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Computational Methods for Model Predictive ControlNew Opportunities for Computational Scientists
Jørgensen, John Bagterp; Boiroux, Dimitri; Hovgaard, Tobias Gybel; Halvgaard, Rasmus; Skajaa,Anders; Gade-Nielsen, Nicolai Fog; Standardi, Laura; Sokoler, Leo Emil; Völcker, Carsten; Capolei,Andrea
Publication date:2012
Document VersionPublisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):Jørgensen, J. B. (Author), Boiroux, D. (Author), Hovgaard, T. G. (Author), Halvgaard, R. (Author), Skajaa, A.(Author), Gade-Nielsen, N. F. (Author), ... Duun-Henriksen, A. K. (Author). (2012). Computational Methods forModel Predictive Control: New Opportunities for Computational Scientists. Sound/Visual production (digital),Technical University of Denmark (DTU).
Computational Methods for Model Predictive Control
New Opportunities for Computational Scientists
John Bagterp Jørgensen Dimitri Boiroux, Tobias Gybel Hovgaard, Rasmus Halvgaard, Anders Skajaa, Nicolai Fog Gade-Nielsen, Laura Standardi,
Leo Emil Sokoler, Carsten Völcker, Andrea Capolei, Gianluca Frison, Signe Schmidt, Anne-Katrine Dunn Henriksen
Technical University of Denmark
PARA 2012, Finlandia Hall, Helsinki, Finland June 10-13, 2012
Introduction • Model Predictive Control
– Optimal Experimental Design – Parameter Estimation – State Estimation – Regulation
• Constrained Optimization of Dynamical Systems • Case Studies
– The Artificial Pancreas – Closed-Loop Oil Reservoir Management – Smart Energy Systems
2
MODEL PREDICTIVE CONTROL
3
Systematic Model Building
4
Model Predictive Controller
5
Regulator
Estimator
System
Sensors
Targets Inputs
Model Predictive Controller
Outputs
Measure-ments
State-/parameter-estimate
Model Predictive Control
MPC =
Estimation + Regulation Moving horizon
implementation
6
Filtering and Prediction - EKF
Filtering
Prediction
7
Optimal Control Problem
Integrator (Runge-Kutta Methods) • DOPRI54 (non-stiff systems) • ESDIRK12 / ESDIRK23 / ESDIRK34 (stiff systems)
Sensitivities • Forward, Adjoint
Optimization • SQP • Single-shooting • Multiple-shooting 9
Insulin Administration Systems for
People with Diabetes
The Artificial Pancreas
10
Blood glucose control The blood glucose must stay within certain upper and lower bounds!
– Too low: coma (immediate effect) – Too high: blindness and other long-term effects
11
Insulin Administration Systems Pen or Pump
dosing
Continuous blood glucose monitor
Normal blood glucose level (90 mg/dL)
Control Algorithm
+
-
12
Systems Diagram
Man
BloodGlucose
Insulin infusionrate
Diffusion ofinsulin in
tissue
Diffusion ofglucose in
tissue
ModelPredictiveController
Subcutaneous Glucose
Physical activity /exercise
Insulininjection
Physiological System
GlucoseSensor
InsulinPump
Meal
Artificial Pancreas
GlucoseMeter
BloodGlucoseSetpoint
13
Physiological Models – The Virtual Patient
14
The Cobelli Model – and the Virtual Clinic
• Developed by – University of Virginia – University of Padova – Juvenile Diabetes Research Foundation
• 30 virtual patients in the version that we have a license to • The full version including 300 patients approved to substitute animal
tests by FDA 16
Clinical Trials • Gastric emptying trials (left) • Clinical trials collecting data for modeling
(right)
17
Example of a Clinical Experiment
8:00 Insert lines
12:30 Exercise
15:00 Snack
10:00 Meal/ bolus
18
Identification Results • Representative
model fit
• Very accurate model fit
• Note: Model is fit to the
CGM signal. The intravenous glucose concentration is also shown (thick line) for comparison
19
The DTU Type 1 Diabetes Model
20
Insulin Administration Strategies
NMPC Pre-meal Insulin Allowed
NMPC No Pre-meal Insulin
MDI (Pen Based) Insulin Treatment
21
Closed-Loop Studies by NMPC Meals not announced Meals announced at meal-time
22
Overnight Stabilization – A Cohort
23
Clinical Closed Loop Studies
24
MODEL PREDICTIVE CONTROL FOR MANAGEMENT OF OIL RESERVOIRS
