Symbolic Model Reduction Applied to Realtime Simulation of a Construction Machine

Lars Mikælsons
Institute for Mechatronics and System Dynamics , University of Duisburg-Essen, Germany

Ji Hongchao
Institute for Mechatronics and System Dynamics , University of Duisburg-Essen, Germany

Thorsten Brandt
Institute for Mechatronics and System Dynamics , University of Duisburg-Essen, Germany

Oliver Lenord
Bosch Rexroth AG, Germany

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp09430136

Ingår i: Proceedings of the 7th International Modelica Conference; Como; Italy; 20-22 September 2009

Linköping Electronic Conference Proceedings 43:90, s. 765-774

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Publicerad: 2009-12-29

ISBN: 978-91-7393-513-5

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


The vehicle response of construction machines strongly depends on the tuning of the control system in interaction with the drive system. A compromise between performance and comfort needs to be found to fulfill the operators requirements on a high usability of the machine. In order to achieve an optimal behavior Hardware-in-the-Loop simulation techniques offer a suitable approach to determine the overall behavior in advance. Prerequisition is a realtime capable simulation model of the considered system. Therefore; in this paper the mathematical model of the system is automatically adapted by symbolic model reduction algorithms in order to match real-time requirements on a given hardware. Inputs to the automatic reduction algorithm are the complex mathematical system model; the desired realtime cycle and the number of floating operations per second (flops); which can be realized by the chosen target hardware. The outputs of the algorithm are the automatically reduced model; which is guaranteed to run in realtime on the target hardware and the maximal model error for the test scenario. In this paper; the reduction procedure is demonstrated for the complex hydromechanical model of a so-called kid steer loader. Summarizing; the proposed procedure of symbolic model reduction helps to reduce the developing phase of mechatronic prototypes dramatically as the adaptation of the system model with respect to the target hardware is completely automated.


Symbolic model reduction; realtime; construction maschines; object oriented modelling


[1] E. Bakker; L. Nyborg; and H. Pacejka. Tyre modelling for use in vehicle dynamics studies. In Society of Automotive Engineers international congress and expo; volume 23; 1987.

[2] C. Borchers. Symbolic behavioral model generation of nonlinear analog circuits. Circuits and Systems II: Analog and Digital Signal Processing; IEEE Transactions on [see also Circuits and Systems II: Express Briefs; IEEE Transactionson]; 45(10):1362–1371; 1998.

[3] H. Dugoff; P.S. Fancher; and L. Segel. Tire Perfomance Characteristics Affecting Vehicle Characteristics to Steering and Braking Control Inputs. Technical report; Highway Safety Research Institute; University of Michigan; 1969.

[4] H. Elmqvist; D. Brück; and M. Otter. Dymola-User’s Manual. Dynasim AB; Research Park Ideon; Lund; Sweden; 1995.

[5] P. Fritzson and V. Engelson. Modelica-a unified object-oriented language for system modeling and simulation. Lecture Notes in Computer Science; 1445:67–90; 1998. doi: 10.1007/BFb0054087.

[6] P. Fritzson; J. Gunnarsson; and M. Jirstrand. MathModelica-an extensible modeling and simulation environment with integrated graphics and literate programming. Proceedings of the 2nd International Modelica Conference; pages 18–19; 2002.

[7] H. Lundvall; P. Fritzson; and B. Bachmann. Event Handling in the OpenModelica Compiler and Runtime System. Linköping University Electronic Press; 2006.

[8] L. Mikelsons and T. Brandt. Symbolic Model Reduction for Interval-Valued Scenarios. To appear in Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference; 2009.

[9] L. Mikelsons; M. Unterreiner; and T. Brandt. Generation of Continuously Adjustable Vehicle Models using Symbolic Reduction Methods. To appear in ECCOMAS Multibody Dynamics; 2009.

[10] R. Sommer; T. Halfmann; and J. Broz. Automated behavioral modeling and analytical model-order reduction by application of symbolic circuit analysis for multi-physical systems. Simulation Modelling Practice and Theory; 2008. doi: 10.1016/j.simpat.2008.04.012.

[11] T. Wichmann. Computer aided generation of approximate DAE systems for symbolic analog circuit design. Proc. AnnualMeeting GAMM; 2000.

[12] T. Wichmann. Transient Ranking Methods for the Simplification of Nonlinear DAE Systems in Analog Circuit Design. PAMM; 2(1):448–449; 2003. doi: 10.1002/pamm.200310208.

< [13] T. Wichmann. Symbolische Reduktionsverfahren für nichtlineare DAE-Systeme. Berichte aus der Mathematik. Shaker Verlag; Aachen; Germany; 2004.

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