get (u(k+1))
!
Wk
Ak
"I
Ak
T0 0
Zk
0 Xk
#
$
% % %
&
'
( ( (
)x
)*
)z
#
$
% % %
&
'
( ( (
=
0
!
xk+1|k " x(k +1)
0
#
$
% % % % %
&
'
( ( ( ( (
Advanced Step Nonlinear MPC (Zavala, B., 2008) Solve NLP in background (between steps, not on‐line) Update using sensiHvity on‐line
x(k) x(k+1) u(k+1)
u(k)
tk tk+1 tk+2 tk+N
xk+1|k
28
Solve NLP(k) in background (between tk and tk+1) SensiHvity to update problem on‐line to get (u(k+1)) Solve NLP(k+1) in background (between tk+1 and tk+2)
Advanced Step Nonlinear MPC (Zavala, B., 2008)
!
min J(x(k +1), u(k +1)) = F(xk+N +1|k+1) + "(xl |k+1,vl |k+1)l= k+2
k+N
#
s.t. xk+2|k+1 = f (x(k +1),u(k +1))
xl+1|k+1 = f (xl |k,vl |k ), l = k +2,...k +N
xl |k+1 $ X, vl |k+1 $U, xk+N +1|k+1 $ X f
Solve NLP in background (between steps, not on‐line) Update using sensiHvity on‐line
tk tk+1 tk+2 tk+N
x(k) x(k+1)
u(k+1) u(k)
xk+2|k+1
6/24/11
15
29
Stability Properties of asNMPC
Robust Stability Theorem (Zavala, B., 2008) Assume that the NLP can be solved within one sampling time, and that robust stability assumptions hold for ideal NMPC (Magni, Scattolini, 2007). Then there exist bounds on the noise, w, and model mismatch, g, for which the cost function JN+1(x), obtained from the asNMPC strategy, is an input-to-state (ISS)-Lyapunov function and the resulting closed-loop system is ISS stable.
Nominal Stability Theorem (Zavala, B., 2008) Assume that the NLP can be solved within one sampling time, nominal stability assumptions hold for ideal NMPC (Mayne, 2000), and the nonlinear model is perfect without measurement noise. Then ideal NMPC controller performance and asNMPC controller performance are identical. Ideal NMPC stability asNMPC stability.
x(k+1) = f(x(k), u(k)) – plant and model identical
x(k+1) = f(x(k), u(k)) + g(x(k), u(k), w(k)) plant and model not identical
30
NMPC for High Purity Distillation
Air Separation Unit in IGCC-based Power Plants • Need for high purity O2 • Respond quickly to changes in process demand • Large, highly nonlinear dynamic separation (MESH) models
Methanol distillation (Diehl, Bock et al., 2005) • 40 trays, 210 DAEs, 19746 discretized equations
Argon Recovery Column • 50 trays, 260 DAEs, 21306 discretized equations
Double Column ASU Case Study • 80 trays, 1520 DAEs, 116,900 discretized equations
6/24/11
16
31
NonlinearModelPredictiveControl:AirSep’nUnit(Huang,B.,2008)
Objective:forcetheproductionratestofollowtheset-points,whilemaintheirpurities.4manipulatedvariables.4outputvariables.
L P Column
HP Column
30
20
31
19
1
15
25
40
26
C rude oxygen
L iquid Nitrogen
U3 (L N)
Heat exchanger & compressor
Gas Nitrogen
C rude Gas Nitrogen
A ir Feed
U1 (EA )
U2 (MA )
Pure oxygen
Pure nitrogenY 1 (POX )
Y 2 (PNI)
Temperature at the 30th trayY 3 (T l30)
Temperature at the 15th trayY 4 (Th15)
Reboiler Condenser
U4 (GN)
Horizon:100minutesin20finiteelements.Samplingtime:5minutes.
