Efficient dominant eigensystem computation using nodal equations

Gómez-Expósito, Antonio; Soler, Alfonso Bachiller; Macías, José Luis Salcini

doi:10.1002/cta.535

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…There are multiple methods to obtain certain sets of eigenvalues, such as the method in [15] to obtain a dominant eigenvalue based on the nodal equations. However, if all eigenvalues are required it is more appropriate to use a method based on matrix transformations, like the classic one explained in Appendix A.…”

Section: Eigensystem-based Solutionmentioning

confidence: 99%

“…• Solving the Vandermonde system (15). In order to obtain all the state variables, the most efficient method is to use LU factorization.…”

Section: Vandermonde Matrixmentioning

confidence: 99%

“…If conventional LU factorization [17] is carried out to solve Equation (15), it should be kept in mind that obtaining other state vector components requires only to obtain the right-hand side vector Equation (17), followed by a forward/backward elimination process.…”

Section: Vandermonde Matrixmentioning

confidence: 99%

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Computational assessment of methods to analytically obtain the transient response of LTI circuits

Soler

Macías

Gómez-Expósito

2012

Circuit Theory & Apps

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SUMMARYThis paper reviews and compares the computational cost of several methods to analytically obtain the natural response of linear time-invariant (LTI) circuits. In particular, the analysis is focused on three methods: eigensystem-based procedure, Vandermonde matrix method and Lagrange interpolation formula. The computational cost of repeated solutions, in which only the initial conditions change, is also studied. Finally, the computational cost of the eigensystem-based approach, the winner of the analytical class of methods, is compared with that of the numerical integration approach for different number of integration steps and scenarios.

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Section: Eigensystem-based Solutionmentioning

confidence: 99%

“…• Solving the Vandermonde system (15). In order to obtain all the state variables, the most efficient method is to use LU factorization.…”

Section: Vandermonde Matrixmentioning

confidence: 99%

See 1 more Smart Citation

Computational assessment of methods to analytically obtain the transient response of LTI circuits

Soler

Macías

Gómez-Expósito

2012

Circuit Theory & Apps

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“…It allows circuit equations to be easily and systematically obtained without any limitation. This method is used for circuit synthesis of passive descriptor systems in [12] and for computing the smallest, the largest and a given subset of the largest eigenvalues associated with linear time-invariant circuits in [13].…”

Section: Introductionmentioning

confidence: 99%

Modified Nodal Analysis-Based Determination of Transfer Functions for Multi-Inputs Multi-Outputs Linear Circuits

Yıldız

2010

Automatika

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Original scientific paperA generalized method for determination of transfer functions of circuits with multi-inputs multi-outputs is introduced. The paper proposes a systematic and efficient formulation for generating the transfer matrix containing transfer functions, necessary to model these kinds of circuits. The modified nodal analysis, whose application is simpler than the state-space analysis, is used in obtaining the system equations. The method is a matrix-based approach. It is suitable for both symbolic manipulation and numeric processes. Furthermore, the frequency domain analysis is realized using the system model. Application examples are included to illustrate the method. Key words: Transfer function, Transfer matrix, Modified nodal approach, Frequency analysisModificirana metodačvorova u svrhu odreivanja prijenosne funkcije linearnih sustava s više izlaza i više ulaza. Predstavljena je općenita metoda za odreivanje prijenose funkcije sustava s više ulaza i više izlaza. U ovomečlanku predložena je sistematična i efikasna formulacija za računanje prijenosne matrice koja sadrži prijenosne funkcije, nužne za modeliranje sustava ovakvog tipa. Modificirana metodačvorova,čija je primjena jednostavnija nego analiza u prostoru stanja, koristi se za odreivanje jednadžbi sustava. Predložena metoda temelji se na matričnom računu. Prikladna je za simboličko i numeričko računanje. Nadalje, koristeći model sustava napravljena je i frekvencijska analiza. Takoer, priloženi su i primjeri radi ilustracije primjene metode.

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Real‐valued MUSIC algorithm for power harmonics and interharmonics estimation

Cai

Duan

Liu

et al. 2011

Circuit Theory & Apps

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SUMMARYRecently, advanced spectrum estimation methods, including the MUSIC (Multiple Signal Classification) algorithms, are being gradually employed for high-resolution power harmonics analysis. However, most of them are proposed to detect frequencies of complex-valued signals, so that any real-valued signal should be transformed into complex form. This data pre-treatment may lead to additional computation burden. In addition, the picket-fence effects also exist as in the FFT algorithm and cause poor frequency resolution. To overcome these drawbacks, a real-valued MUSIC algorithm is proposed for power harmonics analysis in this paper. The algorithm is based on the subspace decomposition theory and the computation of pseudospectrum is also provided. Additionally, to improve the measuring precision, the Newton-Raphson algorithm is adopted to optimize the harmonic frequencies significantly. Simulation results show that, in the real-valued MUSIC pseudospectrum, the spectral peaks of actual harmonic components can be more easily distinguished from the false peaks caused by noise, and the computational complexity is notably lower than that of the classic complex MUSIC, as well as the detecting accuracy is close to that of root-MUSIC algorithm which is quite time consuming. Experimental results prove that the proposed strategy is more suitable for high-resolution power harmonics estimation.

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Efficient dominant eigensystem computation using nodal equations

Cited by 3 publications

References 16 publications

Computational assessment of methods to analytically obtain the transient response of LTI circuits

Computational assessment of methods to analytically obtain the transient response of LTI circuits

Modified Nodal Analysis-Based Determination of Transfer Functions for Multi-Inputs Multi-Outputs Linear Circuits

Real‐valued MUSIC algorithm for power harmonics and interharmonics estimation

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