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Research Papers

A Stable Inversion Method for Feedforward Control of Constrained Flexible Multibody Systems

[+] Author and Article Information
Olivier Brüls

e-mail: o.bruls@ulg.ac.be

Guaraci Jr. Bastos

e-mail: g.bastos@ulg.ac.be

Department of Aerospace
and Mechanical Engineering (LTAS),
University of Liège,
Chemin des chevreuils 1 (B52),
Liège 4000, Belgium

Robert Seifried

Institute of Engineering
and Computational Mechanics,
University of Stuttgart,
Pfaffenwaldring 9,
Stuttgart 70569, Germany
e-mail: robert.seifried@itm.uni-stuttgart.de

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 11, 2013; final manuscript received May 23, 2013; published online October 15, 2013. Assoc. Editor: Hiroyuki Sugiyama.

J. Comput. Nonlinear Dynam 9(1), 011014 (Oct 15, 2013) (9 pages) Paper No: CND-13-1034; doi: 10.1115/1.4025476 History: Received February 11, 2013; Revised May 23, 2013

The inverse dynamics of flexible multibody systems is formulated as a two-point boundary value problem for an index-3 differential-algebraic equation (DAE). This DAE represents the equation of motion with kinematic and trajectory constraints. For so-called nonminimum phase systems, the remaining dynamics of the inverse model is unstable. Therefore, boundary conditions are imposed not only at the initial time but also at the final time in order to obtain a bounded solution of the inverse model. The numerical solution strategy is based on a reformulation of the DAE in index-2 form and a multiple shooting algorithm, which is known for its robustness and its ability to solve unstable problems. The paper also describes the time integration and sensitivity analysis methods that are used in each shooting phase. The proposed approach does not require a reformulation of the problem in input-output normal form, which is known from nonlinear control theory. It can deal with serial and parallel kinematic topology, minimum phase and nonminimum phase systems, and rigid and flexible mechanisms.

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Figures

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Fig. 1

Dynamic system with feedforward and feedback controller

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Fig. 2

Boundary conditions for the zero-dynamics

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Fig. 3

Multiple shooting method

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Fig. 4

Planar serial manipulator with one passive joint

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Fig. 5

Underactuated serial manipulator: discretization in absolute coordinates

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Fig. 6

Serial manipulator: desired trajectory

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Fig. 7

Serial manipulator: results for c = 50 Nm/rad and d = 0.25 Nms/rad

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Fig. 8

Serial manipulator: results for c = 5 Nm/rad and d = 0 Nm s/rad

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Fig. 9

Flexible parallel manipulator

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Fig. 10

Results for the parallel manipulator (solid line: 1 finite element, and dashed line: 2 finite elements)

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