A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels

This paper presents an algorithm for checking and enforcing passivity of behavioral reduced-order macromodels of LTI systems, whose frequency-domain (scattering) responses depend on external parameters. Such models, which are typically extracted from sampled input-output responses obtained from numerical solution of first-principle physical models, usually expressed as Partial Differential Equations, prove extremely useful in design flows, since they allow optimization, what-if or sensitivity analyses, and design centering. Starting from an implicit parameterization of both poles and residues of the model, as resulting from well-known model identification schemes based on the Generalized Sanathanan-Koerner iteration, we construct a parameter-dependent Skew-Hamiltonian/Hamiltonian matrix pencil. The iterative extraction of purely imaginary eigenvalues ot fhe pencil, combined with an adaptive sampling scheme in the parameter space, is able to identify all regions in the frequency-parameter plane where local passivity violations occur. Then, a singular value perturbation scheme is setup to iteratively correct the model coefficients, until all local passivity violations are eliminated. The final result is a corrected model, which is uniformly passive throughout the parameter range. Several numerical examples denomstrate the effectiveness of the proposed approach.Comment: Submitted to the IEEE Transactions on Components, Packaging and Manufacturing Technology on 13-Apr-201

Robust localization methods for passivity enforcement of linear macromodels

In this paper we solve a non-smooth convex formulation for passivity enforcement of linear macromodels using robust localization based algorithms such as the ellipsoid and the cutting plane methods. Differently from existing perturbation based techniques, we solve the formulation based on the direct ℌ∞ norm minimization through perturbation of state-space model parameters. We provide a systematic way of defining an initial set which is guaranteed to contain the global optimum. We also provide a lower bound on the global minimum, that grows tighter at each iteration and hence guarantees δ - optimality of the computed solution. We demonstrate the robustness of our implementation by generating accurate passive models for challenging examples for which existing algorithms either failed or exhibited extremely slow convergenc

A Multi-Stage Adaptive Sampling Scheme for Passivity Characterization of Large-Scale Macromodels

This paper proposes a hierarchical adaptive sampling scheme for passivity characterization of large-scale linear lumped macromodels. Here, large-scale is intended both in terms of dynamic order and especially number of input/output ports. Standard passivity characterization approaches based on spectral properties of associated Hamiltonian matrices are either inefficient or non-applicable for large-scale models, due to an excessive computational cost. This paper builds on existing adaptive sampling methods and proposes a hybrid multi-stage algorithm that is able to detect the passivity violations with limited computing resources. Results from extensive testing demonstrate a major reduction in computational requirements with respect to competing approaches.Comment: Submitted to the IEEE Transactions on Components, Packaging and Manufacturing Technolog

Enforcing passivity of parameterized LTI macromodels via Hamiltonian-driven multivariate adaptive sampling

We present an algorithm for passivity verification and enforcement of multivariate macromodels whose state-space matrices depend in closed form on a set of external or design parameters. Uniform passivity throughout the parameter space is a fundamental requirement of parameterized macromodels of physically passive structures, that must be guaranteed during model generation. Otherwise, numerical instabilities may occur, due to the ability of non-passive models to generate energy. In this work, we propose the first available algorithm that, starting from a generic parameter-depedent state-space model, identifies the regions in the frequency-parameter space where the model behaves locally as a non-passive system. The approach we pursue is based on an adaptive sampling scheme in the parameter space, which iteratively constructs and perturbs the eigenvalue spectrum of suitable Skew-Hamiltonian/Hamiltonian (SHH) pencils, with the objective of identifying the regions where some of these eigenvalues become purely imaginary, thus pinpointing local passivity violations. The proposed scheme is able to detect all relevant violations. An outer iterative perturbation method is then applied to the model coefficients in order to remove such violations and achieve uniform passivity. Although a formal proof of global convergence is not available, the effectiveness of the proposed implementation of the passivity verification and enforcement schemes is demonstrated on several examples

A Multi-Stage Adaptive Sampling Scheme for Passivity Characterization of Large-Scale Macromodels

This paper proposes a hierarchical adaptive sampling scheme for passivity characterization of large-scale linear lumped macromodels. Here, large-scale is intended both in terms of dynamic order and especially number of input/output ports. Standard passivity characterization approaches based on spectral properties of associated Hamiltonian matrices are either inefficient or non-applicable for large-scale models, due to an excessive computational cost. This paper builds on existing adaptive sampling methods and proposes a hybrid multi-stage algorithm that is able to detect the passivity violations with limited computing resources. Results from extensive testing demonstrate a major reduction in computational requirements with respect to competing approaches

