Integration of conditional models
Integration of conditional models means solving dynamic systems of equations (ODEs or DAEs) that contain 'branching' or conditional logic. Such systems are also sometimes termed hybrid systems. For example, if a flow velocity increases over time, we would like the solver to at some point switch from a laminar flow model to a turbulent flow model. This requires a solver that can perform boundary detection and then turn on and off equations within the model, according to which are applicable at that point in the simulation.
This work is proposed as part of the complete integration of the IDA solver in ASCEND.
A good paper containing a discussion of issues relating to the implementation of this is given by Majer et al.
Some discussion of the implications of this approach for 'real' modelling is given by Elmegaard & Houbak. In particular it is interesting to ponder the case of switching with hysteresis, which requires unidirectional boundaries...
Some discussion of the general issues of integration of conditional modelling, aka dynamic simulation with switching, is given by Pantelides and Barton. It might also be interesting to read the perspective of Engell in regard to 'hybrid systems simulation'. Barton and Pantelides have another paper on combined continuous/discrete modelling that looks good. The earliest paper on this topic seems to be by Fahrland.
The implementation of boundary detection for IDA is detailed in the IDA manual
Data structures for conditional modelling in ASCEND already exist that can represent boundaries arising from real-valued inequality relations, see for example models/test/ida/boundaries.a4c. A good starting point is doxy:system/conditional.h for the data structures, and doxy:system/analyse.h for some functions and routines that manipulate those data structures (used by CMSlv).
There is some helpful discussion about algorithms for event handling as implemented in the OpenModelica compiler/runtime system.
- C. Majer, W. Marquardt and E. D. Gilles, 1995, Reinitialization of DAEs after discontinuities, Computers and Chemical Engineering 19, 507-512, doi:10.1016/0098-1354(95)87087-3.
- B Elmegaard and N Houbak, 2005, DNA – A General Energy System Simulation Tool, Proceedings of 46th Conference on Simulation and Modeling (SIMS 2005), Trondheim, Norway (pdf, bibio)
- Pantelides & Barton, 1993, Equation-oriented dynamic simulation current status and future perspectives, Computers & Chemical Engineering, doi:10.1016/0098-1354(93)80240-N
- S Engell, 1998, Modelling and analysis of hybrid systems, Mathematics and Computers in Simulation 46 (5-6), doi:10.1016/S0378-4754(98)00076-7
- P I Barton and C C Pantelides, 1994, Modeling of combined discrete/continuous processes AIChE. J. 40, pp. 966–979, doi:10.1002/aic.690400608
- D A Fahrland, 1970, Combined discrete event continuous systems simulation, Simulation 14 (2) pp.61-72, doi:10.1177/003754977001400203
- Håkan Lundvall and Peter Fritzson, 2005. Event Handling in the OpenModelica Compiler and Runtime System SIMS 05 conference (accessed 23 Mar 2015).