SLIDE 1 Fast Nonlinear Model Predictive Control Algorithms and Applications in Process Engineering
Moritz Diehl, Optimization in Engineering Center (OPTEC) & Electrical Engineering Department (ESAT) K.U. Leuven, Belgium
INRIA-Rocquencourt, May 30, 2007
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Outline of the Talk
K.U.Leuven‘s Optimization in Engineering Center OPTEC Nonlinear Model Predictive Control (NMPC) How to solve dynamic optimization problems? Four crucial features for fast NMPC algorithms Application to a Distillation Column
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OPTEC Aim: Connect Optimization Methods & Applications
Methods: New developments are inspired and driven by application needs Applications: Smart problem formulations allow efficient solution (e.g. convexity)
SLIDE 4 Optimization in Engineering Center OPTEC
Five year project, from 2005 to 2010, 500.000 Euro per year, about 20 professors, 10 postdocs, and 60 PhD students involved in OPTEC research Promoted by four departments: Electrical Engineering Mechanical Engineering Chemical Engineering Computer Science
Many real world applications at OPTEC...
SLIDE 5 Quarterly Stevin Lecture: Everyone Invited!
Quarterly „Simon Stevin Lecture on Optimization in Engineering“:
Larry Biegler, CMU Pittsburgh
Stephen Boyd, Stanford
Steve Wright, Madison, Wisconsin
- Oct 24: Manfred Morari, ETH Zurich
- Dec X:
David Mayne, Imperial, London „K.U. Leuven Seminar on Optimization in Engineering“ :
- Jan. 31: Mario Milanese (Torino): MPC of semi-active damping
- Feb. 8: Philippe Toint (Namur): large scale optimization methods
- Feb. 22: Peter Kuehl (Heidelberg): Robust optimal feedback control
- March 1: Yurii Nesterov (UCL)/ Florian Jarre (Duesseldorf): new
- ptimization algorithms
Simon Stevin, 1548-1620) Lecture and following Reception in Arenberg Castle, Leuven
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Outline of the Talk
K.U.Leuven‘s Optimization in Engineering Center OPTEC
Nonlinear Model Predictive Control (NMPC)
How to solve dynamic optimization problems? Four crucial features for fast NMPC algorithms Online MPC of a combustion engine
SLIDE 7 First Principle Dynamic System Models
E.g. some equations modelling a distillation column (in Stuttgart)
Nonlinear differential algebraic equations (DAE)
- ften in modeling languages like gPROMS,
SIMULINK, Modelica typical order of magnitude: some hundreds to thousands variables difficulties: stiffness, discontinuities, high index
Can we use these models directly for optimization and feedback control?
SLIDE 8 x0
x0 u0
u0
Principle of Optimal Feedback Control / Nonlinear MPC:
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Brain predicts and optimizes: e.g. slow down before curve Nonlinear Model Predictive Control When We Drive a Car Always look a bit into the future!
Main challenge for NMPC: fast and reliable real-time optimization!
SLIDE 10 Distillation column (with
Polymeri- sation reactor (with BASF) Chromatographic Separation (with
Combined Cycle Power Plant (with
PET plant: Plant wide control project with Politecnico di Milano Car Engines: EU Project with Univ. Linz, Stuttgart, Politecnico di Milano
NMPC applications, with decreasing timescales
Looping kites for power generation, with TU Delft, Politecnico di Torino Robot arms (with Columbia Univ. & INRIA Grenoble)
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Outline of the Talk
K.U.Leuven‘s Optimization in Engineering Center OPTEC Nonlinear Model Predictive Control (NMPC)
How to solve dynamic optimization problems?
Four crucial features for fast NMPC algorithms Application to a Distillation Column
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Optimal Control Family Tree
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Optimal Control Family Tree
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Optimal Control Family Tree
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Optimal Control Problem in Simplest Form
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Simplest Approach: Single Shooting
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Nonlinear Program (NLP) in Single Shooting
After control discretization, obtain NLP: Solve with NLP solver, e.g. Sequential Quadratic Programming (SQP)
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Sequential Quadratic Programming (SQP)
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Toy Problem with One ODE for Illustration
Mildly nonlinear and unstable system.
