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Online state and input force estimation for multibody models employing extended Kalman filtering

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Abstract

This paper discusses the use of Subsystem Global Modal Parameterization (SS-GMP) reduced multibody models in an augmented discrete extended Kalman filter (A-DEKF) to generate a general formalism for online coupled state/input estimation in mechanisms. The SS-GMP approach is proposed to reduce a general multibody model of a mechanical system into a real-time capable model without considerable loss in accuracy. In order to use these reduced models with an extended Kalman filter, the necessary derivatives of this model are provided. An exponential integration scheme is used to discretize the model in order to be compatible with discrete time filters. Finally, the augmented approach is used for the estimation, in which the unknown external forces are considered as additional states to be estimated. The proposed approach is validated numerically and compared to three other filtering approaches. The validation demonstrates that the proposed approach provides accurate results while still maintaining real-time performance.

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Notes

  1. The derivative of a matrix A with respect to a variable b is denoted as A ,b .

  2. These variances are averaged over 50 simulation-runs with random noise generated by randn in MATLAB.

  3. All simulations are performed on an Intel Core®2 Duo E6550 2.33 GHz processor without exploitation of multithreading.

References

  1. Kalman, R.E.: A new approach to linear filtering and prediction problems. J. Basic Eng. 82(1), 35–45 (1960)

    Article  Google Scholar 

  2. Simon, D.: Optimal State Estimation: Kalman, H ∞ and Nonlinear Approaches. Wiley, New York (2006)

    Book  Google Scholar 

  3. Siegrist, P.M., McAree, P.R.: Tyre-force estimation by Kalman inverse filtering: applications to off-highway mining trucks. Veh. Syst. Dyn. 44(12), 921–937 (2006)

    Article  Google Scholar 

  4. Daklallah, J., Glaser, S., Mammar, S., Sebsadji, Y.: Tire-road forces estimation using extended Kalman filter and sideslip angle evaluation. In: Proceedings of the 2008 American Control Conference, 11–13 June 2008

    Google Scholar 

  5. Grip, H.F., Imsland, L., Johansen, T.A., Fossen, T.I., Kalkkuhl, J.C., Suissa, A.: Nonlinear vehicle side-slip estimation with friction adaptation. Automatica 44(3), 611–622 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Wasfy, T., Noor, A.: Computational strategies for flexible multibody systems. Appl. Mech. Rev. 56(6), 553–613 (2002)

    Article  Google Scholar 

  7. Cuadrado, J., Dopico, D., Barreiro, A., Delgado, E.: Real-time state observers based on multibody models and the extended Kalman filter. J. Mech. Sci. Technol. 23(4), 894–900 (2009)

    Article  Google Scholar 

  8. Cuadrado, J., Dopico, D., Perez, J.A., Pastorino, R.: Automotive observers based on multibody models and the extended Kalman filter. Multibody Syst. Dyn. 27(1), 3–19 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  9. Brüls, O., Duysinx, P., Golinval, J.-C.: A model reduction method for the control of rigid mechanisms. Multibody Syst. Dyn. 15(3), 213–227 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Brüls, O., Duysinx, P., Golinval, J.-C.: The global modal parameterization for nonlinear model-order reduction in flexible multibody dynamics. Int. J. Numer. Methods Eng. 69(5), 948–977 (2007)

    Article  MATH  Google Scholar 

  11. Naets, F., Heirman, G.H.K., Desmet, W.: Sub-system global modal parameterization for efficient simulation of flexible multibody systems. Int. J. Numer. Methods Eng. 89(10), 1227–1248 (2011)

    Article  MathSciNet  Google Scholar 

  12. Blanchard, E., Sandu, A., Sandu, C.: Parameter estimation for mechanical systems via an explicit representation of uncertainty. Eng. Comput. 26(5), 541–569 (2009)

    Article  Google Scholar 

  13. Blanchard, E., Sandu, A., Sandu, C.: A polynomial chaos-based Kalman filter approach for parameter estimation of mechanical systems. ASME J. Dyn. Syst. Meas. Control, Special Issue on Physical System Modeling 132(6) (2010)

  14. Blanchard, E., Sandu, A., Sandu, C.: Polynomial chaos-based parameter estimation methods applied to vehicle system. Proc. Inst. Mech. Eng., Proc. Part K, J. Multi-Body Dyn. 224(K1), 59–81 (2010)

