Quantization-Based Simulation of Differential Algebraic Equation Systems

This paper studies the use of first and second order Quantized State Systems methods (QSS and QSS2) in the simulation of Differential Algebraic Equation (DAE) systems. A general methodology to obtain the QSS and the QSS2 approximations of a generic DAE of index 1 is provided and their corresponding DEVS implementations are developed. Further, an alternative method is given based on the block–by–block translation from Block Diagrams containing algebraic loops into coupled DEVS representations of the corresponding QSS and QSS2 approximations. We show that the main advantages provided by the quantization–based methods in the simulation of Ordinary Differential Equations (ODE) –stability properties, reduction of computational costs, sparsity exploitation, etc.– are still verified in DAEs. These advantages are illustrated and discussed in the simulation of two examples which show the main features of the methodology.