generalized mathematical model
topological and parametric equations
V. N. Efanov, A. V. Bondarev
In problem of mathematical modeling of the processes of the measurement, the processing and control important importance have a study to abilities electronic device to save their own features in condition intensive external and internal indignations.
As source model under investigation device is considered its equivalent scheme, given in the manner of electric multiterminal circuit. We Suppose that this multiterminal circuit contains n branches and k nodes. Then number unknown variable his(its) full-size mathematical model is 2n. In turn closed system of the equations such multiterminal circuit will include the collection of the parametric equations, describing relationship between current and voltage for each electric branch, and collection of the topological equations, describing structure of the joining the branches in multiterminal circuit.
The Building of the system of the parametric equations for outraged state of working provides the study of the behaviour current and voltages for corresponding to branches in vicinities of the accounting mode. For this purpose decomposition of the nonlinear dependencies is conducted in row Taylor, and are fixed the condition to convergence of this row for given range of the change current and voltages. Such a analysis allows to select deterministic forming parametric model and value the value vague factor, not amenable analytical description.
In given work are considered questions of the building generalised mathematical model device named class, allowing value their robustness in step of scheme of the technical designing.
Algorithmic solubility got generalised model is conditioned by structure of the system of the equations. Happen to the condition to algorithmic solubility got models in ambience of the interval calculations.