    Google Scholar 

  15. Kitanidis, P.K.: Unbiased minimum-variance linear state estimation. Automatica 23(6), 775–778 (1987)

    Article  MATH  Google Scholar 

  16. Darouach, M., Zasadzinski, M.: Unbiased minimum variance estimation for systems with unknown exogenous inputs. Automatica 33(4), 717–719 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ray, L.R.: Nonlinear state and tire force estimation for advanced vehicle control. IEEE Trans. Control Syst. Technol. 3(1), 117–124 (1995)

    Article  Google Scholar 

  18. Ray, L.R.: Nonlinear tire force estimation and road friction identification: simulation and experiments. Automatica 33(10), 1819–1833 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ishikawa, J., Tomizuka, M.: Pivot friction compensation using an accelerometer and a disturbance observer for hard disk drives. IEEE/ASME Trans. Mechatron. 3(3), 194–201 (1998)

    Article  Google Scholar 

  20. Szabat, K., Orlowska-Kowalska, T.: Performance improvement of industrial drives with mechanical elasticity using nonlinear adaptive Kalman filter. IEEE Trans. Ind. Electron. 55(3), 1075–1084 (2008)

    Article  Google Scholar 

  21. Mitsantisuk, C., Katsura, S., Ohishi, K.: Kalman-filter-based sensor integration of variable power assist control based on human stiffness estimation. IEEE Trans. Ind. Electron. 56(10), 3897–3905 (2009)

    Article  Google Scholar 

  22. Hostetter, G.H., Meditch, J.S.: On the generalization of observers to systems with unmeasurable, unknown inputs. Automatica 9(6), 721–724 (1973)

    Article  MATH  Google Scholar 

  23. Ma, C.-K., Ho, C.-C.: An inverse method for the estimation of input forces acting on non-linear structural systems. J. Sound Vib. 275(3–5), 953–971 (2001)

    Google Scholar 

  24. Gillijns, S., De Moor, B.: Unbiased minimum-variance input and state estimation for linear discrete-time systems with direct feedthrough. Automatica 43(5), 934–937 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  25. Radke, A., Gao, Z.: A survey of state and disturbance observers for practitioners. In: Proceedings of the 2006 American Control Conference, 14–16 June, Minneapolis, Minnesota, USA (2006)

    Google Scholar 

  26. Lourens, E., Reynders, E., De Roeck, G., Degrande, G., Lombaert, G.: An augmented Kalman filter for force identification in structural dynamics. Mech. Syst. Signal Process. 27, 446–460 (2012)

    Article  Google Scholar 

  27. Ros, J., Yoldi, R., Plaza, A., Angeles, J.: Exponential integration schemes in multibody dynamics. In: Proceedings of the Second Joint International Conference on Multibody System Dynamics, Stuttgart, Germany, May 29–June 1 2012

    Google Scholar 

  28. Naets, F., Desmet, W.: Super-element global modal parameterization for efficient inclusion of highly nonlinear components in multibody simulation. Multibody Syst. Dyn. (2013). doi:10.1007/s11044-013-9342-2

    Google Scholar 

  29. Hernandez, E.M.: Optimal model-based state estimation in mechanical and structural systems. Structural control and health monitoring (2011). doi:10.1002/stc.513

  30. Naets, F., Cuadrado, J., Desmet, W.: Stable force identification in structural dynamics using Kalman filtering and dummy-measurements. Mech. Syst. Signal Process. (Submitted)

  31. Garcia de Jalon, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems. Springer, New York (1994)

    Book  Google Scholar 

  32. Brüls, O., Arnold, M.: The generalized-alpha scheme as a linear multistep integrator: Towards a general mechatronic simulator. ASME J. Comput. Nonlinear Dyn. 3(4) (2008)

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Acknowledgements

The research of Frank Naets is funded by a Ph.D. grant of the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen) and his research stay at LIM-UDC was funded by a grant from the Fund of Scientific Research (FWO).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Katholieke Universiteit Leuven, Celestijnenlaan 300B, 3001, Heverlee, Belgium

    Frank Naets, Roland Pastorino & Wim Desmet

  2. Mechanical Engineering Laboratory, University of La Corũna, Escuela Politécnica Superior, Mendizábal s/n, 15403, Ferrol, Spain

    Javier Cuadrado

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  1. Frank Naets
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  2. Roland Pastorino
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  4. Wim Desmet
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Correspondence to Frank Naets.

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Naets, F., Pastorino, R., Cuadrado, J. et al. Online state and input force estimation for multibody models employing extended Kalman filtering. Multibody Syst Dyn 32, 317–336 (2014). https://doi.org/10.1007/s11044-013-9381-8

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  • DOI: https://doi.org/10.1007/s11044-013-9381-8

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