Söderman, U. and Strömberg, J.-E. (1995). Switched Bond Graphs: Multiport Switches, Mathematical Characterization and Systematic Composition of Computational Models. Technical Report LiTH-IDA-R-95-07, Department of Computer and Information Science, Linköping University, Sweden.
Abstract: Classical bond graphs are in principal restricted to the modelling of continuous physical systems only. In previous work we have extended classical bond graphs to systems involving abrupt changes as well. This extension is centered around the introduction of an ideal primitive switch concept. In this paper we continue this work and extend it in a number of important directions. We present the multiport generalization of the previously introduced primitive one-port switch. We elaborate on the mathematical semantics of individual switch elements as well as complete switched bond graphs, i.e. bond graphs involving one or more switch elements. We discuss the systematic composition of computational models for switched bond graphs and for this purpose we introduce a constructive composition operator. Finally, we also discuss some ideas to deal with model complexity and 'non-physical' modes. Here, the multiport switch plays an important role. For the representation of the composed computational models of switched bond graphs we introduce a mathematical structure related with state automata. This structure is referred to as mode transition systems. For the mathematical characterization of individual switch elements a simplified version of this structure, referred to as switch transition systems, is introduced.
Söderman, U., Strömberg, J.-E., and Top, J. (1995). Mode Invariant Modelling. Technical Report LiTH-IDA-R-95-04, Department of Computer and Information Science, Linköping University, Sweden.
Abstract: Modelling of physical systems is a difficult task, in particular if mode switching is allowed. Automated support can be supplied, if two conditions are fulfilled. First, a set of suitable {\em qualitative} concepts has to be availiable as a tool box for constructing adequate models. Second, powerful computational machinery must handle model complexity. In this paper we introduce both a conceptual basis and a computational algorithm for dealing with mode switching physical systems. Our approach is more effective than current AI-based methods since it is based on general physical principles at the proper level of abstraction, expressed in terms of bond graphs. The latter formalism is extended in order to deal with mode switching. All meaningful causal modes and transitions between modes are derived automatically. A power electronic circuit serves a guiding example.
Strömberg, J.-E. and Söderman, U. (1995). Modular Modelling of Mode-switching Systems. Technical Report LiTH-IDA-R-95-06, Department of Computer and Information Science, Linköping University, Sweden.
Abstract: By a mode-switching system we mean a physical engineering system in which there are fast switching devices such as diodes, check-valves, free-wheeling devices etc. or other similar effects. For the proper conceptualisation of such systems, we have earlier presented switched bond graphs; an extension of the classical bond graph language with an ideal primitive switch concept. In this paper we study the potentials of systematically deriving computational models from switched bond graphs. The underlying requirement is to preserve the modularity provided by classical bond graphs. The resulting computational model is hybrid in the sense that it combines systems of continuous differential and algebraic equations and discrete mode transitions, and is suitable for control, simulation and design.
Söderman, U. (1994). Conceptual Modelling of Physical Systems - a Frame od Reference. Technical Report LiTH-IDA-R-94-39, Department of Computer and Information Science, Linköping University, Sweden.
Abstract: The construction of models of physical systems that are adequate for effective model based reasoning is generally recognized as a difficult task. The use of computer aided modelling systems, which provide high-level support and enhance the modelling task, is therefore most attractive. In the Artificiell Intelligence subfield of Qualitative Physics, a number of approaches to representation, automatic selection and composition of models have been proposed over the years. However, these approaches stem from research governed by different goals and motivations and they tend, therefore, to provide their own sets of ontological primitives, their own representation schemes, creation and selection processes, and different illustrating examples. As a consequence it can often be hard to grasp what the proposed approaches have in common and what the differences are.In this paper we present a frame of reference for physical systems modelling. It is intended to facilitate and support future discussions and comparisons of other approaches. In addition, it provides good insight into modelling and may therefore also serve as a useful reference in the development of computer aided modelling systems. The frame takes the form of an approach to modelling in its own right and is referred to as the reference approach.In the reference approach, modelling starts with a real world system, or a design of it, and finishes with a model for prediction of the system's behaviour. In the reference approach we emphasize the conceptual side of modelling and deemphasize the numerical side. The principal contents of the reference approach are: An ontology incorporating a small and well defined set of generic ontological primitives; a network model having a clear syntax and semantics; guidelines for the mathematical characterization; a clear notion of causality; and a causality assignment procedure.
