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

2018 ◽  
Author(s):  
Qinbo Zhou ◽  
Xiaoting Rui
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody Systems ◽  
Signal Flow ◽  
Signal Flow Graphs ◽  
Transfer Equations ◽  
Mechanical Element ◽  
Flow Graphs

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.

Riccati Transfer Equations for Linear Multibody Systems with Indeterminate In-Span Conditions

2019 ◽  
Vol 86 (6) ◽  
Author(s):  
Jianshu Zhang ◽  
Xiaoting Rui ◽  
Junjie Gu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody Systems ◽  
Internal Force ◽  
State Variables ◽  
Transfer Matrices ◽  
Transfer Equations ◽  
Mechanical Elements

The transfer matrix method for linear multibody systems is capable of providing precise solutions for the dynamics of various mechanical systems, but it may also suffer from numerical instability in some cases, where serial chains with a large number of mechanical elements are involved or high-frequency harmonic responses are computed. Combining such a transfer strategy with the Riccati transformation yields the Riccati transfer matrix method (RTMM), which can help improve the numerical stability. According to the existing method, the conventional transfer matrices of all the mechanical elements should be obtained first; in other words, the existence of conventional transfer matrices is a prerequisite for the application of the RTMM. Thus, it seems that the RTMM is incapable of performing the dynamics analysis of linear multibody systems with indeterminate in-span conditions due to the nonexistence of the corresponding conventional transfer matrices. Observe that, for any state variables with indeterminate input–output relationships, the complementary state variables (the complementary state variable of a displacement is the corresponding internal force and vice versa) are identically equal to zero, and that the dimension of the Riccati transfer equation is only half of that of the conventional transfer equation. It reveals that the Riccati transfer equations for the connection points associated with indeterminate in-span conditions can be formulated directly, and that there is no need to rely on the conventional transfer equation. Two numerical examples are simulated and the computational results are compared with those obtained by the finite element method, which verifies the proposed method.

Application of the Transfer Matrix Method for Multibody Systems in Dynamics of the Self-Propelled Artillery

2018 ◽  
Author(s):  
Qicheng Zha ◽  
Xiaoting Rui ◽  
Feifei Liu ◽  
Hailong Yu ◽  
Jianshu Zhang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
The Self ◽  
System Matrix ◽  
Topological Graph ◽  
Fast Calculation ◽  
Transfer Equations ◽  
Model Transfer

Transfer Matrix Method for Multibody Systems (MSTMM) has the advantages of no need to establish the global system dynamics equations, low order of the system matrix, high programming, and fast calculation speed compared to the ordinary dynamics methods. In this paper, the topological graph of the dynamics model, transfer equations, transfer matrix of overall system and the simulation program of dynamics of the self-propelled artillery system are established by using the new version of the transfer matrix method for multibody systems and the automatic deduction theorem of overall transfer equation of systems. Realize the rapid calculation of the deviation of the pitch angle and the revolution angles of the turret versus time in the self-propelled artillery. It provides a theoretical basis and simulation means for the dynamics analysis of the self-propelled artillery.

Riccati Transfer Matrix Method for Linear Tree Multibody Systems

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Junjie Gu ◽  
Xiaoting Rui ◽  
Jianshu Zhang ◽  
Gangli Chen ◽  
Qinbo Zhou
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Numerical Stability ◽  
Matrix Method ◽  
Multibody Systems ◽  
Method Comparison ◽  
Harmonic Excitation ◽  
State Response ◽  
Multiple Input ◽  
Transfer Equations

The Riccati transfer matrix method (RTMM) improves the numerical stability of analyzing chain multibody systems with the transfer matrix method for multibody systems (MSTMM). However, for linear tree multibody systems, the recursive relations of the Riccati transfer matrices, especially those for elements with multiple input ends, have not been established yet. Thus, an RTMM formulism for general linear tree multibody systems is formulated based on the transformation of transfer equations and geometrical equations of such elements. The steady-state response under harmonic excitation of a linear tree multibody system is taken as an example and obtained by the proposed method. Comparison with the finite-element method (FEM) validates the proposed method and a numerical example demonstrates that the proposed method has a better numerical stability than the normal MSTMM.

Study on Response of Launch Vehicle Under Ground Wind Loads Based on Transfer Matrix Method for Multibody Systems

2018 ◽  
Author(s):  
Xun Wang ◽  
Xiaoting Rui ◽  
Fufeng Yang
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Multibody Systems ◽  
Launch Vehicle ◽  
Wind Loads ◽  
Dynamics Response ◽  
Domain Dynamics ◽  
Dynamics Method

In order to study dynamics response of a launch vehicle under ground wind loads, the dynamics model of a launch vehicle erected on the pad is developed based on transfer matrix method for multibody systems and the theory of structural wind engineering. The overall transfer equation, overall transfer matrix, and characteristics equation of the system are deduced based on the automatic deduction theorem of overall transfer equation of multibody system. The equation governing the motion of the launch vehicle is obtained by using the orthogonality of augmented eigenvector. The vibration characteristics, and frequency domain and time domain dynamics response under ground wind loads of the launch vehicle are simulated. The simulation results show that the eigenfrequencies obtained by the proposed method and ordinary dynamics method have good agreements. The paper provides an effective approach to compute the dynamics response of the launch vehicle under ground wind loads.

scholarly journals Controller Parameters Tuning Based on Transfer Matrix Method for Multibody Systems

2014 ◽  
Vol 6 ◽  
pp. 957684 ◽  
Author(s):  
Hossam Hendy ◽  
Xiaoting Rui ◽  
Qinbo Zhou ◽  
Mostafa Khalil
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Parameters Tuning
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