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Research Papers

A Method for Solving Large-Scale Multiloop Constrained Dynamical Systems Using Structural Decomposition

[+] Author and Article Information
Tao Xiong

National Engineering Research Center of CAD
Software Information Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: xiongtao39@hust.edu.cn

Jianwan Ding

National Engineering Research Center of CAD
Software Information Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: dingjw@hust.edu.cn

Yizhong Wu

National Engineering Research Center of CAD
Software Information Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: cad.wyz@mail.hust.edu.cn

Liping Chen

National Engineering Research Center of CAD
Software Information Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: chenlp@tongyuan.cc

Wenjie Hou

Eaton (China) Investments Co. Ltd.,
Shanghai 200335, China
e-mail: houwj@hust.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 9, 2015; final manuscript received June 14, 2016; published online December 5, 2016. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 12(3), 031005 (Dec 05, 2016) (13 pages) Paper No: CND-15-1364; doi: 10.1115/1.4034044 History: Received November 09, 2015; Revised June 14, 2016

A structural decomposition method based on symbol operation for solving differential algebraic equations (DAEs) is developed. Constrained dynamical systems are represented in terms of DAEs. State-space methods are universal for solving DAEs in general forms, but for complex systems with multiple degrees-of-freedom, these methods will become difficult and time consuming because they involve detecting Jacobian singularities and reselecting the state variables. Therefore, we adopted a strategy of dividing and conquering. A large-scale system with multiple degrees-of-freedom can be divided into several subsystems based on the topology. Next, the problem of selecting all of the state variables from the whole system can be transformed into selecting one or several from each subsystem successively. At the same time, Jacobian singularities can also be easily detected in each subsystem. To decompose the original dynamical system completely, as the algebraic constraint equations are underdetermined, we proposed a principle of minimum variable reference degree to achieve the bipartite matching. Subsequently, the subsystems are determined by aggregating the strongly connected components in the algebraic constraint equations. After that determination, the free variables remain; therefore, a merging algorithm is proposed to allocate these variables into each subsystem optimally. Several examples are given to show that the proposed method is not only easy to implement but also efficient.

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Figures

Grahic Jump Location
Fig. 1

Problems processed through divide and conquer

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Fig. 3

A good choice of triple pendulum

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Fig. 4

A general choice of triple pendulum

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Fig. 5

A poor choice of triple pendulum

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Fig. 6

Aggregate of strongly connected components in MG¯1t and MG¯2t

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Fig. 10

Maximum matching of minimum reference degree

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Fig. 11

Two-loop mechanism

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Fig. 12

Tree structure after cutting

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Fig. 13

Matching process of the two-loop mechanism

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Fig. 14

Maximum matching MHn of Hn

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Fig. 15

Aggregation graph of the two-loop mechanism

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Fig. 16

Decomposition of the two-loop mechanism

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Fig. 17

Simulation curves of L8: (a) undecomposed and (b) decomposed

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Fig. 18

Four-loop mechanism

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Fig. 19

Decomposition of the four-loop mechanism

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Fig. 20

Excavator jib of three degrees-of-freedom

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Fig. 21

Tree structure after cutting

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Fig. 22

Matching process of the excavator jib

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Fig. 23

Maximum matching MHh of Hh

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Fig. 24

Aggregation graph of the excavator jib

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Fig. 25

Decomposition of the excavator jib

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Fig. 26

Simulation curves for p10 using (a) dymola and (b) mworks

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Fig. 27

Simulation curves for r2 using (a) dymola and (b) mworks

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