System Properties of Implicit Passive Electrical Networks Descriptions

Abstract

Abstract Redesigning systems by changing elements, topology, organization, augmenting the system by the addition of subsystems, or removing parts, is a major challenge for systems and control theory. A special case is the redesign of passive electric networks which aims to change the natural dynamics of the network (natural frequencies) by the above operations leading to a modification of the network. This requires changing the system to achieve the desirable natural frequencies and involves the selection of alternative values for dynamic elements and non-dynamic elements within a fixed interconnection topology and/or alteration of the interconnection topology and possible evolution of the network (increase of elements, branches). The use of state-space or transfer function models does not provide a suitable framework for the study of this problem, since every time such changes are introduced, a new state space or transfer function model has to be recalculated. The use of impedance and admittance modeling, provides a suitable framework for the study of network properties under the process of re-engineering transformations. This paper deals with the fundamental system properties of the impedance-admittance network description which provide the appropriate framework for network re-engineering. We identify the natural topologies expressing the structured transformations linked to the impedance-graph, admittance graph-topology of the network and examine issues such as network regularity, number of finite frequencies and provide characterization of them in terms of the basic network matrices. The implicit network representation introduced provides a natural framework for expressing the different types of re-engineering transformations which can be used for the study of the natural frequencies assignment.