## Bond Graph Modeling and Simulation

 The course lectures: Bond graphs are a domain-independent graphical description of dynamic behavior of physical systems. This means that systems form different domains (cf. electrical, mechanical) are described in the same way. The basis is that bond graphs are based on energy and energy exchange. Bond graphs are labeled and directed graphs, in which the vertices represent submodels and the edges represent an ideal energy connection between power ports. The vertices are idealized descriptions of physical phenomena: they are concepts, denoting the relevant (i.e. dominant and interesting) aspects of the dynamic behavior of the system. It can be bond graphs itself, thus allowing hierarchical models, or it can be a set of equations in the variables of the ports (two at each port). The edges are called bonds. They denote point-to-point connections between submodel ports. When preparing for simulation, the bonds are embodied as two-signal connections with opposite directions. Furthermore, a bond has a power direction and a computational causality direction. Proper assigning the power direction resolves the sign-placing problem when connecting submodels structures. See also the Bond Graph Primer which contains further references. Time and place: The course takes place on April 15th at the Helsinki University of Technology (room U352). The program includes lecture (9.15-12.00) and exercises (13.15-17.00). Teachers: The course is given by Professor Jan Broenink, University of Twente, Netherlands. Course material: The participants should download the course material Introduction to Physical Systems Modeling with Bond Graphs (BondGraphs.pdf, 28 pages) and Tutorial Introduction to 20-sim 2.X (Tutorial.pdf, 16 pages) Further reading: Karnopp D.C, and Rosenberg R.C., (1990) System dynamics: a unified approach, J Wiley, New York, 2nd Edition Passing procedure: Active participation in the lecture and exercise and extra homework gives 0.5-1 credit units depending on the amount of homework. Participants: Participants of the Eurosim'98 conference and master's and doctoral students in Helsinki University. Basic knowlegde of engineering dynamics and mathematics on ordinary differential equations and familiarity with programming and windows95/nt is needed. Registration to this tutorial by sending email to anu.kettunen@hut.fi is necessary. There is a maximum number of attendees. Preliminary program: In the first part, (morning), we give an overview on bond graphs. First we introduce the bond graph method by some examples, where we start from a given network composed of ideal physical models. Transformation to a bond graph leads to a domain independent model. Then, we introduce the foundations of bond graphs, and present the basic bond graph elements. After that we discuss a systematic method for deriving bond graphs from engineering systems and present a method to systematically derive equations from the resulting bond graph. Demonstrations on bond-graph modeling using bond-graph software (20-SIM) are presented throughout the lecture. In the second part, (afternoon), exercises using 20-SIM are presented to gain hands-on experience with a contemporary bond graph modeling and simulation tool. Besides basic examples to explore the tool, some comprehensive examples concerning simulation and modeling are taught. Attendants get an educational license of 20-SIM (Windows95/NT) for free. Further information: Send email to Anu Kettunen@hut.fi