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Research Papers

Flexible Multibody System Linear Modeling for Control Using Component Modes Synthesis and Double-Port Approach

[+] Author and Article Information
Jose Alvaro Perez

Department of Flight Dynamics and Control,
ONERA Toulouse,
Toulouse 31055, France
e-mail: jose-alvaro.perez_gonzalez@onera.fr

Daniel Alazard

Professor
System Dynamics and Control,
ISAE-SUPAERO Toulouse,
Toulouse 31055, France
e-mail: daniel.alazard@isae.fr

Thomas Loquen

Department of Flight Dynamics and Control,
ONERA Toulouse,
Toulouse 31055, France
e-mail: thomas.loquen@onera.fr

Christelle Pittet

Department of AOCS,
CNES Toulouse,
Toulouse 31055, France
e-mail: christelle.pittet@cnes.fr

Christelle Cumer

Department of Flight Dynamics and Control,
ONERA Toulouse,
Toulouse 31055, France
e-mail: christelle.cumer@onera.fr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received July 23, 2015; final manuscript received June 29, 2016; published online August 17, 2016. Assoc. Editor: Tarunraj Singh.

J. Dyn. Sys., Meas., Control 138(12), 121004 (Aug 17, 2016) (16 pages) Paper No: DS-15-1336; doi: 10.1115/1.4034149 History: Received July 23, 2015; Revised June 29, 2016

The main objective of this study is to propose a methodology for building a parametric linear model of flexible multibody systems (FMS) for control design. This new method uses a combined finite element (FE)–state-space approach based on component mode synthesis and a double-port approach. The proposed scheme offers the advantage of an automatic assembly of substructures, preserving the elastic dynamic behavior of the whole system. Substructures are connected following the double-port approach for considering the dynamic coupling among them, i.e., dynamic coupling is expressed through the transfer of accelerations and loads at the connection points. The proposed model allows the evaluation of arbitrary boundary conditions among substructures. In addition, parametric variations can be included in the model for integrated control/structure design purposes. The method can be applied to combinations of chainlike or/and starlike flexible systems, and it has been validated through its comparison with the assumed modes method (AMM) in the case of a rotatory spacecraft and with a nonlinear model of a two-link flexible arm.

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Figures

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Fig. 1

Substructure displacements decomposition

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Fig. 2

Substructure A linked to structure P

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Fig. 3

Block diagram representation of the connections of appendage A, projected in the frame Ra

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Fig. 4

Substructure A linked to structure P and substructure Q in chainlike assembly

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Fig. 5

Block diagram of the TITOP model

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Fig. 6

Appendage A in connection with P through a revolute joint along ea

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Fig. 7

Taking into account a local mechanism model K(s) in the two-port model of a body A

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Fig. 9

FMS modeling with the TITOP model (mast II is not represented for simplicity)

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Fig. 10

The TITOP LFR model, which takes into account parametric variations inside the block Δ

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Fig. 11

Maneuverable flexible spacecraft configuration

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Fig. 12

TITOP modeling of each appendage Ai

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Fig. 13

TITOP modeling of the whole structure

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Fig. 14

Root-mean-square (RMS) error for each method for the first six flexible modes: RMS=16Σi=16(ωi−ωirefωiref)2

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Fig. 15

Frequency response comparison: from hub torque to hub acceleration, for Mt=2.290 kg

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Fig. 16

Frequency response comparison: from hub torque to tip acceleration, for Mt=2.290 kg

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Fig. 17

Frequency response comparison: from hub torque to tip acceleration, for Mt = 0 kg

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Fig. 18

Frequency response comparison: from hub torque to tip acceleration, for Mt=114.5 kg

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Fig. 19

Rotatory spacecraft final assembly when considering length and tip mass variations in all the appendages

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Fig. 20

Bode system comparison when varying length and tip mass for all the appendages simultaneously

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Fig. 21

Bode system comparison when varying length and tip mass for one appendage only

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Fig. 22

The planar two-link flexible arm

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Fig. 23

TITOP assembly of a single flexible link i

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Fig. 24

TITOP assembly of the inverse dynamics model of the two-link flexible arm

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Fig. 25

Dynamic evolution of link 1 (α1) and link 2 (α2) under step input (αref1=60 deg) and fully extended arm (α2(0)=0 deg)

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