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Research Papers

The Generalized-α Scheme as a Linear Multistep Integrator: Toward a General Mechatronic Simulator

[+] Author and Article Information
Olivier Brüls

Department of Aerospace and Mechanical Engineering (LTAS), University of Liège, Chemin des Chevreuils 1, B52/3, Liège 4000, Belgiumo.bruls@ulg.ac.be

Martin Arnold

NWF III-Institute of Mathematics, Martin Luther University Halle-Wittenberg, Theodor-Lieser-Strasse 5, Halle (Saale) 06120, Germanymartin.arnold@mathematik.uni-halle.de

J. Comput. Nonlinear Dynam 3(4), 041007 (Aug 21, 2008) (10 pages) doi:10.1115/1.2960475 History: Received June 01, 2007; Revised February 16, 2008; Published August 21, 2008

This paper presents a consistent formulation of the generalized-α time integration scheme for mechanical and mechatronic systems. The algorithm can deal with a nonconstant mass matrix, controller dynamics, and kinematic constraints. The theoretical background relies on the analogy with linear multistep formulas, which leads to elegant results related to consistency, order conditions for constant and variable step-size methods, as well as global convergence. Those results are illustrated for a controlled spring-mass system, and the method is also applied for the simulation of a vehicle semi-active suspension.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Block diagram model of a mechatronic system

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Figure 2

Projections of a vector v in the q-space (t is frozen)

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Figure 3

Position of the mass

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Figure 5

Convergence of the simulation results (fixed step-size)

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Figure 6

Convergence of the simulation results (variable step-size)

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Figure 7

Audi A6—Corner accelerometers

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Figure 8

Mechanical model of the car

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Figure 9

Semi-active damper

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Figure 10

Semi-active control strategy

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Figure 11

Lane change maneuver (standard qualification test)

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Horizontal trajectory of the car-body

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Figure 13

Angles of the car-body

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Figure 14

Electrical current in the valves

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Figure 15

Hydraulic pressures in the rear right damper

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