Inline integration for real-time simulation
Andreas Fransson · 2014
In this thesis, an implementation of inline integration is described and examined. Inline integration is a mixed symbolic and numerical method for simulating fully implicit ordinary differential equations (DAE:s) whereby discretizations are introduced symbolically at model level. A generalized solution to the discretized model containing tailored iterative solving schemes and symbolic solutions is then found using a set of symbolic algorithms. Since the integration scheme is brought into the realm of symbolic solving, it is possible to find more efficient ways to solve the equation systems that arise when applying implicit numerical algorithms. For this reason inline integration is particularly useful in realtime simulation of stiff systems. The implementation of this project is carried out on the Modelica compiler of JModelica.org, which is an open source simulation and optimization platform. Modelica is a high level object-oriented modeling language. With JModelica.org, the discretized models are compiled into Functional Mock-up Units for Model-Exchange (ME-FMU:s), which are compliant with the Functional Mock-up Interface (FMI) standard. The inlined numerical algorithm used is the Implicit Euler method and the implementation is veried on a set of example models from the Modelica Standard Library (MSL). Positive results are seen when comparing the structure of the example models with and without inline integration as well as when comparing execution times. The time improvement rate is seen to vary by a factor of up to 7 between the different example models. (Less)