Linearly variable networks: II— synthesis (original) (raw)
Linearly variable networks— I. analysis
Journal of the Franklin Institute, 1980
A linearly variable element is any passive two-terminal network element in which the immittance uaries linearly with respect to an independent (of frequency) real variable, x. A definite set of fundamental passive two terminal network elements (Felements) consisting of fixed passive elements and linearly variable elements is presented. It is shown that any network consisting of only F-elements has a driving point immittance, D(s, x), that is positive real for s complex, x real and positiue real for x complex, s real. Conditions on the variable coefficients, degree and location of zeros and poles of D(s, x) are established. A method of testing whether D(s, x) is positive real for one complex and one real variable is developed. This testing is accomplished by extending the Hurwitz and Sturm tests to one complex and one real variable.
IEEE Transactions on Automatic Control, 2000
This paper classifies the positive-real biquadratic functions which can be realized by five-element networks. The concept of regular positive-real functions is introduced to facilitate this classification. Networks are grouped into quartets which may sometimes reduce to two or one network(s). It is shown that a biquadratic can be realized by a series-parallel network with two reactive elements if and only if it is regular. Moreover, there are two such network quartets which can realize all regular biquadratics. It is shown that the only five-element networks which can realize nonregular biquadratics can be arranged into three network quartets. The quartets comprise: 1) two bridge networks with two reactive elements; 2) four series-parallel networks with three reactive elements; and 3) two bridge networks with three reactive elements. The necessary and sufficient realizability conditions are derived for each of these networks. The results are motivated by an approach to passive mechanical control which makes use of the inerter device.
Special Synthesis Techniques for Driving Point Impedance Functions
IEEE Transactions on Circuits and Systems I-regular Papers, 1955
An important problem in network design is the synthesis of driving-point impedance functions. As is well known, O. Brune was the first to state the necessary and sufficient conditions for physical realizability. Unfortunately, the synthesis technique which he proposed leads in general to perfectly coupled transformers. This is true also in the ease of the contributions made later by S. Darlington. Perfect transformers were eliminated by R. Bott and R. J. Duffin. However, their solution is, in general, expensive in terms of the number of elements that are required. Since the publication of their letter, many attempts have been made to find a solution that would lead to networks containing a number of elements closer to the minimum specified by Brune. An advance in this direction has been made by F. Miyata for a restricted class of positive real functions. He bas centered attention on the even part of the impedance function. The following paper exploits this point of view and amplifies some of the ideas given by Miyata. In addition, several new ideas are described relative to methods of decomposing the even part of the impedance function in such a way as to obtain a network without perfect transformers.
IEEE Transactions on Circuits and Systems, 1980
Abstm-llds paper presents results for some auafysis and synthesis problems of nouhear &procal networks. In particular, for special systems such as lossless reciprocal networks and nonlinear RC reciprocal netwok+ synthesll techniques are introduced. The central feature of these techniques is the methud of lindlng au appropriate stored energy function for the syuthesizing network from prescribed network equations. Under certain assumptions, the stored energy function can be determined directly from the controllability and observabiity matrices 'of a system obtained by fkarizatlon around any state of the orfgiual system.
Synthesis of simple feed-forward networks: a first-order example
2005
Stability analysis of networks has been the focus of much research over the past decade. Presently, researchers are investigating performance and synthesis of controllers and channel coding schemes in networks. Such design problems are difficult in general, as there is a strong interplay between control objectives and communication constraints, which forces the synthesis of controllers and channel encoders to be done simultaneously. Current approaches typically fix one, while the other is designed to meet some objective. In this paper, we consider a simple network, in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a noisy discrete channel. We first construct a model matching performance metric that captures the tradeoffs between coding the reference command to achieve more accuracy at the remote site and designing a controller to meet performance. We then simultaneously synthesize the controller and encoder block lengths that meet the specified objective for a first-order plant and model case. Finally, we illustrate performance sensitivity to the poles of the plant and model, and to the channel noise.
The McMillan degree of implicit transfer functions of RLC networks
2017
The McMillan degree of an implicit network transfer function defines the minimum number of dynamic elements which are necessary to fully describe the network. It is therefore a measure for the complexity of a network. Using modified nodal analysis models, which are linked directly to the natural network topology, we show that the McMillan degree equals the sum of the number of capacitors and inductors minus the number of fundamental loops of capacitors and fundamental cutsets of inductors. Exploiting this representation we derive a minimal realization of a RLC network, that is one where the number of involved (independent) differential equations equals the McMillan degree.
Alternative Dynamic Network Structures for Non-linear System Modelling
Hopfield Neural Networks have been used as universal identifiers of non-linear systems, because of their inherent dynamic properties. However the design decision of the number of neurons in the Hopfield network is not easy to make, in order for the network model to have the necessary complexity, extra neurons are required. This poses a problem since the role of the states that these neurons represent is not clear. Adding a hidden layer in the Hopfield network model increases the complexity of the model without posing the extra states problem. Alternatively breaking the problem down by having different interconnected Hopfield networks modeling each state, also increase the complexity of the problem. A comparison between the three approaches (traditional Hopfield, Hopfield with a hidden layer, and multiple interconnected Hopfield networks) indicates equivalence between the three structures, but with the alternative cases having increased connectivity in the feedback matrix, and limite...
Mathematical Problems in Engineering, 2008
A novel procedure for explicit construction of the entries of real symmetric matrices with assigned spectrum and the entries of the corresponding orthogonal modal matrices is presented. The inverse eigenvalue problem of symmetric matrices with some specific sign patterns (including hyperdominant one) is explicitly solved too. It has been shown to arise thereof a possibility of straightforward solving the inverse eigenvalue problem of symmetric hyperdominant matrices with assigned nonnegative spectrum. The results obtained are applied thereafter in synthesis of driving-point immittance functions of transformerless, common-ground, two-element-kindRLCnetworks and in generation of their equivalent realizations.
Feedforward ANN for 2-1 fixed point ALUs
Proceedings of the Fourth International Conference on Microelectronics for Neural Networks and Fuzzy Systems, 1994
Investigates the possibility of constructing fixed point units using feedforward neural networks. The authors investigate the possibility of constructing small depth neural networks for operations usually defined in general purpose computer architectures. In particular the authors show that fixed operations require no more depth than the networks for binary addition. The authors show that depth-3 networks with bounded weights and