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Simulation and Optimization of Modelica Models with Optimica and JModelica.org

Outline

•  The JModelica.org open source project •  Dynamic optimization and Optimica •  The JModelica.org platform •  Tutorial examples •  What’s next?

Outline

•  The JModelica.org open source project •  Dynamic optimization and Optimica •  The JModelica.org platform •  Tutorial examples •  What’s next?

The JModelica.org open source project

What? JModelica.org is an extensible Modelica-based open source platform for optimization, simulation and analysis of complex dynamic systems.

Origin: JModelica.org is the result of research at the Department of Automatic control, Lund University, and is now maintained and developed by Modelon AB in cooperation with academia.

Our mission: To offer a community-based, free, open source, accessible, user and application oriented Modelica environment for optimization and simulation of complex dynamic systems, built on well-recognized technology and supporting major platforms

JModelica.org •  Simulation •  Optimization •  Analysis •  Visualization

Industrial Applications •  Grade change optimization •  Polyethylene production •  Decision support •  Flexible production •  Raw material prices vary •  Minimize off-spec

•  JModelica.org for optimization •  Grade changes and parameter

estimation •  Collaboration between Lund Univ.

and Borealis •  Per-Ola Larsson •  Niklas Andersson

Benefits •  Increased flexibility •  React quickly to market changes •  Economic optimization

JModelica.org is open source

•  Source code is freely available   Open Source Initiative approved licenses   GPL (CPL)

•  Infrastructure supporting a community   Transparency of development   Interactive web site   User forums

•  Dual licensing   Commercial licenses available   Bundling with commercial solvers   Support

One year with JModelica.org JM-1.5 •  FMU export •  Symbolic algs. •  External funcs. •  Sparse solvers •  Sampled systems

JM-1.4 •  Python model classes •  Enumerations •  Sensitivity alalysis •  Improved initialization

JM-1.3 •  FMU simulation •  Stream connectors •  Redeclare/replaceable

JM-1.2 •  Vectors •  Functions •  Assimulo

April 2010

March 2011

Outline

•  The JModelica.org open source project •  Dynamic optimization and Optimica •  The JModelica.org platform •  Tutorial examples •  What’s next?

Optimization and Modelica •  Modelica increasingly used in industry

  Expert knowledge   Capital investments

•  Mainly simulation... ...but new areas emerge   Model reduction   Parameter identification   Dynamic optimization   Model predictive control

•  Usages reported so far   Cope with simulation-oriented interfaces   Treat model essentially as a black box

•  Fast algorithms explores model structure   Real-time optimization

Dynamic optimization

•  Many algorithms   Applicability highly model-dependent (ODE, DAE, PDE, hybrid)

•  Calculus of variations •  Single/Multiple shooting •  Simultaneous methods •  Simulation-based methods (GA, simulated annealing)

•  Analogy with different simulation algorithms   Heavy burden to use numerical algorithms   Fortran, C, (AMPL)

•  Engineering need for high-level descriptions   Shift focus from encoding   to formulation of optimization problem

Typical workcycle

Modelica

Optimica

Result C code The Optimica Compiler

Executable

Generate and solve

Analyze and tune

Dynamic optimization

Optimization with Modelica

•  Strong support for modeling of dynamic systems •  Missing elements

  Cost function   Constraints   What to optimize   Initial guesses

•  Optimica   Small extension of Modelica   Enable high-level formulation of optimization problems

An example

A Modelica model

An Optimica model

Optimal Start-up of a Plate Reactor

•  Start-up of a plate reactor with exothermic reaction •  Tubular reactor inside a heath-exchanger •  Multiple injection points (hot spots) •  Generate open loop start-up trajectories using dynamic

optimization •  Large scale system

  >100 equations and variables

•  Multiple objectives   Bounded temperature profiles   Maximum conversion   Minimum start-up times   Robust to parameter variations

Plate reactor results

Reactant injection rates

Sta

te p

rofil

es

Feed and cooling temperatures

Inpu

t pro

files

Benefits •  Faster start-up sequences

  Profitability

•  Safety •  Process understanding •  Rapid design cycle

Outline

•  The JModelica.org open source project •  Dynamic optimization and Optimica •  The JModelica.org platform •  Tutorial examples •  What’s next?

