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Optimal Control in Proactive Chassis Dynamics: A Fixed Step Size Time-Stepping Scheme for Complementarity Problems

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Part of the book series: Mathematics in Industry ((TECMI,volume 19))

Abstract

This paper is about a fixed step size time-stepping scheme for the computation of solutions of complementarity problems. As we want to optimise chassis dynamics by solving optimal control problems, we took a closer look at modeling contact conditions. The latter are important, as the contact force is directly related to handling caracteristics of the automobile. This plays an important role particularly in certain driving situations, e.g. driving over a pothole. Hereafter the motivation for the development is carried out and the components of the scheme are explained. At the end we compare the calculation of a quartercar with a spring-damper road to wheel interaction to those resulting from the complementarity problem.

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References

  1. Brogliato, B.: Nonsmooth Mechanics. Models, Dynamics and Control. Communications and Control Engineering Series, 2nd edn. Springer, London (1999)

    Google Scholar 

  2. Gill, P.E., Murray, W., Saunders, M.A.: User’s guide for snopt version 7: software for large-scale nonlinear programming. Office 11(1), 1–116 (2008)

    MathSciNet  Google Scholar 

  3. Hac, A., Youn, I.: Optimal semi-active suspension with preview based on a quarter car model. In: American Control Conference, pp. 433–438 (1991)

    Google Scholar 

  4. Pfeiffer, F., Glocker, C.: Multibody Dynamics with Unilateral Contacts. Wiley-VCH Verlag GmbH, New York (2008)

    Google Scholar 

  5. Rettig, U., von Stryk, O.: Optimal and robust damping control for semi-active vehicle suspension. In: 5th EUROMECH Nonlinear Dynamics Conference (ENOC), Eindhoven, pp. 20–316 (2005)

    Google Scholar 

  6. Stewart, D.E.: Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgements

This work was partially funded by the German Federal Ministry of Education and Research (BMBF), grant no. 05M10WNA.

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Correspondence to Johannes Michael .

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© 2014 Springer International Publishing Switzerland

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Michael, J., Gerdts, M. (2014). Optimal Control in Proactive Chassis Dynamics: A Fixed Step Size Time-Stepping Scheme for Complementarity Problems. In: Fontes, M., Günther, M., Marheineke, N. (eds) Progress in Industrial Mathematics at ECMI 2012. Mathematics in Industry(), vol 19. Springer, Cham. https://doi.org/10.1007/978-3-319-05365-3_37

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