A Representation of the Transfer Matrix Method for Linear Controlled Multibody Systems Using Matrix Signal Flow Graph

The obtaining of the overall transfer equation of a linear controlled multibody system is one of the key problems when the transfer matrix method for multibody systems (MSTMM) is applied to study controlled multibody dynamics. This paper applies the theory of matrix signal flow graphs (MSFG) to MSTMM. The transfer matrix signal flow graphs (TMSFG) of a mechanical element and a control subsystem can be drawn according to their transfer equations. By merging the nodes corresponding to the same state vector, the TMSFG of the entire system can be obtained. Eventually, the overall transfer equation of the linear controlled system can be systematically obtained according to the reduction rules of MSFG. An example is taken to sketch the idea and the simulation results are compared with other ordinary dynamics methods to validate the proposed method. This paper lays a foundation for automatic deduction of overall transfer equations of linear controlled multibody systems.