Technologies •  Modelica •  JastAdd meta-compiler tool

  Modelica/Optimica compiler front-ends pure Java   Easily embedded jar-files

•  Python   Scientific computing environment   Scripting and visualization   Custom application development

•  XML   Model meta data

•  Eclipse   Modelica IDE

Python

•  Open source language (tools) •  Interpreted language •  Object-oriented •  Many OSS packages

  NumPy   SciPy   Matplotlib   OpenOpt

•  Easy to interface C, Java, Fortran…   Compiled JModelica.org models   SUNDIALS   Commonly used as ”glue language”

Optimization

•  Optimization is a standard engineering technology •  Automate manual search procedures •  Problem classes

  Parameter optimization   Optimal control   On-line state estimation   Model predictive control   Design optimization

•  Focus on high-performance methods   Expose model structure   Analytic derivatives   Sparsity   Fast convergence

Algorithms in JModelica.org

•  Simultaneous Collocation optimization algorithm   JMI/C   Large but sparse non-linear program   Numerical solver Ipopt

•  Pseudospectral collocation method   AD tool CasADi   XML export/import   Convenient scripting in Python   Ipopt

JModelica.org architecture Modelica

Optimica

Compiler Fr

ont-

end

Mid

dle-

end

Bac

k-en

d Eclipse plugin (IDE)

C

XML ODE Opt. DAE Init.

DAE

FMI/JMI Runtime Library

Generated Code DLL

Python Integration

Algorithms

Scripts User Applications

Community

• Documentation • News • Forums

• Transparency • Track activity • Releases

Ecosystem

Department of Automatic Control (LU)

Department of Computer Science (LU)

Department of Mathematics

(LU)

Modelon AB

Texas A&M USA

Illmenau Germany

Heidelberg Germany

Leuven Belgium

Industry

Industry

Industry

Outline

•  The JModelica.org open source project •  Dynamic optimization and Optimica •  The JModelica.org platform •  Tutorial examples •  What’s next?

Tutorial 1: Simulation of FMUs (UG 4.3)

•  The Van der Pol Oscillator

•  Compile Modelica models into FMUs •  Load compiled models into Python •  Set model parameter values •  Batch simulation •  Visualization •  Scripting in Python

Tutorial 2 – Hicks Ray CSTR (UG 8.4)

•  Optimal control of the Hicks Ray Continuously Stirred Tank Reactor (CSTR)

•  Exothermic reaction A+BC •  Constant inflow F0 and input concentration c0

•  States   Concentration of reactant A, c   Reactor temperature, T

•  Control variable   Temperature of cooling liquid, Tc

Tutorial 2

1.  Compile models   Modelica models and Optimica models   Compile sources into C code   Compile a DLL and load it into Python

2.  Solve DAE initialization problems   Computation of stationary operating points

3.  Solve an optimal control problem   Transfer state from point A to point B   Bounded input profile   Bound on reactor temperature

4.  Plot results

Outline

•  The JModelica.org open source project •  Dynamic optimization and Optimica •  The JModelica.org platform •  Tutorial examples •  What’s next?

What’s next?

•  Improved Modelica compliance   MSL support   Hybrid systems   Strings

•  Graphical editing   Eclipse plugin

•  Analytical Jacobians   Extension of FMI (within OPENPROD)

•  Continued work on optimization algorithms   Integration of CasADi   Derivative free optimization (DFO)

JModelica.org in research

•  Continued work on Optimica language extension   Execution of Model predictive controllers

•  PIC-LU (Process Industrial Center at Lund University)   Grade change optimization at Borealis   Poly-ethane process   Economic optimization

•  Parallelization of optimization algorithms   Explore the power of multi and many core   Decomposition schemes in interior point methods

•  Safe refactoring   Exploit research related to JastAdd   Adapt and extend framework developed for Java

Commercial packaging

•  The Modelica Physical Modeling Toolbox for Matlab   Intelligent Modelica editor   Export of compiled models (FMUs)   Simulation of Modelica models in Simulink   Simulation of Modelica models in Matlab scripts

•  Python   Commercial optimization algorithms

•  Support

JModelica.org Vendor session

Monday March 21 5:20pm-6:05pm

Room: HS2

Join the community

•  Use in industrial applications •  Education •  Interfacing your algorithms •  Research •  Develop