Fredrik Magnusson
Department of Automatic Control, Lund University, Lund, Sweden
Karl Berntorp
Department of Automatic Control, Lund University, Lund, Sweden
Björn Olofsson
Department of Automatic Control, Lund University, Lund, Sweden
Johan Åkesson
Department of Automatic Control, Lund University, Lund, Sweden/Modelon AB, Ideon Science Park, Lund, Sweden
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http://dx.doi.org/10.3384/ecp140961027Published in: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Linköping Electronic Conference Proceedings 96:107, p. 1027-1036
Published: 2014-03-10
ISBN: 978-91-7519-380-9
ISSN: 1650-3686 (print), 1650-3740 (online)
Dynamic optimization problems involving differential-algebraic equation (DAE) systems are traditionally solved while retaining the semi-explicit or implicit form of the DAE. We instead consider symbolically transforming the DAE into an ordinary differential equation (ODE) before solving the optimization problem using a collocation method. We present a method for achieving this; which handles DAE-constrained optimization problems. The method is based on techniques commonly used in Modelica tools for simulation of DAE systems.
The method is evaluated on two industrially relevant benchmark problems. The first is about vehicletrajectory generation and the second involves startup of power plants. The problems are solved using both the DAE formulation and the ODE formulation and the performance of the two approaches is compared. The ODE formulation is shown to have roughly three times shorter execution time. We also discuss benefits and drawbacks of the two approaches.
