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Journal of Computational and Nonlinear Dynamics | Volume 3 | Issue 4 | Research Paper
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
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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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+Block diagram model of a mechatronic system
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Block diagram model of a mechatronic system
Figure 1

Block diagram model of a mechatronic system

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+Projections of a vector v in the q-space (t is frozen)
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Projections of a vector v in the q-space (t is frozen)
Figure 2

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

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+Position of the mass
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Position of the mass
Figure 3

Position of the mass

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+Actuator force
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Actuator force
Figure 4

Actuator force

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+Convergence of the simulation results (fixed step-size)
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Convergence of the simulation results (fixed step-size)
Figure 5

Convergence of the simulation results (fixed step-size)

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+Convergence of the simulation results (variable step-size)
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Convergence of the simulation results (variable step-size)
Figure 6

Convergence of the simulation results (variable step-size)

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+Audi A6—Corner accelerometers
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Audi A6—Corner accelerometers
Figure 7

Audi A6—Corner accelerometers

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+Mechanical model of the car
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Mechanical model of the car
Figure 8

Mechanical model of the car

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+Semi-active damper
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Semi-active damper
Figure 9

Semi-active damper

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+Semi-active control strategy
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Semi-active control strategy
Figure 10

Semi-active control strategy

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+Lane change maneuver (standard qualification test)
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Lane change maneuver (standard qualification test)
Figure 11

Lane change maneuver (standard qualification test)

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+Horizontal trajectory of the car-body
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Horizontal trajectory of the car-body
Figure 12

Horizontal trajectory of the car-body

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+Angles of the car-body
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Angles of the car-body
Figure 13

Angles of the car-body

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+Electrical current in the valves
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Electrical current in the valves
Figure 14

Electrical current in the valves

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+Hydraulic pressures in the rear right damper
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Hydraulic pressures in the rear right damper
Figure 15

Hydraulic pressures in the rear right damper

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