Coordinated Science Laboratory progress report for December 1965, January, and February 1966

Studies in mechanical damping in possible gyro materials, electron scattering from surface of tungsten, and control system

Implicit network descriptions of RLC networks and the problem of re-engineering

The thesis deals with aspects of Systems Re-engineering specialised to the case of passive electrical networks. Re-engineering is a problem different from traditional control problems and this emerges when it is realised that the systems designed in the past cannot perform according to the new performance requirements and such performance cannot be improved by traditional control activities. Re-engineering implies that we intervene in early stages of system design involving sub-processes, values of physical elements, interconnection topology, selection of systems of inputs and outputs and of course retuning of control structures. This is a very challenging problem which has not been addressed before in a systematic way and needs fundamental new thinking, based on understanding of structure evolution during the stages of integrated design. A major challenge in the study of this problem is to have a system representation that allows study of evolution of system properties as well as structural invariants. For linear systems the traditional system representations, such as transfer functions, state space models and polynomial type models do not provide a suitable framework for study structure and property evolutions, since for every change we need to compute again these models and the transformations we have used do not appear in an explicit form in such models. It is for this reason, for a general system, such system representations are not suitable for study of system representations on re-engineering. It has been recognized that for the special family of systems defined by the passive electrical networks (RLC), there exists a representation introduced by the loop/ nodal analysis, expressed by the impedance/admittance integral-differential models, which have the property of re-engineering transformations of the following type: 1. Changing the values or possible nature of existing elements without changing the network topology, 2. Modifying the network topology without changing network cardinality, that is number of independent loops or nodes, 3. Augmenting or reducing the network by addition or deletion of sub-networks, 4. Combination of all the above transformations. These kinds of transformations may be represented as perturbations on the original impedance/admittance models. The above indicates that impedance/admittance integral-differential models, which from now on will be referred to as Implicit Network Descriptions is the natural vehicle for studying re-engineering on electrical networks. Although issues related to realisation of impedance/admittance transfer functions within RLC topologies, has been the topic of classical network synthesis, the system aspects of such descriptions have not been properly considered. Addressing problems of network re-engineering requires the development of the fundamental system aspects of such new descriptions in terms of McMillan degree, regularity and a number of other properties. Certain problems of evolution (of system properties) are linked to Frequency Assignment, as far as natural frequencies under re-engineering and this requires use of techniques developed within control theory for Frequency Assignment Problems