State-Space Formulation for Bond Graph Models of Multiport Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 35-40 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
State Space ◽  
Bond Graph ◽  
Graph Representation ◽  
Initial System ◽  
Field Equations ◽  
Graph Models ◽  
Reduction Procedure ◽  
Space Formulation ◽  
Systematic Reduction

A novel procedure for systematically generating state-space equations for multiport systems is presented. The method is based upon a bond graph representation of the system and causal manipulation of the field equations. Principal advantages of the method are the ability to anticipate formulation properties before writing equations, the availability of a simple check for correctness of the initial system relations, and the specification of a systematic reduction procedure for obtaining state-space equations in terms of energy variables.

Multiport Models in Mechanics

1972 ◽  
Vol 94 (3) ◽  
pp. 206-212 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
State Space ◽  
Large Scale ◽  
Force Fields ◽  
Digital Simulation ◽  
Bond Graph ◽  
Rigid Bodies ◽  
System Structure ◽  
Graph Models ◽  
Geometric Variables ◽  
Scale Motion

Problems in mechanics involving rigid bodies in large-scale motion in force fields of both conservative and nonconservative types are approached from a multiport viewpoint. A procedure for constructing bond graph models based on key geometric variables and the velocity transformations relating them is described. Contributions of such models to improving the representation and communication of system structure, the formulation of governing state-space equations, and the direct digital simulation of complicated mechanics problems are suggested.

Zero Dynamics of Physical Systems From Bond Graph Models—Part I: SISO Systems

1999 ◽  
Vol 121 (1) ◽  
pp. 10-17 ◽  
Author(s):  
S. Y. Huang ◽  
K. Youcef-Toumi
Keyword(s):  
System Analysis ◽  
Mimo Systems ◽  
Geometric Approach ◽  
Bond Graph ◽  
Graph Representation ◽  
Zero Dynamics ◽  
Feedback Systems ◽  
State Equations ◽  
Graph Models ◽  
Physical Systems

Zero dynamics is an important feature in system analysis and controller design. Its behavior plays a major role in determining the performance limits of certain feedback systems. Since the intrinsic zero dynamics can not be influenced by feedback compensation, it is important to design physical systems so that they possess desired zero dynamics. However, the calculation of the zero dynamics is usually complicated, especially if a form which is closely related to the physical system and suitable for design is required. In this paper, a method is proposed to derive the zero dynamics of physical systems from bond graph models. This method incorporates the definition of zero dynamics in the differential geometric approach and the causality manipulation in the bond graph representation. By doing so, the state equations of the zero dynamics can be easily obtained. The system elements which are responsible for the zero dynamics can be identified. In addition, if isolated subsystems which exhibit the zero dynamics exist, they can be found. Thus, the design of physical systems including the consideration of the zero dynamics become straightforward. This approach is generalized for MIMO systems in the Part II paper.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

Delay-Bond Graph Models for Geared Torsional Systems

1974 ◽  
Vol 41 (2) ◽  
pp. 366-370 ◽  
Author(s):  
N. T. Tsai ◽  
S. M. Wang
Keyword(s):  
Transmission Line ◽  
Gear Tooth ◽  
Nonlinear Damping ◽  
Bond Graph ◽  
Dynamic Responses ◽  
State Variables ◽  
Graph Models ◽  
Wave Variables ◽  
Tooth Stiffness ◽  
Line Elements

The dynamic responses of geared torsional systems are analyzed with the delay-bond graph technique. By transforming the power variables into torsional wave variables, the torsional elements are modeled as transmission line elements. The nonlinear elements, e.g., varying tooth stiffness, gear-tooth backlash, and nonlinear damping, are incorporated into the ideal transmission line element. A computational algorithm is established where the state variables of the system are expressed in terms of wave scattering variables and the dynamic responses are then obtained in both time and space domains. The simulation results of several simple examples of linear and nonlinear geared torsional systems are presented to demonstrate the feasibility of this algorithm.

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