Abstract
Due to the increased computing power in the last decade, more and more complex vehicle models were developed. Nowadays even complex multibody models can be generated via graphical user interfaces in object-oriented simulation tools like Dymola or SimulationX. On the other hand, the available computing power in electronic control units is still limited, mostly by the cost pressure in the automotive industry. Hence, it is not possible to generate a complex model by drag and drop via a graphical user interface and run it in real-time within a desired time cycle on an ECU inside the vehicle. The same holds for HIL-testbeds and driving simulators, where the model must run in real-time as well. Thus, generally the model is adjusted in an iterative process until the model can be integrated in real-time on the particular ECU. In other words, a model has to be generated that is on the one hand complex enough to reproduce the desired physical effects and on the other hand simple enough to fulfill the real-time requirements. As it is easy to generate a complex model nowadays, an algorithm for the automated reduction of the model is required. Equation-based reduction techniques are a tool for the automated reduction of a given DAE-system for a defined error bound. This approach was already adopted and extended to generate vehicle models with an adjustable accuracy. In this contribution, equation-based reduction techniques are extended to generate models, which are guaranteed to run in real-time on a given real-time target within a given real-time cycle.
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References
Ackermann, J., Sienel, W.: Robust Yaw Rate Control. IEEE Transactions on Control and System Technology 1, 1–15 (1993)
Andreasson, J.: Vehicle Dynamics Library. In: 3rd International Modelica Conference (2003)
Beutlich, T.: Real-Time Simulation of Modelica-based Models. In: 7th International Modelica Conference (2009)
Borchers, C.: Symbolic behavioral model generation of nonlinear analog circuits. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 45(10), 1362–1371 (1998)
Burgermeister, B., Arnold, A., Eichberger, A.: Smooth Velocity Approximation for Constrained Systems in Real-Time Simulation. In: ECCOMAS Thematic Conference Multibody Dynamics (2009)
Cao, Y., Li, S., Petzold, L.: Adjoint sensitivity analysis for differential-algebraic equations: Algorithms and software. Journal of computational and applied mathematics 149(1), 171–191 (2002)
Cao, Y., Li, S., Petzold, L., Serban, R.: Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal on Scientific Computing 24(3), 1076 (2003)
Dongarra, J.: Performance of Various Computers Using Standard Linear Equations Software. Technical Report of the Electrical Engineering and Computer Science Department, University of Tennessee (2009)
Dongarra, J., Luszczek, P., Petitet, A.: The LINPACK Benchmark: past, present and future. Concurrency and Computation: Practice and Experience 15(9), 803–820 (2003)
Gorban, A., Kazantzis, N., Kevrekidis, I., Ottinger, H., Theodoropoulos, C.: Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena (2006)
Hesse, B., Hiesgen, G., Brandt, T., Schramm, D.: Ein Fahrsimulator als Werkzeug zur frühzeitigen Eigenschaftsabsicherung von Mensch-zentrierten mechatronischen Systemen. VDI Mechatronik (2009)
Hindmarsh, A., Brown, P., Grant, K., Lee, S., Serban, R., Shumaker, D., Woodward, C.: SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers. ACM Transactions on Mathematical Software (TOMS) 31(3), 363–396 (2005)
Li, S., Petzold, L.: Software and algorithms for sensitivity analysis of large-scale differential algebraic systems. Journal of computational and applied mathematics 125(1-2), 131–145 (2000)
Maly, T., Petzold, L.: Numerical methods and software for sensitivity analysis of differential-algebraic systems. Applied Numerical Mathematics 20(1), 57–82 (1996)
Mikelsons, L., Unterreiner, M., Brandt, T.: Generation of Continuously Adjustable Vehicle Models using Symbolic Reduction Methods. In: ECCOMAS Thematic Conference Multibody Dynamics (2009)
Rill, G.: Simulation von Kraftfahrzeugen. Vieweg (1994)
Wichmann, T.: Transient Ranking Methods for the Simplification of Nonlinear DAE Systems in Analog Circuit Design. PAMM 2(1), 448–449 (2003)
Wichmann, T.: Symbolische Reduktionsverfahren für nichtlineare DAE-Systeme. In: Berichte aus der Mathematik. Shaker Verlag, Germany (2004)
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Mikelsons, L., Brandt, T., Schramm, D. (2011). Real-Time Vehicle Dynamics Using Equation-Based Reduction Techniques. In: Stépán, G., Kovács, L.L., Tóth, A. (eds) IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. IUTAM Bookseries, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1643-8_11
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DOI: https://doi.org/10.1007/978-94-007-1643-8_11
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