Söderman, U. and and, J.-E. S. (1994). Switched Bond Graphs: Towards Systematic Composition of Computational Models. Accepetd to The International Conference on Bond Graph Modeling and Simulation ICBGM95, Las Vegas, USA, January 1995. Technical Report LiTH-IDA-R-94-38, Department of Computer and Information Science, Linköping University, Sweden.
Abstract: In classical bond graph modelling, a computational model is systematically composed from the parts without having to introduce local or global patches. Unfortunately this has not yet been fully carried over to switched bond graphs, i.e. bond graphs employing the ideal switch concept. The focus of this paper is on the systematic composition of the discrete mode transitions. To this end we provide a mathematical structure for the composed computational model and a procedural composition operator. We also outline an algorithm to localize and adjust the composed system in those cases where the composition operator fails. An important concept in this treatment is the generalization of primitive switches to multiport switch fields.
Söderman, U. and Strömberg:, J.-E. (1991). Combining Qualitative and Quantitative Knowledge to Generate Models of Physical Systems. Technical Report LiTH-IDA-R-91-15, Department of Computer and Information Science, Linköping University, Sweden. A Short version is accepted to the 12th International Joint Conference on Artificial Intelligence (IJCAI-91) Sydney, Australia, August 24-30, 1991.
Abstract: All major approaches to Qualitative Reasoning rely on the existence of a model of the physical system. However, the task of finding a model is usually far from trivial. Within the area of electrical engineering, model building methods have been developed to automatically deduce models from measurements. In this paper we explicitly show how to incorporate qualitative knowledge in order to apply these methods to situations where they do not behave satisfactorily. A program has been developed and applied to a non-trivial example. The qualitative input, in terms of an incomplete bond graph, and the resulting output can be used to form a more complete bond graph. This more informative model is suitable for further reasoning.
Söderman, U., Top, J., and Strömberg, J.-E. (1994). The Conceptual Side of Mode Switching. Technical Report LiTH-IDA-R-94-07, Department of Computer and Information Science, Linköping University, Sweden. Accepted to 1993, IEEE International Conference on Systems, Man and Cybernetics, Le Touquet, France, October 1993.
Abstract: For continuous dynamic systems there are many powerful methods for modelling. However, when dealing with systems undergoing abrupt behavioural changes, i.e. mode switching systems, the picture suddenly is changed. We here claim that the reason for this is that mode switching traditionally is treated by mathematical and/or logical solutions only. That is, at the wrong level of abstraction. We present several arguments supporting this view, and finally present our solution to this problem: the ideal switch concept.
Söderman, U., Top, J., and Strömberg, J. E. (1994). Modelling Physical Systems with Changing Structure. Technical Report LiTH-IDA-R-94-06, Department of Computer and Information Science, Linköping University, Sweden.
Abstract: Causality plays an important role in essentially any aspect of reasoning about physical systems. However, causal directedness is problematic when the physical structure, i.e. the interaction between subsystems changes. This is due to the fact that causality is a global property. This problem can in principle be solved by specifying acausal models and to derive causality afterwards for the complete model. This is possible because physical systems are connected through bilateral signal flows, with no a priori fixed direction.Sofar, there has been no systematic and efficient way to represent acausal models of structures that undergo change. This would be an important feature of automated modelling and reasoning systems. In this paper we propose the definition of an ideal, generic switching element solving exactly this representation problem. The definition also adds a new ontological primitive to the bond graph language, though the general definition is not restricted to any specific modelling approach. Furthermore, the clear and explicit bond graph method to derive the overall causality can be reused unaltered. Several examples are presented to illustrate our approach.
