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Deduction method of the overall transfer equation of linear controlled multibody systems

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Abstract

The transfer matrix method for multibody systems (MSTMM), which is a highly efficient and novel approach for multibody system dynamics, was proposed and perfected in the past 20 years. The deduction of the overall transfer equation of the system is one of the key techniques in MSTMM. The topology figure of the dynamics model of multibody systems is a novel pictorial expression to describe the relationship among the state vectors of connection points of different elements in MSTMM. In this paper, the block diagram in control theory is introduced and incorporated into the topology figure of the dynamics model to represent the connection relationship between different mechanical elements in the system as well as the control relations. Meanwhile, the transfer equations of the controlled element, control subsystem and the overall transfer equation of the linear controlled multibody systems are deduced. The proposed method greatly reduces the efforts to study the linear controlled multibody systems since the procedures are stylized. Two numerical examples are given to validate the proposed method.

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Acknowledgements

The first author wishes to thank Prof. Dieter Bestle in Brandenburg University of Technology Cottbus and Prof. Laith K. Abbas in Nanjing University of Science and Technology for their important discussions. Indebted appreciation should also be given to Associate Prof. Ryan Krauss in Southern Illinois University for providing the dynamics parameters in Table 2. The research was supported by the Research Fund for the Doctoral Program of Higher Education of China (20113219110025), the Research Innovation Program 2013 for Graduates in Common Universities of Jiangsu Province (CXLX13_203), and National Natural Science Foundation of Country (Grant No. 61304137).

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  1. Institute of Launch Dynamics, Nanjing University of Science and Technology, Nanjing, 210094, P.R. China

    Qinbo Zhou, Xiaoting Rui, Yu Tao, Bo Li, Jianshu Zhang & Wei Zhu

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  1. Qinbo Zhou
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  2. Xiaoting Rui
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  3. Yu Tao
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Correspondence to Xiaoting Rui.

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Zhou, Q., Rui, X., Tao, Y. et al. Deduction method of the overall transfer equation of linear controlled multibody systems. Multibody Syst Dyn 38, 263–295 (2016). https://doi.org/10.1007/s11044-015-9487-2

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