32
• Mesh Equations for Distillation Column
Mass balance:
Component balance:
Energy balance:
Phase equilibrium:
Hydrodynamics :
Assumption: Vapor holdups are negligible. Ideal vapor phases. Well mixed entering streams. Constant pressure drop. Equilibrium stage model.
Summation:
Mi
Li Vi+1
Vi Li-1
Index 2 system.
dM idt = L i ¡ 1 + Vi + 1 ¡ L i ¡ Vi + F i
Reformulated index 1 system contains 320 ODEs, 1200 AEs.
Fi
Case Study: Basic Air Separation Unit
6/24/11
17
33
ASUNonlinearMPC-Case1
OutputVariablesManipulatedVariablesThegreendot-dashedlinesaretheset-points,thebluedashedlinesarethelinearcontrollerprofilesandredsolidlinesareAS-NMPCprofile.
t=30-60min,productratesarerampeddownby30%.t=1000-1030min,theyarerampedback.AS-NMPCiscomparedtoMPCwithlinearinput-outputempiricalmodel.
Allthetuningparametersarefavoredtothelinearcontroller.
34
BluedashedlinesareidealNMPCprofileRedlinesareAS-NMPCprofile.Incontrast,linearizedcontrollerisunstable
Att=30-60min,productratesarerampeddownby40%.Att=1000-1030min,theyarerampedback.5%disturbanceisaddedtoMi.
N=20,K=3320ODEs,1200AEs.Variables:117,140Constraints:116,900400NLPssolvedBackground:200CPUs,6iters.Online:1CPUsComputationalFeedbackDelayReducedfrom2001second.
NMPCofAirSeparationUnit–Case2(Huang,B.,2009)
6/24/11
18
35
Parameter/State Estimation
Process
NMPC Controller
d : disturbances z : differential states y : algebraic states
u : manipulated variables
ysp : set points
( )( )dpuyzG
dpuyzFz,,,,0,,,,
=
=′
NMPC Estimation and Control Moving Horizon Estimation? Estimate a finite number of
states and model parameters (unmeasured disturbances, rate constants, transport parameters)
Compensate for process drifts and slowly changing conditions
Allow better controller performance
Model Updater
( )( )dpuyzG
dpuyzFz,,,,0,,,,
=
=′
Parameter Estimation Subproblem
36
Moving Horizon Estimation (MHE)
Large State Dimensionality
Degrees of Freedom
Solution Time Order of Minutes Highly Nonlinear, Ill-Conditioned?
Linear Systems, No inequalities Kalman Filter for State Estimation Nonlinear Systems: Extended Kalman Filters in Practice Moving Horizon Estimation:
+ directly captures nonlinear dynamics, statistical behavior - need to solve NLP on-line
Can MHE be improved?
6/24/11
19
37
Advanced Step Moving Horizon Estimation (as-MHE)
Given yl, zl, set “fake measurement” Solve MN in background (between tl and tl+1)
!
zl +1= f (zl ,wl ), y l +1
" #(zl +1)
Obtain measurement at tl+1, use KKT sensiHvity on‐line to get zl+1 Solve P(l+1) in background (between tl+1 and tl+2)
38
Offset-free Formulation • Apply MHE results as state and output corrections for NMPC problem • Modify with an advanced step approach as-MHE
Combining MHE & NMPC (Huang,Patwardhan,B.,2010)
6/24/11
20
39
Combined MHE and NMPC for ASU (Huang,B.,2010)
AMPL/IPOPT (DuoCore 2.4 GHz) NMPC background (6 iter/200 CPUs) MHE background (15 iter/90 CPUs)
• N=5, K=3 • 29,285 constraints • 30,885 variables
Online NMPC+MHE ~ 2 CPUs
Change in model mismatch (hydraulic parameter) • Setpoint • MHE/NMPC with correction • NMPC without correction
40
D-RTO with Economic Objectives Beyond NMPC Tracking
Plant
DR-PE c(x, u, p) = 0
RTO c(x, u, p) = 0
APC
y
p
u
w
Plant
DR-PE c(x, x’, u, p) = 0
D-RTO c(x, x’, u, p) = 0
PC
y
p
u
m
Benefits of combining RTO with NMPC? • Direct, dynamic production maximization • Remove artificial tracking objective • Remove artificial steady state problem
6/24/11
21
41
Challenges with D-RTO Replace regulation objective with economic objective in NMPC?
