Fast Nonlinear Model Predictive Control Algorithms and Applications in
Process EngineeringMoritz Diehl,
Optimization in Engineering Center (OPTEC) &Electrical Engineering Department (ESAT)
K.U. Leuven, Belgium
INRIA-Rocquencourt, May 30, 2007
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
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)
Optimization in Engineering Center OPTEC
Five year project, from 2005 to 2010, 500.000 Euro per year, about 20 professors, 10 pos tdocs, 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...
Quarterly Stevin Lecture: Everyone Invited!
�Quarterly „Simon Stevin Lecture on Optimization in Engineering“:• Dec 6: Larry Biegler , CMU Pittsburgh• Apr 18: Stephen Boyd , Stanford• July 9: 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
optimization algorithms
Simon Stevin, 1548-1620)
Lecture and following Reception in Arenberg Castle, Leuven
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
First Principle Dynamic System Models
E.g. some equations modelling a distillation column (in Stuttgart)
� Nonlinear differential algebraic equations (DAE)
� often 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?
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Principle of Optimal Feedback Control / Nonlinear MPC:
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!
Distillationcolumn (withUniv. Stuttgart)
Polymeri-sation reactor (withBASF)
ChromatographicSeparation (withUniv. Dortmund)
Combined CyclePower Plant (withUniv. Pavia)
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)
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
Optimal Control Family Tree
Optimal Control Family Tree
Optimal Control Family Tree
Optimal Control Problem in Simplest Form
Simplest Approach: Single Shooting
Nonlinear Program (NLP) in Single Shooting
�After control discretization, obtain NLP:
�Solve with NLP solver, e.g. Sequential Quadratic
Programming (SQP)
Sequential Quadratic Programming (SQP)
Toy Problem with One ODE for Illustration
Mildly nonlinear and unstable system.
Single Shooting
Single Shooting: First Iteration
Single Shooting: Second Iteration
Single Shooting: Third Iteration
Single Shooting: 4th Iteration
Single Shooting: 5th Iteration
Single Shooting: 6th Iteration
Single Shooting: 7th Iteration (Solution)
Single Shooting: Pros and Cons
Alternative: Direct Multiple Shooting [Bock, Plitt 1981]
Nonlinear Program in Multiple Shooting
SQP for Multiple Shooting
Summarize NLP:
Toy Example: Multiple Shooting Initialization
Multiple Shooting: First Iteration
Multiple Shooting: Second Iteration
Multiple Shooting: 3rd Iteration (already solution!)
Multiple Shooting: 3rd Iteration (already solution!)
Single shooting converged much slower!
The MUSCOD-II Developer Team [Heidelberg, Leuven, Madrid]
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
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 of 10-20 milliseconds [Ferreau et al. ‘06]
5*60*1000 / 20 = 15 000 times faster , due toMoore‘s law + Algorithm Development
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 of 10-20 milliseconds [Ferreau et al. ‘06], [Albersmeyer, Findeisen `06]
5*60*1000 / 20 = 15 000 times faster , due toMoore‘s law + Algorithm Development
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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ConventionalConventional::Initial Initial Value Value Embedding:Embedding:
Never simulate a nonlinear system open-loop!
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Real-Time Iterations minimize feedback delay
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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
Transient in 15 minutes instead of 2 hours!
Conclusions
�Recent progress makes Nonlinear MPC with first principles models in millisecond range possible (now 15 000 x faster than1998)
�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
An Invitation
�13th Czech-French-German Conference onOptimization (CFG07), Heidelberg, Germany, September 17-21, 2007. (inv. speakers: Fletcher, Scherer, Trelat, Waechter,...) Traditionally strong in optimal control.
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)
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