Uniformly Stable Parameterized Macromodeling through Positive Definite Basis Funtions

Reduced-order models are widely used to reduce the computational cost required by the numerical assessment of electrical performance during the design cycle of electronic circuits and systems. Although standard macromodeling algorithms can be considered to be well consolidated, the generation of macromodels that embed in a closed form some dependence on the design variables still presents considerable margins for improvement. One of these aspects is enforcement of uniform stability throughout the parameter space of interest. This paper proposes a novel parameterized macromodeling strategy, which enforces by construction that all macromodel poles are stable for any combination of possibly several independent design variables. The key enabling factor is adoption of positive definite multivariate basis functions for the representation of model variations induced by the parameters. This representation leads to robust model generation from tabulated frequency responses, at a computational cost that is dramatically reduced with respect to competing approaches. This result arises from a number of algebraic constraints for stability enforcement that depends on the model complexity (number of basis functions) and not on the model behavior as a function of the parameters. As a byproduct, the proposed strategy lends itself to much improved scaling with the dimension of parameter space, allowing to circumvent the curse of dimensionality that may occur when the number of independent parameters grows beyond few units. To this end, we exploit representations based on positive definite radial basis functions. The benefits of the proposed approach are demonstrated through an extensive experimental campaign applied to both passive and active devices and components, comparing the performance of different model parameterizations in terms of accuracy, time requirements and model compactness

Black-box passive macromodeling in electronics: trends and open problems

Design and verification flows in the electronics industry are relying more and more on behavioral models of components, electrical interconnects, and subsystems. Such models are often derived from tabulated frequency responses obtained via direct measurements or through electromagnetic field solvers. Model extraction from this data involves a mix of system identification and approximation in the complex frequency domain. This problem becomes difficult or badly scalable due to the presence of passivity constraints, which must be enforced during model extraction. We review recent trends to deal with this complexity, and related open issues

Convex optimization methods for model reduction

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 153-161).Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied.Parameterized reduced order modeling is important for rapid design and optimization of systems containing parameter dependent reducible sub-circuits such as interconnects and RF inductors. The first part of the thesis presents a quasi-convex optimization approach to solve the parameterized model order reduction problem for linear time-invariant systems. Formulation of the model reduction problem as a quasi-convex program allows the flexibility to enforce constraints such as stability and passivity in both non-parameterized and parameterized cases. Numerical results including the parameterized reduced modeling of a large RF inductor are given to demonstrate the practical value of the proposed algorithm.A majority of nonlinear model reduction techniques can be regarded as a two step procedure as follows. First the state dimension is reduced through a projection, and then the vector field of the reduced state is approximated for improved computation efficiency. Neither of the above steps has been thoroughly studied. The second part of this thesis presents a solution to a particular problem in the second step above, namely, finding an upper bound of the system input/output error due to nonlinear vector field approximation. The system error upper bounding problem is formulated as an L2 gain upper bounding problem of some feedback interconnection, to which the small gain theorem can be applied. A numerical procedure based on integral quadratic constraint analysis and a theoretical statement based on L2 gain analysis are given to provide the solution to the error bounding problem. The numerical procedure is applied to analyze the vector field approximation quality of a transmission line with diodes.(Cont) The application of Volterra series to the reduced modeling of nonlinear systems is hampered by the rapidly increasing computation cost with respect to the degrees of the polynomials used. On the other hand, while it is less general than the Volterra series model, the Wiener-Hammerstein model has been shown to be useful for accurate and compact modeling of certain nonlinear sub-circuits such as power amplifiers. The third part of the thesis presents a convex optimization solution technique to the reduction/identification of the Wiener-Hammerstein system. The identification problem is formulated as a non-convex quadratic program, which is solved by a semidefinite programming relaxation technique. It is demonstrated in the thesis that the formulation is robust with respect to noisy measurement, and the relaxation technique is oftentimes sufficient to provide good solutions. Simple examples are provided to demonstrate the use of the proposed identification algorithm.by Kin Cheong Sou.Ph.D