Active ongoing activity: • Bartusiak (2007) • Chachuat et al. (2008) • Dadhe and Engell (2008), Engell (2007, 2009) • Diehl and Rawlings (2009), Rawlings and Amrit (2009) • Kadam et al. (2008) • Zavala, B. (2009) • Swartz et al. (2010)
must be a K∞ function Sufficient Condition:
• Satisfy weak controllability condition
• Regularize economic objective so that NLP satisfies SSOC (and LICQ, SC)
Many Open Questions Still Remain
- need to assume an optimal steady state profit?
- how to consider periodic problems?
!
Min wl"(z
l,u
l){ } + F(z
N)
l
#
!
"(z,u)
42
Chain-Transfer Agent
LDPE
Flowrate Ethylene Inlet Temperatures
Low-Pressure Recycle
Hyper-Pressure Recycle
Ethylene Cold-Shots
Centralized Control Objectives: + Capture Complex Multivariable Interactions Between Zones
Control of Product Quality, Fouling Management + Perform Fast Grade Transitions (Highly Frequent)
Initiators Initiators Initiators Initiators
Centralized Model-Based Control
Recycle System and Flash Separation
Low-Density Polyethylene Process (Zavala, B., 2009)
6/24/11
22
43
LDPE Kinetic Model
~ 35 Elementary Reactions ~100 Kinetic Parameters
Complex Kinetic Mechanisms
44
Time (Days)
Heat Transfer Coefficient
Fouling
Defouling
Persistent Dynamic Disturbances – Strong Effect on Profitability
Cannot Remove Heat of Reaction - Drop Production to Avoid Runaway
Potential Economic Benefits + 1% Production 0.01 x (300,000 Ton/yr) x (1,500 $/Ton) = +4,500,000 $/yr
Case Study: Low-Density Polyethylene Process
6/24/11
23
45
LDPE Process Model Cw Cw
1 2 NZ
Cw Cw
Cw
Cw
Ethylene
Initiator(s) Initiator(s)
LDPE
Reaction Cooling Reaction
Conservation Mass, Energy, Momentum Thermodynamic & Transport Properties
Boundary Conditions
• Fouling must be estimated (using MHE) • Reference tracking inadequate!
Initial Conditions
Output Mapping Measured Outputs
States Inputs Parameters
46
NMPC-MHE Scenario LDPE NMPC – Computational Performance - Full-Discretization + IPOPT (MA57) - NLP ~ 50,000 Constraints, 300 Degrees of Freedom (DOF)
Sampling Time = 2 min
- Scale-Up With Prediction Horizon and Effect of KKT Matrix Reordering
NLP with 350,000 Constraints and 1,000 DOF Solved in ~ 2-3 Minutes
Nested Dissection Minimum Degree
Original
Reordered
6/24/11
24
47
3% More Production
NMPC Case Study – Economic Objective Maximize Production
Reference Profile
Economics-Oriented NMPC Moves Away from Suboptimal Reference Profile
Distributes Production Efficiently - More Production in Less Fouled Zones
Purely Economic Objective Leads to Ill-Posed Problems Need Regularization Term Due to Guarantee Stability
Minimize Transition Time
Core Temperature
Overall Production
Economics-Oriented Tracking
48
Dynamic optimization essential for many processes Batch processes Polymer processes (especially grade transitions) Periodic adsorption processes
Chemical Process Operations: RTO D-RTO Need for First-Principles Dynamic Models Extension to On-Line Economic Decision-Making NMPC and MHE Computational Strategies Full-Discretization + Fast Sensitivity Calculations Large Scale Models Basic ASU process with DAE model LDPE Process with NMPC and RTO Advantages over linear MPC Extension to Uncertainties – NMPC + MHE Formulations
