1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Mechanical Engineering, Technical University of Denmark3 Department of Applied Mathematics and Computer Science, Technical University of Denmark4 Technical Information Center of Denmark, Technical University of Denmark
Differential algebraic equations (DAEs) constitute a fundamental model class for many modelling purposes in engineering and other sciences, especially for dynamical simulation of component based systems. This thesis describes a practical methodology and approach for analysing general DAE. The methodology is mainly based on strutural index analysis which is not limited by the index of the DAE as other methodologies. As a result of structural index analysis one can perform index reduction of the DAE and obtain the so-called augmented underlying ODE. It is also described, how to use the augmented underlying ODE for finding consistent initial values and solve the initial value problem for the original DAE. As a methodology for integrating the augmented underlying ODE, the dummy derivative method is investigated. The methodology avoids the traditional stability and drift-of problems of using the underlying ODE. The investigations concern the identification of quantities that can trigger the automatic choice of new dummy derivatives during integration. This is a practical problem that needs to be solved before implementations of the method are possible. The general methodology is tested in practice, by the implementation of the Simpy tool box. This is an object oriented system implemented in the Python language. It can be used for analysis of DAEs, ODEs and non-linear equation and uses e.g. symbolic representations of expressions and equations. The presentations of theory and algorithms for structural index analysis of DAE is original in the sense that it is based on a new matrix representation of the structural information of a general DAE system instead of a graph oriented representation. Also the presentation of the theory is found to be more complete compared to other presentations, since it e.g. proves the uniqueness of the structural index reduction process. Also included, is a discussion of criticism and defence of structural analysis.
differential algebraic aquations; structural analysis; component based modelleing