Applied Mathematical ModellingCircuit AnalysisEngineeringModel-based Control TechniqueMechanical SystemsComputer EngineeringModelling MethodologySystems EngineeringEngineering MathematicsComplex ModelingModeling And SimulationTransmission SystemControl TechnologySystematic DerivationEngineering SystemsSystem Dynamic
The thesis presents a modelling methodology for the systematic derivation of mathematical behaviour mod els of engineering systems , i. e. systems constructed by engineers. The first part presents the theoretical and philosophical foundation underlying a dass of methods generally referred to as physical modelling. The fundamental idea is to systematically employ first principles of physics. The specific method employed here is that provided by energy-oriented bond graphs; a graphical modelling language developed by Henry M. Paynter in the late fifties. Since bond graphs are firmly grounded in fundamental laws of physics, they allow for modelling of continuous mechanisms only. From a computational point of view, this corresponds to continuous (possibly non-linear) differential and algebraic equation systems (DAES).In many practical systems though, there are rapid switching devices such as pressure relief valves, diodes, dutches, free-wheeling devices, check valves, relays et c. which are all intentionally designed to implement near ideal switching behaviour. For this dass of 'mixed' engineering systems, also referred to as mode switching systems, we would hence prefer a discontinuous idealization of the switching mechanisms. The main contribution of this thesis is an extension of the bond graph language to allow for such an idealization of mode switching systems. This extended language, here referred toas switched bond graphs is so constructed that it preserves all the essential properties of dassical bond graphs. The choice made, was to accept rather than reject the variable causality that follows as a consequence. As opposed to previous work, which focus on means to circumvent this consequence, we rather study the effects of accepting it as is. From a computational point of view, a switched bond graph corresponds to a so called hybrid system, i.e. a mixture of DAES and binary decisions.The thesis finally deals with an important computational issue, namely that of tuning a hybrid system to measurements. The approach presented is an extension of the tree induction principles developed within machine learning. The thesis is conduded by applying the presented modelling methodology on a siphon pump machine that was originally designed by Christoffer Polhem in 1697.