Stability robustness of almost linear state equations

1993 ◽  
Vol 38 (2) ◽  
pp. 262-266 ◽  
Author(s):  
I. Lewkowicz ◽  
R. Sivan
Keyword(s):  
State Equations ◽  
Stability Robustness ◽  
Linear State

Experimental and numerical investigation of railroad vehicle braking dynamics

2009 ◽  
Vol 223 (3) ◽  
pp. 255-267
Author(s):  
C Mellace ◽  
A P Lai ◽  
A Gugliotta ◽  
N Bosso ◽  
T Sinokrot ◽  
...  
Keyword(s):  
Equations Of Motion ◽  
The Body ◽  
Computer Algorithms ◽  
Coordinate Systems ◽  
State Equations ◽  
Relative Coordinates ◽  
Linear State ◽  
Cartesian Coordinate ◽  
Railroad Vehicle ◽  
Braking Dynamics

One of the important issues associated with the use of trajectory coordinates in railroad vehicle dynamic algorithms is the ability of such coordinates to deal with braking and traction scenarios. In these algorithms, track coordinate systems that travel with constant speeds are introduced. As a result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinates to be effectively used in modelling braking and traction dynamics. One of the objectives of this investigation is to demonstrate that by using track coordinate systems that can have an arbitrary motion, the trajectory coordinates can be used as the basis for developing computer algorithms for modelling braking and traction conditions. To this end, a set of six generalized trajectory coordinates is used to define the configuration of each rigid body in the railroad vehicle system. This set of coordinates consists of an arc length that represents the distance travelled by the body, and five relative coordinates that define the configuration of the body with respect to its track coordinate system. The independent non-linear state equations of motion associated with the trajectory coordinates are identified and integrated forward in time in order to determine the trajectory coordinates and velocities. The results obtained in this study show that when the track coordinate systems are allowed to have an arbitrary motion, the resulting set of trajectory coordinates can be used effectively in the study of braking and traction conditions. The results obtained using the trajectory coordinates are compared with the results obtained using the absolute Cartesian-coordinate-based formulations, which allow modelling braking and traction dynamics. In addition to this numerical validation of the trajectory coordinate formulation in braking scenarios, an experimental validation is also conducted using a roller test rig. The comparison presented in this study shows a good agreement between the obtained experimental and numerical results.

A Logical Procedure for the Construction of Bond Graphs in Systems Modeling

1972 ◽  
Vol 94 (3) ◽  
pp. 183-188 ◽  
Author(s):  
H. R. Martens ◽  
A. C. Bell
Keyword(s):  
Complex Model ◽  
Bond Graphs ◽  
State Equations ◽  
Final Model ◽  
Resonance Behavior ◽  
Modeling Process ◽  
Step Procedure ◽  
Internal Dissipation ◽  
Linear State ◽  
Experimental Values

The problem of deriving a suitable mathematical model for complex devices is discussed. A small vibratory air pump is used as the medium of presentation. The modeling process begins with the basic coupling structure of the device. In a logical step-by-step procedure the initial model is built up to satisfy a number of functional considerations inherent to the device, such as the resonance behavior, input impedance, output impedance, and internal dissipation. At each step in the modeling process the completeness and suitability of the model is examined. Bond graphs drawn for the successively larger and more complex model clearly predict the shortcomings of the partial model and point the way to the next step. It is evident that the principle of causal relations forms a most important guiding element in the modeling process. The final model is in the form of a set of linear state equations, and scaling of the A-matrix indicates the relative importance of parameters when experimental values are substituted for literals.

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