26 research outputs found
An Application of Volterra Series to IC Buffer Models
International audienceThis paper presents a Volterra-based method of behavioral modeling for the I/O buffers of digital ICs. While this technique brings a slight improvement in accuracy over previous ones, its main strength is a greater degree of generality. With a modeling approach less dependent on the nature of the devices and more easily extendable to include the effects of multiple inputs one may hope better meet the challenges of advancing technology. The proposed models can be obtained from device port transient responses only and can be easily implemented in any simulation environment, including SPICE-based circuit description software. Two illustrative examples conclude the paper
Statically constrained nonlinear models with application to IC buffers
"©2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."International audienceVolterra series are well known approaches to modeling non-linear systems. In recent works a properly weighted combination of Volterra models have been used to successfully mimic the behavior of the output port of an integrated circuit buffer. The current paper focuses on a novel mechanism for controlling the static characteristic of such models. A commercial driver example is used to illustrate the efficiency of the technique to guarantee accurate static levels during time-domain simulations
A simple algorithm for stable order reduction of z-domain Laguerre models
International audienceDiscrete-time Laguerre series are a well known and efficient tool in system identification and modeling. This paper presents a simple solution for stable and accurate order reduction of systems described by a Laguerre model
Tensor Network alternating linear scheme for MIMO Volterra system identification
This article introduces two Tensor Network-based iterative algorithms for the
identification of high-order discrete-time nonlinear multiple-input
multiple-output (MIMO) Volterra systems. The system identification problem is
rewritten in terms of a Volterra tensor, which is never explicitly constructed,
thus avoiding the curse of dimensionality. It is shown how each iteration of
the two identification algorithms involves solving a linear system of low
computational complexity. The proposed algorithms are guaranteed to
monotonically converge and numerical stability is ensured through the use of
orthogonal matrix factorizations. The performance and accuracy of the two
identification algorithms are illustrated by numerical experiments, where
accurate degree-10 MIMO Volterra models are identified in about 1 second in
Matlab on a standard desktop pc
Identificação e controle de processos via desenvolvimentos em séries ortonormais. Parte A: identificação
In this paper, an overview about the identification of dynamic systems using orthonormal basis function models, such as those based on Laguerre and Kautz functions, is presented. The mathematical foundations of these models as well as their advantages and limitations are discussed within the contexts of linear, robust, and nonlinear identification. The discussions comprise a broad bibliographical survey on the subject and a comparative analysis involving some specific model realizations, namely, linear, Volterra, fuzzy, and neural models within the orthonormal basis function framework. Theoretical and practical issues regarding the identification of these models are also presented and illustrated by means of two case studies related to a polymerization process.O presente artigo apresenta uma visĂŁo geral do estado da arte na área de identificação de sistemas utilizando modelos dinâmicos com estrutura desenvolvida atravĂ©s de bases de funções ortonormais, como as funções de Laguerre, Kautz ou funções ortonormais generalizadas. Discute-se as vantagens e possĂveis limitações desse tipo de estrutura bem como os fundamentos matemáticos dos modelos correspondentes nos contextos de identificação linear, linear com incertezas paramĂ©tricas (identificação robusta) e nĂŁo linear, incluindo uma revisĂŁo bibliográfica abrangente sobre o tema. Diferentes realizações de modelos com funções de base ortonormal, a saber, modelos lineares, de Volterra, fuzzy e neurais, sĂŁo detalhadas e discutidas comparativamente em termos de capacidade de representação, parcimĂ´nia, complexidade de projeto e interpretabilidade. Aspectos práticos da identificação desses modelos sĂŁo tambĂ©m apresentados e ilustrados atravĂ©s de dois casos de estudo envolvendo um processo simulado de polimerização isotĂ©rmica.301321Conselho Nacional de Desenvolvimento CientĂfico e TecnolĂłgico (CNPq
Optimal expansions of discrete-time Volterra models using Laguerre functions
This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. Fu and Dumont (IEEE Trans. Automatic Control 38(6) (1993) 934) indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated Laguerre expansion of impulse response models, which are equivalent to first-order Volterra models. A generalization of the work mentioned above focusing on Volterra models of any order is presented in this paper. The main result is the derivation of analytic strict global solutions for the optimal expansion of the Volterra kernels either using an independent Laguerre basis for each kernel or using a common basis for all the kernels
Modelagem de Sistemas Dinâmicos Não Lineares via RBF-GOBF.
Trata-se neste trabalho trata da modelagem e identificação de sistemas dinâmicos nĂŁo lineares estáveis representáveis por modelos de Wiener por um estrutura formada por bases de funções ortonormais generalizadas (Generalized Orthonormal Basis Functions - GOBF) com funções internas e redes neurais com funções de base radial (Radial Basis Functions - RBF). Os modelos GOBF com funções internas sĂŁo capazes de representar dinâmicas lineares intrincadas com uma parametrização que se vale apenas de valores reais, sejam os polos do sistema a ser representado complexos e/ou reais. Com informações de entrada e saĂda do sistema a ser identificado Ă© possĂvel obter um modelo GOBF-RBF inicial. Os clusters que determinam os parâmetros inciais das RBFs (centros das funções gaussianas e larguras ou spreads) sĂŁo obtidos pelo mĂ©todo fuzzy C-means, o qual Ă© inicializado com um nĂşmero de centros prĂ©-determinado, obtido pela tĂ©cnica subtractive clustering, garantindo clusters com volume e densidade apropriados. SĂŁo propostas duas tĂ©cnicas para o ajuste dos parâmetros da estrutura. A primeira delas se baseia em um mĂ©todo de otimização nĂŁo linear e os gradientes exatos da estrutura. Apresenta-se um procedimento para a obtenção dos cálculos analĂticos dos gradientes de saĂda do modelo GOBF-RBF em relação a seus parâmetros (polos da base ortonormal, centros, larguras e pesos de saĂda da rede RBF). A segunda proposta se vale de um mĂ©todo metaheurĂstico chamado otimização por enxame de partĂculas com comportamento quântico. As metodologias sĂŁo validadas com suas aplicações em trĂŞs diferentes sistemas nĂŁo lineares associados a modelos de processos práticos
Optimal expansions of discrete-time Volterra models using Laguerre functions
This paper is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. Fu and Dumont (1993) approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated Laguerre expansion of impulse response models, which are equivalent to first-order Volterra models. The present work generalizes the work mentioned above to Volterra models of any order. The main result is the derivation of analytic strict global solutions for the optimal expansion of the Volterra kernels either using an independent Laguerre basis for each kernel or using a common basis for all the kernels