25
An Offshore Oil Reservoir
26
Mathematical Model
27
Closed-Loop Reservoir Management
28
t
x Experimental setup Seismic data
Applied Seismology: Subsurface Imaging
29
The Computational Challenge: Integrated Inversion of Seismic and Production Data
Seismic inversion History matching
Seismic data Oil production data
30
History Matching (State and Parameter Est) + Seismic Data
=> Permeability Field
31
Optimization Problem
• Single-Shooting and SQP • ESDIRK methods tailored for this problem • Gradients computed by the adjoint method
32
Objective Function is the Net Present Value
33
Optimal Oil Field Development - MVs
34
Optimal Oil Field Development - CVs
35
Oil Field Development Using NMPC
36
MODEL PREDICTIVE CONTROL OF SMART ENERGY SYSTEMS
37
Smart Energy Systems
38
Wind Power
0%
20%
40%
60%
80%
100%
120%
01-2007 03-2007 05-2007 07-2007 09-2007 11-2007 01-2008
Wind power / consumption DK-W
Wind power share in the western part of Denmark: 24 %
39
Wind Power Production and Imbalances
0%
20%
40%
60%
80%
100%
120%
0 5 10 15 20 25 30 35Wind speed [m/s]
Pro
duct
ion
in %
of t
otal
inst
alle
d ca
paci
ty % of installed capacity
1 m/s change in wind speed changes the production by 350
MW (DK West)
40
Power System Development – DK West
Centralized system of the mid 1980s
Primary production plants
Local plants
Wind turbines
More decentralized system of today 41
Load Balancing Controller
42
Models of Energy Components
43
Controllable Power Generators
46
MPC for Economic Power Portfolio Optimization
47
Soft Economic MPC
48
Simple Test Example
49
Optimal Production Profiles
50
Cooling Houses – A Flexible Consumer • Motivation: • Refrigeration and air-conditioning consume
substantial amounts of energy. • E.g. up to 80% of energy consumed by
supermarkets goes to refrigeration.
• Methods: • Economic MPC:
Minimize the cost of cooling subject to temperature limits
• Predictions of weather, energy prices and load profiles.
• Implementation on industrial hardware.
Evaporator
Compressor
Expansionvalve
Condenser
Cold RoomOutdoorsurroundings
Suction Pressure controller
Condenser Pressure Controller
NEF
NCF
NC
Tcr
PC
PE
Qload
Pc,ref=PdewT(Ta+DT) Stored goods
MPC
Cooling system used in refrigerators and cooling houses
FPGA
52
Power Management 2 Power Plants and 1 Cooling House
• Economic Optimizing MPC • Minimize power consumption and costs without lowering the cooling quality • Load shifting utilizing the thermal capacity of the cooling house
53
Online Computing Time Tailored Primal-Dual Interior Point Algorithm
54
Warm Start Interior Point Methods
55
Accelerating LP Algorithms with GPUs
56
Implementation Details
57
Speed-Up with GPU
58
Dantzig-Wolfe Decomposition
59
Uncertainty
60
Uncertainty Scenarios
61
The Extended LQ Problem
62
KKT System for the Extended LQ Problem
63
KKT System for the Extended LQ Problem
64
Numerical Results
65
1 1.5 2 2.5-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1C code, N=100
log10(nx)
log 10
(wal
l clo
ck ti
me)
Riccati, nu=1Riccati, nu=2Riccati, nu=5Condensing, nu=1Condensing, nu=2Condensing, nu=5MA57, nu=1MA57, nu=2MA57, nu=5
Numerical Results
66
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2-3
-2.5
-2
-1.5
-1
-0.5C code, nx=50, nu=5
log10(N)
log 10
(CPU
tim
e)
RiccatiCondensingMA57
Summary
• There is a need for HPC software supporting MPC – QP, LP, SOCP algorithms – ODE/PDE solvers equipped with sensitivity computing
abilities (adjoints) – SQP / NLP algorithms – Efficient direct sparse and iterative methods for KKT
systems (even when they are ill-conditioned) • The number of potential applications is very large
67
Center for Energy Ressources Engineering (CERE) Consortium www.cere.dtu.dk
Novo Nordisk A/S, Hvidovre Hospital, Medtronic Danfoss A/S, DONG Energy A/S, Vestas A/S, GEA Process Engineering A/S The Danish Strategic Research Council The Danish Research Council for Production and Technology Sciences
68
