Published: 2013-03-27
ISBN: 978-91-7519-621-3 (print)
ISSN: 1650-3686 (print), 1650-3740 (online)
This paper analyzes the current use of artificial states in modeling practice and proposes a new form of equations for the purpose of modeling dynamic systems. These balance dynamics equations are used to formulate dynamic processes that help to find the solution of non-linear systems of equations.
artificial states; continuation methods; language design.
[1] Eugene L. Allgower and Kurt Georg. Introduction to Numerical Continuation Methods; SIAM Classics in Applied Mathematics 45. 2003.
[2] U. Ascher; H. Huang; and K. van den Doel. Artificial Time Integration. BIT Numerical Mathematics; 47(1): 3-25; 2007.
[3] Dymola: available at www.dymola.com
[4] The Modelica Association. Modelica® A Unified Object-Oriented Language for Systems Modeling - Language Specification Version 3.3; Available at www.modelica.org; 2012
[5] PyCont available at: www2.gsu.edu/~matrhc/PyCont.html
[6] Rolls Royce. The Jet Engine. Rolls Royce Plc. Derby England. 278p. 1996.
[7] M. Sielemann; T. Giese; B. Oehler; M. Gräber; Optimization of an Unconventional Environmental Control System Architecture. In: SAE International Journal of Aerospace; 4(2):1263-1275. 2011
[8] M. Sielemann et. al.; Robust Initialization of Differential-Algebraic Equations Using Homotopy. In: Proceedings of 8th International Modelica Conference. Dresden; Germany; 2011
[9] M. Sielemann and G. Schmitz; A quantitative metric for robustness of nonlinear algebraic equation solvers. In: Mathematics and Computers in Simulation; 81 (12); pp 2673-2687. Elsevier; 2011.
[10] D. Zimmer and D. Schlabe; Implementation of a Modelica Library for Energy Management based on Economic Models. Proceedings of the 9th International Modelica Conference ; Munich; Germany (2012)
[11] D. Zimmer; Equation-Based Modeling of Variable Structure Systems. PhD Thesis; ETH Zürich; 219 p. 2010