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Vibrating 3-dimensional mechanical systems are described by hybrid graphs. By dividing the hybrid graph into a tree and associated co-tree it is possible to describe in terms of matrices: across-flow-variables, stiffness and flexibility. The application of the formalism of graphs makes it possible to analyze mechanical systems in terms of dynamic characteristic and trajectory motion of determinate points.
Content available remote A note on model matching for nonrealizable nonlinear systems
In this technical note the model matching problem for nonlinear systems not admitting the state space realization is discussed. Both continuous- and discrete-time cases are addressed. It is demonstrated, by using a transfer function formalism, that even in case of nonrealizable systems it is sometimes still possible to find realizable compensators.
Content available remote Construction of the non-rigid Earth rotation series
Last years a lot of attempts to derive a high-precision theory of the non-rigid Earth rotation are carried out. For these purposes different transfer functions are used. Usually these transfer functions are applied to the series representing the nutation in the longitude and the obliquity of the rigid Earth rotation with respect to the ecliptic of date. The aim of this investigation is a construction of new high-precision non-rigid Earth rotation series (SN9000), dynamically adequate to the DE404/LE404 ephemeris over 2000 time span years, which are presented as functions of the Euler angles ψ, θ and φ with respect to the fixed ecliptic plane and equinox J2000.0.
Content available remote Robust performance of a class of control systems
Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also presented.
A new method for computation of minimal compartmental realizations of a proper transfer function is proposed. The method is based on a suitable transformation of an asymptotically stable positive realization to the desired compartmental realization. The transformation is characterized by a generalized permutation matrix. Sufficient conditions for the existence of minimal compartmental realizations are established. Two-step procedures for computation of minimal compartmental realizations for both continuous-time and discrete-time linear systems are derived and illustrated by a numerical example.
The paper gives a review of research works focused on cutting process during machine tools working conditions. The main result deals with assessing dynamie compliance (stiffness). The simplified experimental modal analysis of machine tools was carried out. This analysis results in determination the direction of the maximal compliance of a machine structure. The measurements are arranged into a diagram giving overview about the most important properties of the machine tool for operational conditions during machining process. The new measurement method gives the possibility to prevent inaccuracies in production after regular machine inspection
Content available remote Towards a Framework for Continuous and Discrete Multidimensional Systems
Continuous multidimensional systems described by partial differential equations can be represented by discrete systems in a number of ways. However, the relations between the various forms of continuous, semi-continuous, and discrete multidimensional systems do not fit into an established framework like in the case of one-dimensional systems. This paper contributes to the development of such a framework in the case of multidimensional systems. First, different forms of partial differential equations of physics-based systems are presented. Secondly, it is shown how the different forms of continuous multidimensional systems lead to certain discrete models in current use (finite-difference models, multidimensional wave digital filters, transfer function models). The links between these discrete models are established on the basis of the respective continuous descriptions. The presentation is based on three examples of physical systems (heat flow, transmission of electrical signals, acoustic wave propagation).
Content available remote The Stability of an Irrigation Canal System
In this paper we examine the stability of an irrigation canal system. The system considered is a single reach of an irrigation canal which is derived from Saint-Venant's equations. It is modelled as a system of nonlinear partial differential equations which is then linearized. The linearized system consists of hyperbolic partial differential equations. Both the control and observation operators are unbounded but admissible. From the theory of symmetric hyperbolic systems, we derive the exponential (or internal) stability of the semigroup underlying the system. Next, we compute explicitly the transfer functions of the system and we show that the input-output (or external) stability holds. Finally, we prove that the system is regular in the sense of (Weiss, 1994) and give various properties related to its transfer functions.
A method based on the transfer function has been used more and more frequently for investigation of transformer windings. It is applied more and more widely as a maintenance procedure lor the identification of damage and deformation of transformer windings as well as it might be used to estimate the condition of an insulating system. The method can also he used to detect possible manufacturing damages or to check minor dislocations of the windings. It is based on the comparison of current measurements of the transfer function with reference measurements. The application of this method in the investigation ol transformers is determined by an exact measurement of the transfer function by experiment and by mathematical modelling. Both methods of determining the transfer function of the transformer are being refined and developed. Transfer function measurement, analysis and evaluation methods are presented in this paper. Described methods were applied for measuring and calculating of the transfer function for two of transformer windings.
Uzwojenia transformatorów są badane coraz częściej przy zastosowaniu metody, której podstawą jest funkcja przenoszenia. Jest ona wykorzystywana do wykrywania uszkodzeń oraz zniekształceń uzwojeń. Może być także stosowana do oceny stanu układu izolacyjnego oraz do kontroli procesu produkcyjnego lub do wykrywania przemieszczeń uzwojeń. Metoda polega na porównaniu wyniku pomiaru funkcji przenoszenia z pomiarami odniesienia. Zastosowanie tej metody w badaniach transformatorów jest zależne od dokładnych pomiarów lub modelowania matematycznego funkcji przenoszenia. Obie metody wyznaczania funkcji przenoszenia są obecnie rozwijane i doskonalone. W artykule przedstawiono pomiary funkcji przenoszenia, analizę i rozwój metod. Porównano wyniki pomiarów i obliczeń funkcji przenoszenia dwu różnych uzwojeń transformatora.
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