Niels Houbak

Solving differential-algebraic equation systems by means of index reduction methodology

Abstract With the overall goal of optimizing the design and operation of steam boilers, a model for optimizing the dynamic performance has been developed. The model has been developed as three sub-models that are integrated into an overall model for the complete boiler. Each of the sub-models consist of a number of differential equations and algebraic equations—a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers . For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper, it is shown how the equation system, by means of an index reduction methodology , can be reduced to a system of ordinary differential equations—ODEs.

Simulation of energy systems—guidelines and pitfalls

This paper is a survey paper on simulation of energy systems. It covers important aspects of the different phases of modeling an energy system. It also gives a short introduction to robust numerical methods which it is strongly recommended to use. Finally, 3 short examples illustrates some of the problems a modeler still has to face despite the developments in modern simulation software.

Higher Order Continuous SI Engine Observers

A nonlinear compensator for the fuel film dynamics and a second order nonlinear observer for a spark ignition engine are presented in this paper. The compensator and observer are realized as continuous differential equations and an especially designed integration algorithm is used to integrate them in real time. Using these means, accurate steady state and transient air/fuel control can be obtained with excellent robustness properties. Some useful condition monitoring facilities are also available in the observer. The compensator and observer are based on a Mean Value Engine Model (MVEM) presented earlier. A MVEM is one which predicts the mean value of the engine states and internal variables over time scales which are large compared to the cyclic engine process.