Article | Proceedings of the 10<sup>th</sup> International Modelica Conference; March 10-12; 2014; Lund; Sweden | Discontinuities handled with events in Assimulo
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Title:
Discontinuities handled with events in Assimulo
Author:
Emil Fredriksson: Modelon AB, Sweden/ Christian Andersson: Modelon AB, Sweden/Department of Numerical Analysis, Lund Unversity, Sweden Johan Åkesson: Modelon AB, Sweden/Department of Automatic Control, Lund University, Sweden
DOI:
10.3384/ecp14096827
Download:
Full text (pdf)
Year:
2014
Conference:
Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden
Issue:
096
Article no.:
086
Pages:
827-836
No. of pages:
10
Publication type:
Abstract and Fulltext
Published:
2014-03-10
ISBN:
978-91-7519-380-9
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


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Often integrating ordinary differential equations or differential algebraic equations (DAE) do not constitute the problem alone. A common complement is finding the root of an algebraic function (an event function) that depends on the states of the problem. This formulation of a model enables the possibility of including discontinuities; an important part of the Functional Mock-up Interface standard which allows hybrid models of differential algebraic equations. The problem of root-finding during integration is however difficult. Both in a theoretical aspect and as a software problem.

An implementation of software for root-finding is done in Assimulo; a Python/Cython wrapper for integrators. The implementation takes the Functional Mock-up Interface standard into consideration. The implementation is made usable for a wide variety of integration algorithms and is also verified and benchmarked with advanced industrial models; showing good indications of being robust and scaling well for large systems.

Keywords: FMI; JModelica.org; Assimulo; events; discontinuities; Illinois algorithm; safeguard

Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Author:
Emil Fredriksson, Christian Andersson, Johan Åkesson
Title:
Discontinuities handled with events in Assimulo
DOI:
http://dx.doi.org/10.3384/ecp14096827
References:

[1] CARVER, M. Efficient integration over discontinuities in ordinary differential equation simulations. Mathematics and Computers in Simulation 20 (1978), 190 – 196.

[2] CARVER, M., AND MACEWEN, S. Numerical analysis of a system described by implicitydefined ordinary differential equations containing numerous discontinuities. Applied Mathematical Modelling 2 (1978), 280 – 286.

[3] EICH-SOELLNER, E., AND FĂśHRER, C. Numerical methods in multibody dynamics, corr. repr.; 2. corr. repr., 2008 ed. Teubner, [Lund], 2002.

[4] ENRIGHT, W., JACKSON, K., NORSETT, S., AND THOMSEN, P. Interpolants for Runge-Kutta formulas. ACM Transactions on Mathematical Software 12, 3 (1986), 193–218.

[5] FORD, J. Improved Algorithms of Illinois-type for the Numerical Solution of Nonlinear Equations. University of Essex, Department of Computer Science, 1995.

[6] GEAR, C. W., AND OSTERBY, O. Solving ordinary differential equations with discontinuities. ACM Transactions on Mathematical Software 10, 1 (1984), 23.

[7] GILL, P. E., MURRAY, W., AND WRIGHT, M. H. Practical optimization. Academic Press, London, 1981.

[8] GRABNER, G., AND KECSKEMETHY, A. An integrated Runge-Kutta root finding method for reliable collision detection in multibody systems. MULTIBODY SYSTEM DYNAMICS 14, 3-4 (2005), 301 – 316.

[9] HAIRER, E., NORSETT, S. P., AND WANNER, G. Solving ordinary differential equations i: Nonstiff problems (e. hairer, s. p. norsett, and g. wanner). SIAM Review 32, 3 (1990), 485.

[10] HAIRER, E., AND WANNER, G. Solving Ordinary Differential Equations II [Elektronisk resurs] : Stiff and Differential-Algebraic Problems / by Ernst Hairer, Gerhard Wanner. Springer Series in Computational Mathematics: 14. Berlin, Heidelberg : Springer Berlin Heidelberg, 2010., 2010.

[11] HIEBERT, K., AND SHAMPINE, L. Implicitly defined output points for solutions of odes. Sandia National Laboratory Report SAND80-0180 (1980).

[12] HINDMARSH, A., BROWN, P., GRANT, K., LEE, S., SERBAN, R., SHUMAKER, D., AND WOODWARD, C. Sundials: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software 31, 3 (2005), 363–396.

[13] MOLER, C. Are we there yet? zero crossing and event handling for differential equations. EE Times Simulink 2 Special Edition (1997), 16–17.

[14] OLSSON, H. Runge-Kutta solution of initial value problems : methods, algorithms and implementation / Hans Olsson. Lund : Univ., 1998, 1998.

[15] PARK, T., AND BARTON, P. I. State event location in differential-algebraic models. ACM Transactions on Modeling and Computer Simulation 6, 2 (1996), 137–165.

[16] SHAMPINE, L., AND THOMPSON, S. Event location for ordinary differential equations. Computers and Mathematics with Applications 39, 5-6 (2000), 43–54.

[17] SHAMPINE, L. F., GLADWELL, I., AND BRANKIN, R. W. Reliable solution of special event location problems for odes. ACM Transactions on Mathematical Software 17, 1 (1991), 11.

[18] XU, Y., IWASE, M., AND FURUTA, K. Time optimal swing-up control of single pendulum. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME 123, 3 (2001), 518–527.

Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Author:
Emil Fredriksson, Christian Andersson, Johan Åkesson
Title:
Discontinuities handled with events in Assimulo
DOI:
http://dx.doi.org/10.3384/ecp14096827
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