Strömberg, J.-E., Söderman, U., and Top, J. (1992). Bond Graph Supported Estimation of Discretely Changing Parameters. Technical Report LiTH-IDA-R-92-37, Department of Computer and Information Science, Linköping University, Sweden. Accepted to 1992 International Conference on Bond Graph Modeling and Simulation ICBGM 93, San Diego, USA, Januari 1993.
Abstract: A key factor in parameter estimation is the selection of model structure within which the fit to observed data is to be achieved. For linear systems, bond graphs have proven to give excellent support in this respect. However, for systems undergoing abrupt transitions between different (linear) modes of behaviour, the situation is far more complex. To handle this, we exploit the features of the ideal switching element as introduced by Strömberg, Top and Söderman. This solves the question of physical modelling as well as how to derive the supporting information. The approach is demonstrated on a non-trivial example using a multiple Kalman filter estimator.
Strömberg, J.-E., Söderman, U., and Top, J. (1994). Conceptual Modelling of Hybrid Systems. Technical Report LiTH-IDA-R-94-40, Department of Computer and Information Science, Linköping University, Sweden. Accepted to The European Simulation Conference ESM'94 Barcelona, Spain, June 1994.
Abstract: For continuous physical systems there are many powerful methods for modelling, one of them being the conceptual modelling technique as supported by the bond graph language. However, when dealing with systems undergoing abrupt behavioural changes, i.e. mode switching or hybrid systems, the picture is quite different. The reason for this is that mode switching traditionally is treated by means of mathematical and logical concepts only instead of by more physically oriented concepts. This implies adhoc constructs and limited possibilities for automation. It is our claim that a proper concept at the physical level effectively can eliminate this modelling bottleneck. We present several arguments supporting this view, and present our solution: the ideal switch concept. An example is provided to show its practical application
Strömberg, J.-E., Top, J., and Söderman, U. (1992). Modelling Mode Switching in Dynamical Systems. Technical Report LiTH-IDA-R-92-38, Department of Computer and Information Science, Linköping University, Sweden. Accepted to ECC-93 - 2nd European Control Conference, Gröningen, Holland.
Abstract: Finding uniform formalisms to represent mode switching in models of dynamical systems is a goal that has long been strived for -- not the least within the automatic control community. Here we claim that the main reason for not reaching this goal is the tendency to confound modelling and computation. We will conjecture that the level of computation, i.e. the mathematical representation, is too low a level to yield any hope for a solution. Thus, we have chosen to search the solution at the physical level of representation; here by means of the bond graph formalism. By carefully defining a new ideal bond graph switching element, we have ensured a clear distinction between the physical and computational levels. With this minor addition to the original formalism, we maintain the abstraction level of bond graphs and hence keep all the conceptual properties of bond graphs, facilitating powerful guidelines to systematise the modelling process and tools to perform model validation already at the conceptual level.
Strömberg, J.-E., Top, J., and Söderman, U. (1992). Variable Causality in Bond Graphs Caused by Discrete Effects. Technical Report LiTH-IDA-R-92-36, Department of Computer and Information Science, Linköping University, Sweden. Accepted to 1993 International Conference on Bond Graph Modeling and Simulation ICBGM 93, San Diego, USA, Januari 1993.
Abstract: Current approaches to the problem of switching between modes in continuous dynamic system models tend to confound modelling and computation. Here we introduce an alternative approach ensuring a clear distinction between the physical and computational levels. Our method is centered around the idea that the variability of causal directions should be accepted rather than being alleviated. Hence, we define an ideal bond graph switching element, to deal with this variability in a bond graph uniform and systematic way.We hereby maintain the abstraction level of the bond graph language as well as the possibility to perform initial model validation directly in the graph.