Passivity enforcement via chordal methods

Orientador: Prof. Dr. Gustavo Henrique da Costa OliveiraTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa : Curitiba, 27/08/2019Inclui referências: p. 164-175Resumo: Neste documento são propostos três algoritmos inéditos associados aos problemas subsequentes de aferição e imposição da passividade, a qual é uma propriedade qualitativa, geral e fundamental na modelagem matemática de transitórios eletromagnéticos de sistemas elétricos passivos, como transformadores. Esses algoritmos baseiam-se numa combinação de teoria dos grafos e otimização convexa. O primeiro deles consiste na aferição de subsistemas passivos contidos num sistema não passivo, intuitivamente busca-se partes passivas contidas num todo não passivo. Já na etapa de imposição de passividade, o segundo algoritmo é consequência natural do primeiro: retendo apenas os parâmetros associados às partes passivas e descartando os demais, parte-se de um sistema passivo parcialmente especificado para se determinar novos parâmetros em substituição àqueles descartados de modo que o sistema como um todo seja passivo. A possibilidade de determinação dos novos parâmetros depende de uma propriedade topológica de um grafo associado às matrizes de parâmetros do modelo, tal propriedade é denominada cordalidade. O terceiro algoritmo aborda novamente a questão de imposição da passividade e também faz uso da cordalidade, não mais como condição de existência de solução, mas sim como uma forma de explorar a esparsidade das matrizes de parâmetros. O problema de imposição da passividade encerra dois desafios no seu processo de solução, a saber: (i) compensação de parâmetros resultando na degradação do modelo bem como (ii) longos tempos de solução. Os algoritmos ora propostos são uma resposta a essas questões e os resultados obtidos demonstraram-se comparáveis àqueles já existentes na literatura especializada, em alguns casos apresentando melhorias, seja em termos de aproximação ou tempo computacionais. Os algoritmos foram testados a partir de dados de medição de um Transformador de Potencial Indutivo bem como de um Transformador de Potência. Palavras-chave: Macro-modelagem Passiva. Teoria de Sistemas. Álgebra Linear Aplicada. Análise de Transitórios. Transformadores.Abstract: Three novel algorithms are herein proposed to solve passivity assessment and enforcement problems. Passivity is a general, qualitative and fundamental property pertaining to the modeling associated with electromagnetic transients in passive power systems, such as transformers. These algorithms make combined use of Graph Theory and Convex Optimization. The first algorithm is concerned with passivity assesment. In particular, it searches for passive subsystems embedded into a larger nonpassive system and eventually specifies a partially specified passive system. Focusing on the subsequent step, algorithm two is a natural consequence of the preceeding one: retaining only the parameter set associated with passive subsystems as determined before, this partially specified passive system is used to further determine the remaining parameters so that the entire system be fully specified and passive. The existence condition for finding a fully specified system hinges on the fulfillment of a topological property of the graph associated the parameter matrices, namely chordality. The third algorithm also solves the passivity enforcement problem by making use of chordality, not as an existence condition, but rather by exploiting chordal sparsity patterns obtained with the parameter matrices. Solving passivity enforcement problems entails two persisting challenges, namely: (i) passivity compensations to parameters prompting increased model degradation as well as (ii) large computation times. The algorithms herein proposed tackle these issues and yield results comparable to those already in use, sometimes resulting in improved performance in terms of either approximation accuracy or runtime. These results herein reported entail data from actual measurements of an Inductive Voltage Transformer and a Power Transformer. Keywords: Passive Macromodeling. System Theory. Applied Linear Algebra. Transient Analysis. Transformers

Haptics in Robot-Assisted Surgery: Challenges and Benefits

Robotic surgery is transforming the current surgical practice, not only by improving the conventional surgical methods but also by introducing innovative robot-enhanced approaches that broaden the capabilities of clinicians. Being mainly of man-machine collaborative type, surgical robots are seen as media that transfer pre- and intra-operative information to the operator and reproduce his/her motion, with appropriate filtering, scaling, or limitation, to physically interact with the patient. The field, however, is far from maturity and, more critically, is still a subject of controversy in medical communities. Limited or absent haptic feedback is reputed to be among reasons that impede further spread of surgical robots. In this paper objectives and challenges of deploying haptic technologies in surgical robotics is discussed and a systematic review is performed on works that have studied the effects of providing haptic information to the users in major branches of robotic surgery. It has been tried to encompass both classical works and the state of the art approaches, aiming at delivering a comprehensive and balanced survey both for researchers starting their work in this field and for the experts