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

System Dynamics and Control,
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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Wasfy, T. , and Noor, A. , 2003, “ Computational Strategies for Flexible Multibody Systems,” ASME J. Appl. Mech., 56(6), pp. 553–613. [CrossRef]
Schoen, M. P. , Hoover, R. C. , Chinvorarat, S. , and Schoen, G. M. , 2009, “ System Identification and Robust Controller Design Using Genetic Algorithms for Flexible Space Structures,” ASME J. Dyn. Syst. Meas. Control, 131(3), p. 031003. [CrossRef]
Masoudi, R. , and Mahzoon, M. , 2011, “ Maneuvering and Vibrations Control of a Free-Floating Space Robot With Flexible Arms,” ASME J. Dyn. Syst. Meas. Control, 133(5), p. 051001. [CrossRef]
Guy, N. , Alazard, D. , Cumer, C. , and Charbonnel, C. , 2014, “ Dynamic Modeling and Analysis of Spacecraft With Variable Tilt of Flexible Appendages,” ASME J. Dyn. Syst. Meas. Control, 136(2), p. 021020. [CrossRef]
Chatlatanagulchai, W. , and Meckl, P. H. , 2009, “ Model-Independent Control of a Flexible-Joint Robot Manipulator,” ASME J. Dyn. Syst. Meas. Control, 131(4), p. 041003. [CrossRef]
Boscariol, P. , Gasparetto, A. , and Zanotto, V. , 2010, “ Active Position and Vibration Control of a Flexible Links Mechanism Using Model-Based Predictive Control,” ASME J. Dyn. Syst. Meas. Control, 132(1), p. 014506. [CrossRef]
Usoro, P. , Nadira, R. , and Mahil, S. , 1986, “ A Finite Element/Lagrange Approach to Modeling Lightweight Flexible Manipulators,” ASME J. Dyn. Syst. Meas. Control, 108(3), pp. 198–205. [CrossRef]
Rong, B. , Rui, X. , and Wang, G. , 2011, “ Modified Finite Element—Transfer Matrix Method for Eigenvalue Problem of Flexible Structures,” ASME J. Appl. Mech., 78(2), p. 021016. [CrossRef]
Dokainish, M. , 1972, “ A New Approach for Plate Vibrations: Combination of Transfer Matrix and Finite Element Technique,” ASME J. Eng. Ind., 94(2), pp. 526–530. [CrossRef]
Rui, X. , Wang, G. , Lu, Y. , and Yun, L. , 2008, “ Transfer Matrix Method for Linear Multibody System,” Multibody Syst. Dyn., 19(3), pp. 179–207. [CrossRef]
Tan, T. , Yousuff, A. , Bahar, L. , and Konstantinidis, M. , 1990, “ A Modified Finite Element—Transfer Matrix for Control Design of Space Structures,” Comput. Struct., 36(1), pp. 47–55. [CrossRef]
Krauss, R. , and Book, W. J. , 2010, “ Transfer Matrix Modelling of Systems With Noncollocated Feedback,” ASME J. Dyn. Syst. Meas. Control, 132(6), p. 061301. [CrossRef]
Hurty, W. , 1965, “ Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Hintz, R. M. , 1975, “ Analytical Methods in Component Modal Synthesis,” AIAA J., 13(8), pp. 1007–1016. [CrossRef]
MacNeal, R. H. , 1971, “ A Hybrid Method of Component Mode Synthesis,” Comput. Struct., 1(4), pp. 581–601. [CrossRef]
Craig, R. R., Jr. , 2000, “ A Brief Tutorial on Substructure Analysis and Testing,” International Modal Analysis Conference (IMAC), San Antonio, TX, Feb. 7–10, Vol. 1, pp. 899–908.
Ersal, T. , Fathy, H. , Rideout, D. , Louca, L. , and Stein, J. , 2008, “ A Review of Proper Modeling Techniques,” ASME J. Dyn. Syst. Meas. Control, 130(6), p. 061008.
