Advertisement

Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control

  • Michael Dellnitz
  • Julian Eckstein
  • Kathrin Flaßkamp
  • Patrick Friedel
  • Christian Horenkamp
  • Ulrich Köhler
  • Sina Ober-Blöbaum
  • Sebastian Peitz
  • Sebastian Tiemeyer
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 22)

Abstract

During the last years, alternative drive technologies, for example electrically powered vehicles (EV), have gained more and more attention, mainly caused by an increasing awareness of the impact of CO2 emissions on climate change and by the limitation of fossil fuels. However, these technologies currently come with new challenges due to limited lithium ion battery storage density and high battery costs which lead to a considerably reduced range in comparison to conventional internal combustion engine powered vehicles. For this reason, it is desirable to increase the vehicle range without enlarging the battery. When the route and the road slope are known in advance, it is possible to vary the vehicles velocity within certain limits in order to reduce the overall drivetrain energy consumption. This may either result in an increased range or, alternatively, in larger energy reserves for comfort functions such as air conditioning. In this presentation, we formulate the challenge of range extension as a multiobjective optimal control problem. We then apply different numerical methods to calculate the so-called Pareto set of optimal compromises for the drivetrain power profile with respect to the two concurrent objectives battery state of charge and mean velocity. In order to numerically solve the optimal control problem by means of a direct method, a time discretization of the drivetrain power profile is necessary. In combination with a vehicle dynamics simulation model, the optimal control problem is transformed into a high dimensional nonlinear optimization problem. For the approximation of the Pareto set, two different optimization algorithms implemented in the software package GAIO are used. The first one yields a global optimal solution by applying a set-oriented subdivision technique to parameter space. By construction, this technique is limited to coarse discretizations of the drivetrain power profile. In contrast, the second technique, which is based on an image space continuation method, is more suitable when the number of parameters is large while the number of objectives is less than five. We compare the solutions of the two algorithms and study the influence of different discretizations on the quality of the solutions. A MATLAB/Simulink model is used to describe the dynamics of an EV. It is based on a drivetrain efficiency map and considers vehicle properties such as rolling friction and air drag, as well as environmental conditions like slope and ambient temperature. The vehicle model takes into account the traction battery too, enabling an exact prediction of the batterys response to power requests of drivetrain and auxiliary loads, including state of charge.

Keywords

Cruise control Multiobjective optimal control Pareto set 

Notes

Acknowledgements

This research was partially funded by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge Cluster ‘Intelligent Technical Systems OstWestfalenLippe’ (it’s OWL) and managed by the Project Management Agency Karlsruhe (PTKA).

References

  1. 1.
    Binder, T., Blank, L., Bock, H., Bulirsch, R., Dahmen, W., Diehl, M., Kronseder, T., Marquardt, W., Schlöder, J., Stryk, O.: Introduction to model based optimization of chemical processes on moving horizons. In: Grötschel, M., et al. (ed.) Online Optimization of Large Scale Systems: State of the Art, pp. 295–340. Springer, Berlin (2001)CrossRefGoogle Scholar
  2. 2.
    Coello Coello, C., Lamont, G., Veldhuizen, D.V.: Evolutionary Algorithms for Solving Multi-Objective Optimization Problems, 2nd edn. Springer, Boston (2007)zbMATHGoogle Scholar
  3. 3.
    Dellnitz, M., Schütze, O., Hestermeyer, T.: Covering pareto sets by multilevel subdivision techniques. J. Optim. Theory Appl. 124(1), 113–136 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler, U., Ober-Blöbaum, S., Peitz, S., Tiemeyer, S.: Development of an intelligent cruise control using optimal control methods. Proc. Technol. 15, 285–294 (2014)CrossRefGoogle Scholar
  5. 5.
    Dib, W., Serrao, L., Sciarretta, A.: Optimal control to minimize trip time and energy consumption in electric vehicles. In: Vehicle Power and Propulsion Conference (VPPC), pp. 1–8 (2011)Google Scholar
  6. 6.
    Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)zbMATHGoogle Scholar
  7. 7.
    Hellström, E., Åslund, J., Nielsen, L.: Design of an efficient algorithm for fuel-optimal look-ahead control. Control Eng. Pract. 18(11), 1318–1327 (2010)CrossRefGoogle Scholar
  8. 8.
    Keichel, M., Schwedes, O.: Das Elektroauto: Mobilität im Umbruch. Springer Vieweg, Wiesbaden (2013)CrossRefGoogle Scholar
  9. 9.
    Li, S., Li, K., Rajamani, R., Wang, J.: Model predictive multi-objective vehicular adaptive cruise control. IEEE Trans. Control Syst. Technol. 19(3), 556–566 (2011)CrossRefGoogle Scholar
  10. 10.
    Logist, F., Houska, B., Diehl, M., Van Impe, J.: Fast Pareto set generation for nonlinear optimal control problems with multiple objectives. Struct. Multidiscip. Optim. 42(4), 591–603 (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Masjosthusmann, C., Köhler, U., Decius, N., Büker, U.: A vehicle energy management system for a battery electric vehicle. In: Vehicle Power and Propulsion Conference (VPPC), pp. 339–344 (2012)Google Scholar
  12. 12.
    Ober-Blöbaum, S., Ringkamp, M., Zum Felde, G.: Solving multiobjective optimal control problems in space mission design using discrete mechanics and reference point techniques. In: 51st IEEE International Conference on Decision and Control, pp. 5711–5716 (2012)Google Scholar
  13. 13.
    Petit, N., Sciarretta, A.: Optimal drive of electric vehicles using an inversion-based trajectory generation approach. In: Proceedings of the 18th IFAC World Congress, pp. 14519–14525 (2011)Google Scholar
  14. 14.
    Romaus, C., Bocker, J., Witting, K., Seifried, A., Znamenshchykov, O.: Optimal energy management for a hybrid energy storage system combining batteries and double layer capacitors. In: Energy Conversion Congress and Exposition (ECCE), 2009, pp. 1640–1647. IEEE, Piscataway (2009)Google Scholar
  15. 15.
    Schütze, O., Witting, K., Ober-Blöbaum, S., Dellnitz, M.: Set oriented methods for the numerical treatment of multiobjective optimization problems. In: Tantar, E., Tantar, A.A., Bouvry, P., Del Moral, P., Legrand, P., Coello Coello, C.A., Schütze, O. (eds.) EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation. Studies in Computational Intelligence, vol. 447, pp. 187–219. Springer, Berlin/Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    Sciarretta, A., Guzzella, L.: Control of hybrid electric vehicles. IEEE Control Syst. 27(2), 60–70 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Michael Dellnitz
    • 1
  • Julian Eckstein
    • 2
  • Kathrin Flaßkamp
    • 1
  • Patrick Friedel
    • 2
  • Christian Horenkamp
    • 1
  • Ulrich Köhler
    • 2
  • Sina Ober-Blöbaum
    • 1
  • Sebastian Peitz
    • 1
  • Sebastian Tiemeyer
    • 2
  1. 1.University of Paderborn and Institute for Industrial MathematicsPaderbornGermany
  2. 2.HELLA KGaA Hueck and Co.LippstadtGermany

Personalised recommendations