Conclusions
6/24/11
25
References F. Allgöwer and A. Zheng (eds.), Nonlinear Model Predictive Control, Birkhaeuser, Basel (2000) R. D. Bartusiak, “NLMPC: A platform for optimal control of feed- or product-flexible manufacturing,” in Nonlinear Model Predictive Control 05, Allgower, Findeisen, Biegler (eds.), Springer (2007) Biegler Homepage: http://dynopt.cheme.cmu.edu/papers.htm Biegler, L. T., Nonlinear Programming: Concepts, Algorithms and Applications to Chemical Engineering, SIAM (2010) Forbes, J. F. and Marlin, T. E.. Model Accuracy for Economic Optimizing Controllers: The Bias Update Case. Ind.Eng.Chem.Res. 33, 1919-1929. 1994 Forbes, J. F. and Marlin, T. E.. “Design Cost: A Systematic Approach to Technology Selection for Model-Based Real-Time Optimization Systems,” Computers Chem.Engng. 20[6/7], 717-734. 1996 M. Grötschel, S. Krumke, J. Rambau (eds.), Online Optimization of Large Systems, Springer, Berlin (2001) K. Naidoo, J. Guiver, P. Turner, M. Keenan, M. Harmse “Experiences with Nonlinear MPC in Polymer Manufacturing,” in Nonlinear Model Predictive Control 05, Allgower, Findeisen, Biegler (eds.), Springer, to appear Yip, W. S. and Marlin, T. E. “Multiple Data Sets for Model Updating in Real-Time Operations Optimization,” Computers Chem.Engng. 26[10], 1345-1362. 2002.
42
References – Some DRTO Case Studies Busch, J.; Oldenburg, J.; Santos, M.; Cruse, A.; Marquardt, W. Dynamic predictive scheduling of operational strategies for continuous processes using mixed-logic dynamic optimization, Comput. Chem. Eng., 2007, 31, 574-587. Flores-Tlacuahuac, A.; Grossmann, I.E. Simultaneous cyclic scheduling and control of a multiproduct CSTR, Ind. Eng. Chem. Res., 2006, 27, 6698-6712. Kadam, J.; Srinivasan, B., Bonvin, D., Marquardt, W. Optimal grade transition in industrial polymerization processes via NCO tracking. AIChE J., 2007, 53, 3, 627-639. Oldenburg, J.; Marquardt, W.; Heinz D.; Leineweber, D. B., Mixed-logic dynamic optimization applied to batch distillation process design, AIChE J. 2003, 48(11), 2900- 2917. E Perea, B E Ydstie and I E Grossmann, A model predictive control strategy for supply chain optimization, Comput. Chem. Eng., 2003, 27, 1201-1218. M. Liepelt, K Schittkowski, Optimal control of distributed systems with breakpoints, p. 271 in M. Grötschel, S. Krumke, J. Rambau (eds.), Online Optimization of Large Systems, Springer, Berlin (2001) V. M. Zavala, and L.T.Biegler, “Optimization-Based Strategies for the Operation of Low-Density Polyethylene Tubular Reactors: Nonlinear Model Predictive Control," Computers and Chemical Engineering, 33, pp. 1735-1746 (2009)
See also Biegler homepage 43
6/24/11
26
51
For more details…
MOS-SIAM Series on Optimization • NLP Theory and Algorithms • Steady State Process Optimization • Dynamic Process Optimization
• Optimal Control • Sequential Approaches • Simultaneous Approaches
• Mathematical Programs with Complementarity Constraints
For more information: http://www.siam.org/catalog