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Single Shooting
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Single Shooting: First Iteration
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Single Shooting: Second Iteration
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Single Shooting: Third Iteration
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Single Shooting: 4th Iteration
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Single Shooting: 5th Iteration
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Single Shooting: 6th Iteration
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Single Shooting: 7th Iteration (Solution)
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Single Shooting: Pros and Cons
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Alternative: Direct Multiple Shooting [Bock, Plitt 1981]
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Nonlinear Program in Multiple Shooting
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SQP for Multiple Shooting
Summarize NLP:
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Toy Example: Multiple Shooting Initialization
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Multiple Shooting: First Iteration
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Multiple Shooting: Second Iteration
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Multiple Shooting: 3rd Iteration (already solution!)
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Multiple Shooting: 3rd Iteration (already solution!)
Single shooting converged much slower!
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The MUSCOD-II Developer Team [Heidelberg, Leuven, Madrid]
SLIDE 39
Outline of the Talk
K.U.Leuven‘s Optimization in Engineering Center OPTEC Nonlinear Model Predictive Control (NMPC) How to solve dynamic optimization problems?
Four crucial features for fast NMPC algorithms
Online MPC of a combustion engine
SLIDE 40 NMPC Computation from 1998 to 2006
1998: 5th order distillation model allows sampling times of only 5 minutes [Allgower,
Findeisen, 1998]
2001: 206th order distillation model, sampling times of 20 seconds [D. et al. ‚01] 2006: 5th order engine model, sampling times
- f 10-20 milliseconds [Ferreau et al. ‘06]
5*60*1000 / 20 = 15 000 times faster, due to Moore‘s law + Algorithm Development
SLIDE 41 NMPC Computation from 1998 to 2006
1998: 5th order distillation model allows sampling times of only 5 minutes [Allgower,
Findeisen, 1998]
2001: 206th order distillation model, sampling times of 20 seconds [D. et al. ‚01] cf. [Biegler] 2006: 5th order engine model, sampling times
- f 10-20 milliseconds [Ferreau et al. ‘06], [Albersmeyer,
Findeisen `06]
5*60*1000 / 20 = 15 000 times faster, due to Moore‘s law + Algorithm Development
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Four Crucial Features for Fast NMPC
Direct, simultaneous optimal control: Multiple Shooting Efficient derivative generation for ODE/DAE solvers Initialization by „Initial Value Embedding“ Real-Time Iterations for fast tracking of optimal solutions
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Conventional Conventional: : Initial Initial Value Value Embedding: Embedding:
Never simulate a nonlinear system open-loop!
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Real-Time Iterations minimize feedback delay
SLIDE 58
Outline of the Talk
K.U.Leuven‘s Optimization in Engineering Center OPTEC Nonlinear Model Predictive Control (NMPC) How to solve dynamic optimization problems? Four crucial features for fast NMPC algorithms
Application to a Distillation Column
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Transient in 15 minutes instead of 2 hours!
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SLIDE 64 Conclusions
Recent progress makes Nonlinear MPC with first principles models in millisecond range possible (now 15 000 x faster than 1998) Emerging consensus for NMPC algorithms:
- employ direct, simultaneous methods
- use Initial Value Embedding (first order predictor)
- perform Real-Time Iterations to trace NMPC problem
solution while data change
- Use SQP type method to track active set changes
SLIDE 65 An Invitation
13th Czech-French-German Conference on Optimization (CFG07), Heidelberg, Germany, September 17-21, 2007.
(inv. speakers: Fletcher, Scherer, Trelat, Waechter,...) Traditionally strong in optimal control.
SLIDE 66 4 PhD Positions in Numerical Optimization:
- Sequential Convex Programming Algorithms for Nonlinear SDP
- Large Scale & PDE Constrained Real-Time Optimization Algorithms
- Fast Model Predictive Control Applications in Mechatronic Systems
- Shape Optimization of Mechanical Parts under Inertia Loading
(deadline: June 21, 2007)