Young, K. D. , 1990, “ Distribute Finite-Element Modeling and Control Approach for Large Flexible Structures,” J. Guid., 13(4), pp. 703–713. [CrossRef]
Su, T. , Babuska, V. , and Craig, R. , 1995, “ Substructure-Based Controller Design Method for Flexible Structures,” J. Guid. Control Dyn., 18(5), pp. 1053–1061. [CrossRef]
Alazard, D. , Cumer, C. , and Tantawi, K. , 2008, “ Linear Dynamic Modeling of Spacecraft With Various Flexible Appendages and On-Board Angular Momentums,” 7th ESA Guidance, Navigation and Control Conference, pp. 11148–11153.
Manceaux-Cumer, C. , and Chretien, J. , 2001, “ Minimal LFT Form of a Spacecraft Built Up From Two Bodies,” AIAA Paper No. 2001-4350.
Alazard, D. , Perez, J. A. , Loquen, T. , and Cumer, C. , 2015, “ Two-Input Two-Output Port Model for Mechanical Systems,” AIAA Paper No. 2015-1778.
Perez, J. A. , Alazard, D. , Loquen, T. , Cumer, C. , and Pittet, C. , 2015, “ Linear Dynamic Modeling of Spacecraft With Open-Chain Assembly of Flexible Bodies for ACS/Structure Co-Design,” Advances in Aerospace Guidance, Navigation and Control, Springer, Cham, Switzerland, pp. 639–658.
Craig, R. , and Bampton, M. , 1968, “ Coupling of Substructures for Dynamic Analysis,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Young, J. , 2000, “ Primer on Craig–Bampton CMS Procedure Method: An Introduction to Boundary Node Functions, Base Shake Analyses, Load Transformation Matrices, Modal Synthesis and Much More,” NASA.
Perez, J. , Pittet, C. , Alazard, D. , Loquen, T. , and Cumer, C. , 2015, “ A Flexible Appendage Model for Use in Integrated Control/Structure Spacecraft Design,” IFAC PapersOnline, 48(9), pp. 275–280. [CrossRef]
Junkins, J. L. , and Kim, Y. , 1993, Introduction to Dynamics and Control of Flexible Structures, AIAA, Reston, VA.
Luca, A. D. , and Siciliano, B. , 1991, “ Closed-Form Dynamic Model of Planar Multilink Lightweight Robots,” IEEE Trans. Syst., Man Cybern., 21(4), pp. 826–839. [CrossRef]
Mucino, V. H. , and Pavelic, V. , 1981, “ An Exact Condensation Procedure for Chain-Like Structures Using a Finite Element—Transfer Matrix Approach,” ASME J. Mech. Des., 103(2), pp. 295–303. [CrossRef]
Alazard, D. , Loquen, T. , de Plinval, H. , Cumer, C. , Toglia, C. , and Pavia, P. , 2013, “ Optimal Co-Design for Earth Observation Satellites With Flexible Appendages,” AIAA Paper No. 2013-4640.
Alazard, D. , Loquen, T. , de Plinval, H. , and Cumer, C. , 2013, “ Avionics/Control Co-Design for Large Flexible Space Structures,” AIAA Paper No. 2013-4638.
Murali, H. , Alazard, D. , Massotti, L. , Ankersen, F. , and Toglia, C. , 2015, “ Mechanical-Attitude Controller Co-Design of Large Flexible Space Structures,” EURO Guidance, Navigation and Control Conference, Toulouse, France, pp. 659–678.
Belcastro, C. M. , Lim, K. B. , and Morelli, E. A. , 1999, “ Computer-Aided Uncertainty Modeling of Nonlinear Parameter-Dependent Systems. II. F-I6 Example,” 1999 IEEE International Symposium on Computer Aided Control System Design, Kohala Coast, HI, pp. 16–23.
Balas, G. , Chiang, R. , Packard, A. , and Safonov, M. , 2005, “ Robust Control Toolbox,” For Use With MATLAB User's Guide, 3, MathWorks, Natick, MA.
Ferreres, G. , 1999, A Practical Approach to Robustness Analysis With Aeronautical Applications, Springer Science & Business Media, Cham, Switzerland.
Elgohary, T. A. , Turner, J. D. , and Junkins, J. L. , 2015, “ Analytic Transfer Functions for the Dynamics & Control of Flexible Rotating Spacecraft Performing Large Angle Maneuvers,” J. Astronaut. Sci., 62(2), pp. 168–195. [CrossRef]


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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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