Research Papers

Approximate End-Effector Tracking Control of Flexible Multibody Systems Using Singular Perturbations

[+] Author and Article Information
Thomas Gorius

e-mail: thomas.gorius@itm.uni-stuttgart.de

Robert Seifried

e-mail: robert.seifried@itm.uni-stuttgart.de

Peter Eberhard

e-mail: peter.eberhard@itm.uni-stuttgart.de
Institute of Engineering
and Computational Mechanics,
University of Stuttgart,
Stuttgart 70569, Germany

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 2, 2012; final manuscript received October 7, 2013; published online November 19, 2013. Assoc. Editor: Hiroyuki Sugiyama.

J. Comput. Nonlinear Dynam 9(1), 011017 (Nov 19, 2013) (9 pages) Paper No: CND-12-1190; doi: 10.1115/1.4025635 History: Received November 02, 2012; Revised October 07, 2013

In many cases, the design of a tracking controller can be significantly simplified by the use of a 2-degrees of freedom (DOF) control structure, including a feedforward control (i.e., the inversion of the nominal system dynamics). Unfortunately, the computation of this feedforward control is not easy if the system is nonminimum-phase. Important examples of such systems are flexible multibody systems, such as lightweight manipulators. There are several approaches to the numerical computation of the exact inversion of a flexible multibody system. In this paper, the singularly perturbed form of such mechanical systems is used to give a semianalytic solution to the tracking control design. The control makes the end-effector to even though not exactly, but approximately track a certain trajectory. Thereby, the control signal is computed as a series expansion in terms of an overall flexibility of the bodies of the multibody system. Due to the use of symbolic computations, the main calculations are independent of given parameters (e.g., the desired trajectories), such that the feedforward control can be calculated online. The effectiveness of this approach is shown by the simulation of a two-link flexible manipulator.

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Grahic Jump Location
Fig. 1

Schematic representation of the differences between a rigid and a flexible manipulator

Grahic Jump Location
Fig. 2

Structure of the approximate feedforward control

Grahic Jump Location
Fig. 3

Calculation of the approximate feedforward control

Grahic Jump Location
Fig. 4

Workflow of the calculations

Grahic Jump Location
Fig. 5

Manipulator with flexible links

Grahic Jump Location
Fig. 6

Simulation results of the two-link manipulator



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