Algorithms for Nonlinear MPC of Large Scale Systems
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Algorithms for Nonlinear MPC of Large Scale Systems
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Algorithms for Nonlinear MPC of Large Scale Systems Moritz Diehl Optimization in Engineering Center (OPTEC) & Electrical Engineering Department (ESAT), K.U. Leuven, Belgium
Industry Workshop on Hierarchical and Distributed Model Predictive Control Leuven, June 24, 2011
OPTEC - Optimization in Engineering Center Center of Excellence of K.U. Leuven, from 2005-2010, 2010-2017 About 20 professors, 10 postdocs, and 40 PhD students involved in OPTEC research Scientists in 5 divisions: Electrical Engineering Mechanical Engineering Chemical Engineering Computer Science Civil Engineering Many real world applications at OPTEC...
Optimization Education & Training
PDE-constrained Optimization
Advanced Linear Systems Analysis & Control
Shape & Topology Optimization
Parameter & State Estimation
Data Driven Modelling
Dynamic & Embedded Optimization
OPTEC: 70 people in six methodological working groups
Integrated Real-World Application Projects
OPTEC: 70 people in six methodological working groups
Optimization Education & Training
Data Driven Modelling Parameter & State Estimation Shape & Topology Optimization Advanced Linear Systems Analysis & Control PDE-constrained Optimization
Integrated Real-World Application Projects
Dynamic & Embedded Optimization
OPTEC: 70 people in six methodological working groups
Optimization Education & Training
Data Driven Modelling Parameter & State Estimation Shape & Topology Optimization Advanced Linear Systems Analysis & Control PDE-constrained Optimization
Integrated Real-World Application Projects
Dynamic & Embedded Optimization
Overview
Linear MPC for Mechatronic System and qpOASES Nonlinear MPC for Distillation Control Nonlinear MPC with ACADO Toolkit Modelica and Automatic Derivative Generation using CasADI Distributed MPC (outlook C. Savorgnan)
with Lieboud Vanden Broeck, Hans Joachim Ferreau, Jan Swevers
Model Predictive Control (MPC) Always look a bit into the future.
Brain predicts and optimizes: e.g. slow down before curve
Linear MPC = parametric QP For • linear dynamic system • linear constraints • quadratic cost Only parametric quadratic program (p-QP) needs to be solved:
Online Active Set Strategy Solve p-QP via „Online Active Set Strategy“:
go on straight line in parameter space from old to new problem data solve each QP on path exactly (keep primal-dual feasibility) Update matrix factorization at boundaries of critical regions Up to 10 x faster than standard QP
qpOASES: open source C++ code by Hans Joachim Ferreau
qpOASES – Online Active Set Strategy qpOASES is an object-oriented C++ implementation of the online active set strategy with dense linear algebra (see www.qpOASES.org, version 3.0beta to be released) Distributed as open-source software under the GNU LGPL Self-contained code: no additional software packages required (but BLAS/LAPACK can be linked) Interfaces to several third-party software packages: • Matlab, Octave, Scilab • Simulink (dSPACE, xPC Target) • ACADO Toolkit • YALMIP (under development)
Time Optimal MPC: a 100 Hz Application Quarter car: oscillating spring damper system MPC Aim: settle at any new setpoint in in minimal time Two level algorithm: MIQP 6 online data 40 variables + one integer 242 constraints (in-&output) use qpOASES on dSPACE CPU time:
